[{"data":1,"prerenderedAt":1162},["ShallowReactive",2],{"questions:sound":3},{"bank":4,"contentHash":1146,"dependencyHashes":1147,"releaseId":1161},{"schemaVersion":5,"conceptId":6,"revision":5,"title":7,"intro":8,"sections":9,"questions":46,"sourceIds":1129,"reviewStatus":1142,"authoring":1143},1,"sound","Sound: question bank","Seventy-two questions across nine sections, from the basics of vibration to Doppler shifts and earthquake waves. Every numeric answer was computed in Python and checked before being written here. Work through a section at a time, use the hints if you are stuck, and read the worked solution even when you get a question right.",[10,14,18,22,26,30,34,38,42],{"id":11,"title":12,"description":13},"vibration","Vibration and medium","What makes a sound, why it needs a material to travel through, and why space is silent.",{"id":15,"title":16,"description":17},"speed","Speed of sound","Speeds in air, water and solids, the effect of temperature, and the thunder rule.",{"id":19,"title":20,"description":21},"echoes","Echoes and sonar","Echo timing, sonar depth-finding and medical ultrasound, all using the same round-trip formula.",{"id":23,"title":24,"description":25},"pitch","Pitch, frequency and wavelength","Hertz, v = f × λ, octaves, and strings and pipes.",{"id":27,"title":28,"description":29},"loudness","Loudness and decibels","Amplitude, the decibel scale, combining sound levels, and hearing safety.",{"id":31,"title":32,"description":33},"ear","The ear and hearing range","How the ear works, hearing range, ultrasound and infrasound.",{"id":35,"title":36,"description":37},"resonance","Resonance and Indian instruments","Natural frequency, sympathetic strings, resonance boxes and harmonics.",{"id":39,"title":40,"description":41},"doppler","Doppler effect and recording","Pitch shifts from motion, digital sampling, bone conduction, and earthquake waves.",{"id":43,"title":44,"description":45},"noise","Noise, microphones and technology","Noise pollution rules, microphones and speakers, and distance versus loudness.",[47,71,89,108,127,139,157,176,196,214,226,238,247,258,268,286,296,308,320,338,348,358,369,377,395,413,422,440,458,468,478,487,497,516,525,534,552,567,577,586,604,623,641,652,663,681,699,716,730,744,755,773,782,799,816,833,851,868,878,887,905,921,938,947,956,974,985,995,1004,1022,1039,1058,1076,1085,1102,1120],{"id":48,"section":11,"level":49,"prompt":50,"check":51,"hints":67,"solution":69,"skills":70},"sound.q001","foundation","What does every sound in the world begin with?",{"kind":52,"options":53,"correct":66},"choice",[54,57,60,63],{"id":55,"label":56},"a","Moving air",{"id":58,"label":59},"b","Something vibrating",{"id":61,"label":62},"c","A loudspeaker",{"id":64,"label":65},"d","An echo",[58],[68],"Think of your throat when you hum.","Every sound starts with a **vibration**: a skin, a string, a column of air, a solid object or your vocal folds. Air only carries the news outward; it does not create it.",[11],{"id":72,"section":11,"level":49,"prompt":73,"check":74,"hints":85,"solution":86,"skills":87},"sound.q002","In a sitar, what part is actually vibrating to make the main sound?",{"kind":52,"options":75,"correct":84},[76,78,80,82],{"id":55,"label":77},"The wooden neck alone",{"id":58,"label":79},"A stretched string",{"id":61,"label":81},"The player's fingers",{"id":64,"label":83},"The floor",[58],[],"The plucked **string** vibrates; the bridge and hollow body then pass that vibration on to the air, making it loud enough to hear.",[11,88],"instruments",{"id":90,"section":11,"level":91,"prompt":92,"check":93,"hints":104,"solution":106,"skills":107},"sound.q003","core","A bansuri makes its sound mainly because of the vibration of",{"kind":52,"options":94,"correct":103},[95,97,99,101],{"id":55,"label":96},"the bamboo tube itself",{"id":58,"label":98},"the player's lips",{"id":61,"label":100},"a column of air inside the tube",{"id":64,"label":102},"the finger holes",[61],[105],"The bamboo just holds something in place.","Blowing across the mouth hole sets the **column of air** inside the bamboo vibrating along its length. The bamboo itself barely moves; it is only a container.",[11,88],{"id":109,"section":11,"level":91,"prompt":110,"check":111,"hints":122,"solution":123,"skills":124},"sound.q004","An electric bell rings inside a sealed glass jar. As air is pumped out, the sound",{"kind":52,"options":112,"correct":121},[113,115,117,119],{"id":55,"label":114},"gets louder",{"id":58,"label":116},"stays exactly the same",{"id":61,"label":118},"fades away to silence, though the hammer keeps moving",{"id":64,"label":120},"changes to a much higher pitch",[61],[],"With less and less air to squash and stretch, less and less of the vibration is carried out of the jar, so the sound **fades to silence** even though you can still see the hammer striking the bell.",[125,126],"vacuum","medium",{"id":128,"section":11,"level":91,"prompt":129,"check":130,"hints":134,"solution":136,"skills":137},"sound.q005","Fill in the blank: a **______** is the material that a sound wave travels through, such as air, water or steel.",{"kind":131,"accept":132},"text",[126,133],"a medium",[135],"It is not the source, and it is not the vibration itself.","The word is **medium**: the material a wave travels through. Sound needs one; a vacuum has none, so sound cannot cross it.",[126,138],"vocabulary",{"id":140,"section":11,"level":141,"prompt":142,"check":143,"hints":154,"solution":155,"skills":156},"sound.q006","stretch","Astronauts on a spacewalk cannot talk directly through the vacuum of space, but they can hear each other by touching helmets together. This shows that",{"kind":52,"options":144,"correct":153},[145,147,149,151],{"id":55,"label":146},"sound cannot travel through any solid",{"id":58,"label":148},"solids can carry sound even when the surrounding vacuum cannot",{"id":61,"label":150},"helmets contain hidden microphones",{"id":64,"label":152},"space is not really a vacuum",[58],[],"The vacuum between them has no matter to carry sound, so direct speech fails. But their touching helmets are a **solid path**, and solids carry sound very well, so vibrations pass helmet to helmet.",[125,126],{"id":158,"section":11,"level":141,"prompt":159,"check":160,"hints":171,"solution":173,"skills":174},"sound.q007","A sound wave in air is described as longitudinal. This means the air particles",{"kind":52,"options":161,"correct":170},[162,164,166,168],{"id":55,"label":163},"move in a full circle",{"id":58,"label":165},"move back and forth along the same line the wave is travelling",{"id":61,"label":167},"move up and down across the direction of travel",{"id":64,"label":169},"do not move at all",[58],[172],"Compare with a slinky pushed along its own length.","In a **longitudinal** wave, particles oscillate back and forth in the same direction the wave travels, creating compressions and rarefactions, unlike a transverse wave where particles move across the direction of travel.",[175],"longitudinal wave",{"id":177,"section":11,"level":178,"prompt":179,"check":180,"hints":191,"solution":192,"skills":193},"sound.q008","challenge","A compression in a sound wave is a region where the air particles are",{"kind":52,"options":181,"correct":190},[182,184,186,188],{"id":55,"label":183},"further apart than normal, with lower pressure",{"id":58,"label":185},"closer together than normal, with higher pressure",{"id":61,"label":187},"completely still",{"id":64,"label":189},"moving in a circle",[58],[],"A **compression** is a crowded region, pressed closer together than normal, which means slightly higher pressure than the surrounding air. The opposite, a spread-out, lower-pressure region, is a rarefaction.",[194,195],"compression","rarefaction",{"id":197,"section":15,"level":49,"prompt":198,"check":199,"hints":210,"solution":211,"skills":212},"sound.q009","Put these in order from slowest to fastest for sound: air, steel, water.",{"kind":52,"options":200,"correct":209},[201,203,205,207],{"id":55,"label":202},"air, water, steel",{"id":58,"label":204},"steel, water, air",{"id":61,"label":206},"water, air, steel",{"id":64,"label":208},"air, steel, water",[55],[],"Sound is slowest in **air** (343 m\u002Fs), faster in **water** (1,480 m\u002Fs), and fastest in **steel** (5,960 m\u002Fs): solids fastest, then liquids, then gases.",[213],"speed of sound",{"id":215,"section":15,"level":49,"prompt":216,"check":217,"hints":222,"solution":224,"skills":225},"sound.q010","Sound travels at 343 m\u002Fs in air. How far, in metres, does it travel in exactly 1 second?",{"kind":218,"answer":219,"tolerance":220,"unit":221},"number",343,0,"m",[223],"Speed already tells you the distance covered in one second.","By definition, a speed of 343 m\u002Fs means sound covers **343 metres** in one second.",[213],{"id":227,"section":15,"level":91,"prompt":228,"check":229,"hints":233,"solution":235,"skills":236},"sound.q011","Using v = 331.3 + 0.606 × T, what is the speed of sound in air, in m\u002Fs, at 25 degrees Celsius? Give your answer to one decimal place.",{"kind":218,"answer":230,"tolerance":231,"unit":232},346.4,0.2,"m\u002Fs",[234],"0.606 × 25 = 15.15, then add 331.3.","331.3 + 0.606 × 25 = 331.3 + 15.15 = **346.4 m\u002Fs**, faster than the 343 m\u002Fs used for 20 °C, since warmer air carries sound a little faster.",[213,237],"temperature",{"id":239,"section":15,"level":91,"prompt":240,"check":241,"hints":243,"solution":245,"skills":246},"sound.q012","Using v = 331.3 + 0.606 × T, what is the speed of sound in air, in m\u002Fs, at 35 degrees Celsius? Give your answer to one decimal place.",{"kind":218,"answer":242,"tolerance":231,"unit":232},352.5,[244],"0.606 × 35 = 21.21.","331.3 + 0.606 × 35 = 331.3 + 21.21 = **352.5 m\u002Fs**.",[213,237],{"id":248,"section":15,"level":91,"prompt":249,"check":250,"hints":253,"solution":255,"skills":256},"sound.q013","You count 9 seconds between a lightning flash and its thunder. Roughly how many kilometres away did the lightning strike? (Use 3 seconds per kilometre.)",{"kind":218,"answer":251,"tolerance":231,"unit":252},3,"km",[254],"Divide the seconds by 3.","9 ÷ 3 = **3 km**. In full: 343 × 9 = 3,087 m, which rounds to about 3.1 km.",[257],"thunder rule",{"id":259,"section":15,"level":91,"prompt":260,"check":261,"hints":264,"solution":266,"skills":267},"sound.q014","You count 18 seconds between a lightning flash and its thunder. Using 343 m\u002Fs for sound in air, how far away, in kilometres, did the lightning strike? Give your answer to two decimal places.",{"kind":218,"answer":262,"tolerance":263,"unit":252},6.174,0.05,[265],"Distance = 343 × seconds, then divide by 1,000 for kilometres.","343 × 18 = 6,174 m = **6.174 km**. The quick rule (18 ÷ 3 = 6 km) is close, since 343 is a little more than 333.",[257],{"id":269,"section":15,"level":91,"prompt":270,"check":271,"hints":282,"solution":283,"skills":284},"sound.q015","Steel is roughly 6,500 times denser than air, yet sound travels about 17 times faster in steel. This shows that",{"kind":52,"options":272,"correct":281},[273,275,277,279],{"id":55,"label":274},"denser materials always carry sound faster",{"id":58,"label":276},"stiffness, not density alone, decides the speed of sound",{"id":61,"label":278},"steel is not really denser than air",{"id":64,"label":280},"sound cannot really travel through steel",[58],[],"Density alone would predict steel should be **slower**. What actually decides the speed is **stiffness**: how tightly the particles are bonded and how fast they spring back. Steel's extreme stiffness far outweighs its extra density.",[213,285],"misconception",{"id":287,"section":15,"level":141,"prompt":288,"check":289,"hints":291,"solution":293,"skills":294},"sound.q016","The speed of sound in sea water is about 4.03 times its speed in fresh water divided incorrectly gives a wrong ratio; using steel (5,960 m\u002Fs) and water (1,480 m\u002Fs), what is the ratio of steel's speed to water's speed? Give your answer to two decimal places.",{"kind":218,"answer":290,"tolerance":263},4.03,[292],"Divide 5,960 by 1,480.","5,960 ÷ 1,480 = **4.03**: sound in steel travels about four times faster than in water.",[213,295],"ratios",{"id":297,"section":15,"level":141,"prompt":298,"check":299,"hints":303,"solution":305,"skills":306},"sound.q017","A sound pulse travels 200 m through water (1,480 m\u002Fs), then continues 100 m through air (343 m\u002Fs) to reach a listener. What is the total travel time, in seconds, to three decimal places?",{"kind":218,"answer":300,"tolerance":301,"unit":302},0.427,0.01,"s",[304],"Work out each leg's time separately using time = distance ÷ speed, then add them.","Water leg: 200 ÷ 1,480 = 0.135 s. Air leg: 100 ÷ 343 = 0.292 s. Total = 0.135 + 0.292 = **0.427 s**. Notice the much longer air leg takes over twice as long despite being half the distance.",[213,307],"multi-step",{"id":309,"section":15,"level":178,"prompt":310,"check":311,"hints":314,"solution":317,"skills":318},"sound.q018","A hiker measures the speed of sound in the air around them as 349.5 m\u002Fs. Using v = 331.3 + 0.606 × T, what was the air temperature, in degrees Celsius?",{"kind":218,"answer":312,"tolerance":5,"unit":313},30,"°C",[315,316],"Rearrange to T = (v − 331.3) ÷ 0.606.","349.5 − 331.3 = 18.2.","T = (349.5 − 331.3) ÷ 0.606 = 18.2 ÷ 0.606 = **30 °C**. Check: 331.3 + 0.606 × 30 = 349.48, which rounds to 349.5. ✓",[213,237,319],"rearranging",{"id":321,"section":19,"level":49,"prompt":322,"check":323,"hints":334,"solution":335,"skills":336},"sound.q019","An echo needs a reflecting surface to be at least how far away to be heard as a separate sound from the original?",{"kind":52,"options":324,"correct":333},[325,327,329,331],{"id":55,"label":326},"About 1 metre",{"id":58,"label":328},"About 17 metres",{"id":61,"label":330},"About 170 metres",{"id":64,"label":332},"About 1,700 metres",[58],[],"The brain needs at least about **0.1 second** between the original sound and its echo to hear them as separate; since sound covers 343 m\u002Fs, that round trip needs a wall at least about **17 metres** away.",[337],"echo",{"id":339,"section":19,"level":49,"prompt":340,"check":341,"hints":344,"solution":346,"skills":347},"sound.q020","A clap's echo returns after 0.2 seconds. Using 343 m\u002Fs for sound in air, how far away is the reflecting wall, in metres? Give your answer to one decimal place.",{"kind":218,"answer":342,"tolerance":343,"unit":221},34.3,0.5,[345],"Find the total round-trip distance first (speed × time), then halve it.","Total distance = 343 × 0.2 = 68.6 m there and back. Halve it for the one-way distance: **34.3 m**.",[337],{"id":349,"section":19,"level":91,"prompt":350,"check":351,"hints":354,"solution":356,"skills":357},"sound.q021","An echo off a canyon wall returns 0.496 seconds after a shout. How far away, in metres, is the wall? Give your answer to the nearest whole metre.",{"kind":218,"answer":352,"tolerance":353,"unit":221},85,2,[355],"Round-trip distance = 343 × 0.496, then halve it.","343 × 0.496 = 170.1 m round trip; half of that is **85 m**.",[337],{"id":359,"section":19,"level":91,"prompt":360,"check":361,"hints":364,"solution":366,"skills":367},"sound.q022","A ship's sonar sends a pulse and the echo returns after 2.5 seconds. Using 1,500 m\u002Fs for sound in sea water, how deep is the water, in metres? Give your answer to two decimal places.",{"kind":218,"answer":362,"tolerance":363,"unit":221},1875,5,[365],"Round-trip distance = speed × time, then halve for depth.","1,500 × 2.5 = 3,750 m round trip. Halve it: **1,875 m** deep.",[368],"sonar",{"id":370,"section":19,"level":91,"prompt":371,"check":372,"hints":373,"solution":375,"skills":376},"sound.q023","A depth sounder's echo returns after 0.04 seconds in sea water (1,500 m\u002Fs). How deep is the water, in metres?",{"kind":218,"answer":312,"tolerance":5,"unit":221},[374],"Multiply speed by time first, then halve.","1,500 × 0.04 = 60 m round trip. Halve it: **30 m** deep.",[368],{"id":378,"section":19,"level":91,"prompt":379,"check":380,"hints":391,"solution":392,"skills":393},"sound.q024","Why does a small, cluttered room not produce a noticeable echo, even though it has hard walls?",{"kind":52,"options":381,"correct":390},[382,384,386,388],{"id":55,"label":383},"Sound cannot bounce off small rooms",{"id":58,"label":385},"The walls are too close for the reflected sound to be heard as separate from the original",{"id":61,"label":387},"Small rooms have no air in them",{"id":64,"label":389},"Furniture makes rooms perfectly silent",[58],[],"A wall needs to be at least about **17 metres** away for the reflected sound to arrive late enough to be heard as a separate echo rather than blending in as reverberation.",[337,394],"reverberation",{"id":396,"section":19,"level":141,"prompt":397,"check":398,"hints":409,"solution":410,"skills":411},"sound.q025","A medical ultrasound scanner uses timed echoes in soft tissue (about 1,540 m\u002Fs) instead of the 343 m\u002Fs used for sound in air, because",{"kind":52,"options":399,"correct":408},[400,402,404,406],{"id":55,"label":401},"the scanner is measuring through tissue, not air, and sound travels differently there",{"id":58,"label":403},"1,540 m\u002Fs is a typo for 343 m\u002Fs",{"id":61,"label":405},"ultrasound does not obey the echo formula at all",{"id":64,"label":407},"tissue has no effect on sound speed",[55],[],"The echo formula (distance = speed × time ÷ 2) is universal, but the **speed** used must match the actual medium the sound is travelling through: soft tissue, not air.",[412,368],"ultrasound",{"id":414,"section":19,"level":178,"prompt":415,"check":416,"hints":418,"solution":420,"skills":421},"sound.q026","A sonar pulse in sea water (1,500 m\u002Fs) returns from the sea floor after 1.0 second. A second, shallower pulse from the same ship returns after 0.24 seconds. What is the difference in depth between the two readings, in metres?",{"kind":218,"answer":417,"tolerance":363,"unit":221},570,[419],"Find each depth separately, then subtract.","Deep reading: 1,500 × 1.0 ÷ 2 = 750 m. Shallow reading: 1,500 × 0.24 ÷ 2 = 180 m. Difference: 750 − 180 = **570 m**.",[368,307],{"id":423,"section":23,"level":49,"prompt":424,"check":425,"hints":436,"solution":437,"skills":438},"sound.q027","What is measured in hertz (Hz)?",{"kind":52,"options":426,"correct":435},[427,429,431,433],{"id":55,"label":428},"Loudness",{"id":58,"label":430},"Frequency",{"id":61,"label":432},"Distance",{"id":64,"label":434},"Time in seconds",[58],[],"**Hertz** is the unit of frequency: how many complete vibrations happen every second. Loudness uses decibels, not hertz.",[439],"frequency",{"id":441,"section":23,"level":49,"prompt":442,"check":443,"hints":454,"solution":455,"skills":456},"sound.q028","You tighten a guitar string and pluck it again. What happens to its pitch?",{"kind":52,"options":444,"correct":453},[445,447,449,451],{"id":55,"label":446},"It gets higher",{"id":58,"label":448},"It gets lower",{"id":61,"label":450},"It stays the same",{"id":64,"label":452},"It becomes silent",[55],[],"A tighter string springs back faster, vibrating more times each second, which raises the **frequency** and so the **pitch**.",[23,457],"strings",{"id":459,"section":23,"level":91,"prompt":460,"check":461,"hints":463,"solution":465,"skills":466},"sound.q029","Using v = f × λ, what is the wavelength, in metres, of a 680 Hz sound in air (343 m\u002Fs)? Give your answer to two decimal places.",{"kind":218,"answer":343,"tolerance":462,"unit":221},0.02,[464],"λ = v ÷ f.","λ = 343 ÷ 680 = **0.50 m** (0.5044 m precisely).",[467],"wavelength",{"id":469,"section":23,"level":91,"prompt":470,"check":471,"hints":474,"solution":476,"skills":477},"sound.q030","What is the frequency, in hertz, of a sound in air (343 m\u002Fs) with a wavelength of exactly 0.343 metres?",{"kind":218,"answer":472,"tolerance":363,"unit":473},1000,"Hz",[475],"f = v ÷ λ.","f = 343 ÷ 0.343 = **1,000 Hz**.",[467,439],{"id":479,"section":23,"level":91,"prompt":480,"check":481,"hints":483,"solution":485,"skills":486},"sound.q031","A guitar string 0.6 m long, of a type that would give a wave speed along the string of 480 m\u002Fs, has a fundamental frequency of f = v ÷ (2L). What is that frequency, in hertz?",{"kind":218,"answer":482,"tolerance":353,"unit":473},400,[484],"Divide 480 by (2 × 0.6).","f = 480 ÷ (2 × 0.6) = 480 ÷ 1.2 = **400 Hz**.",[457,439],{"id":488,"section":23,"level":91,"prompt":489,"check":490,"hints":492,"solution":494,"skills":495},"sound.q032","Using f = v ÷ (2L) for an open pipe, what is the fundamental frequency, in hertz, of an open pipe 0.4 m long, with sound at 343 m\u002Fs? Give your answer to one decimal place.",{"kind":218,"answer":491,"tolerance":5,"unit":473},428.8,[493],"2 × 0.4 = 0.8, then divide 343 by that.","f = 343 ÷ (2 × 0.4) = 343 ÷ 0.8 = **428.8 Hz**.",[496,439],"pipes",{"id":498,"section":23,"level":141,"prompt":499,"check":500,"hints":511,"solution":513,"skills":514},"sound.q033","A note at 220 Hz is played. What frequency is exactly one octave higher?",{"kind":52,"options":501,"correct":510},[502,504,506,508],{"id":55,"label":503},"221 Hz",{"id":58,"label":505},"330 Hz",{"id":61,"label":507},"440 Hz",{"id":64,"label":509},"110 Hz",[61],[512],"An octave is a doubling of frequency.","One octave up means **double** the frequency: 220 × 2 = **440 Hz**. (110 Hz would be an octave lower.)",[515],"octaves",{"id":517,"section":23,"level":141,"prompt":518,"check":519,"hints":521,"solution":523,"skills":524},"sound.q034","Using f = v ÷ (4L) for a closed pipe, what is the fundamental frequency, in hertz, of a closed pipe 0.6 m long, with sound at 343 m\u002Fs? Give your answer to two decimal places.",{"kind":218,"answer":520,"tolerance":343,"unit":473},142.92,[522],"4 × 0.6 = 2.4, then divide 343 by that.","f = 343 ÷ (4 × 0.6) = 343 ÷ 2.4 = **142.92 Hz**.",[496,439],{"id":526,"section":23,"level":178,"prompt":527,"check":528,"hints":530,"solution":532,"skills":533},"sound.q035","An open pipe and a closed pipe are both exactly 0.5 m long, with sound at 343 m\u002Fs. What is the closed pipe's fundamental frequency subtracted from the open pipe's fundamental frequency, in hertz?",{"kind":218,"answer":529,"tolerance":5,"unit":473},171.5,[531],"Open: f = v ÷ (2L). Closed: f = v ÷ (4L). Find both, then subtract.","Open pipe: 343 ÷ (2 × 0.5) = 343 Hz. Closed pipe: 343 ÷ (4 × 0.5) = 171.5 Hz. Difference: 343 − 171.5 = **171.5 Hz** (the closed pipe sounds exactly an octave lower, so the difference equals its own frequency).",[496,307],{"id":535,"section":27,"level":49,"prompt":536,"check":537,"hints":548,"solution":549,"skills":550},"sound.q036","You hit the same drum harder than before. What changes?",{"kind":52,"options":538,"correct":547},[539,541,543,545],{"id":55,"label":540},"The pitch rises",{"id":58,"label":542},"The pitch falls",{"id":61,"label":544},"The loudness rises, the pitch stays the same",{"id":64,"label":546},"Nothing changes",[61],[],"Hitting harder increases the **amplitude** (how far the skin swings), which raises loudness. How *often* it vibrates, and so the pitch, is unchanged.",[551,27],"amplitude",{"id":553,"section":27,"level":49,"prompt":554,"check":555,"hints":563,"solution":564,"skills":565},"sound.q037","What is measured in decibels (dB)?",{"kind":52,"options":556,"correct":562},[557,558,559,561],{"id":55,"label":430},{"id":58,"label":428},{"id":61,"label":560},"Wavelength",{"id":64,"label":16},[58],[],"**Decibels** measure loudness (sound level). Frequency is measured in hertz.",[566],"decibels",{"id":568,"section":27,"level":91,"prompt":569,"check":570,"hints":573,"solution":575,"skills":576},"sound.q038","Using the rule that intensity ratio = 10^(dB ÷ 10), what is the intensity ratio for a level of 40 dB?",{"kind":218,"answer":571,"tolerance":572},10000,100,[574],"10 to the power of (40 ÷ 10) = 10 to the power of 4.","10^(40÷10) = 10^4 = **10,000**: a 40 dB sound carries 10,000 times the reference intensity.",[566],{"id":578,"section":27,"level":91,"prompt":579,"check":580,"hints":582,"solution":584,"skills":585},"sound.q039","Using the same rule, what is the intensity ratio for a level of 50 dB?",{"kind":218,"answer":581,"tolerance":472},100000,[583],"10 to the power of (50 ÷ 10) = 10 to the power of 5.","10^(50÷10) = 10^5 = **100,000**.",[566],{"id":587,"section":27,"level":91,"prompt":588,"check":589,"hints":600,"solution":602,"skills":603},"sound.q040","Two identical loudspeakers, each measuring 75 dB alone, are switched on together. The combined level is closest to",{"kind":52,"options":590,"correct":599},[591,593,595,597],{"id":55,"label":592},"150 dB",{"id":58,"label":594},"78 dB",{"id":61,"label":596},"75 dB, unchanged",{"id":64,"label":598},"37.5 dB",[58],[601],"Two identical sources add about 3 dB, not double the number.","Doubling the sound energy adds only about **+3 dB**: 75 + 3 = **78 dB**, far from a simple doubling of the number.",[566,285],{"id":605,"section":27,"level":91,"prompt":606,"check":607,"hints":618,"solution":619,"skills":620},"sound.q041","India's rules limit firecrackers to a maximum sound level, measured 4 metres away, of approximately",{"kind":52,"options":608,"correct":617},[609,611,613,615],{"id":55,"label":610},"60 dB",{"id":58,"label":612},"85 dB",{"id":61,"label":614},"125 dB",{"id":64,"label":616},"300 dB",[61],[],"India's noise rules cap firecrackers at **125 dB(AI)** measured 4 metres away, already far above the roughly 85 dB level where long exposure damages hearing.",[621,622],"noise pollution","safety",{"id":624,"section":27,"level":141,"prompt":625,"check":626,"hints":637,"solution":638,"skills":639},"sound.q042","Sound exposure guidelines suggest that above about 85 dB, hearing damage risk depends mainly on",{"kind":52,"options":627,"correct":636},[628,630,632,634],{"id":55,"label":629},"the exact pitch of the sound",{"id":58,"label":631},"how loud the sound is and for how long you are exposed to it",{"id":61,"label":633},"the colour of the source",{"id":64,"label":635},"whether the sound is musical or noise",[58],[],"Both **loudness and exposure time** matter: a very loud sound for a short time, or a moderately loud sound for a long time, can both cause damage. A single very loud bang can also cause damage on its own.",[640],"hearing safety",{"id":642,"section":27,"level":141,"prompt":643,"check":644,"hints":648,"solution":650,"skills":651},"sound.q043","Three different noise sources measure 50 dB, 55 dB and 60 dB alone, at the same spot. Using L = 10 × log₁₀(10^(L1÷10) + 10^(L2÷10) + 10^(L3÷10)), what is the combined level, to one decimal place?",{"kind":218,"answer":645,"tolerance":646,"unit":647},61.5,0.3,"dB",[649],"Convert each level to an energy ratio, add them, then convert back with 10 × log₁₀.","10^5 + 10^5.5 + 10^6 ≈ 100,000 + 316,228 + 1,000,000 = 1,416,228. 10 × log₁₀(1,416,228) ≈ **61.5 dB**: only a little above the loudest source alone (60 dB).",[566,307],{"id":653,"section":27,"level":178,"prompt":654,"check":655,"hints":657,"solution":660,"skills":661},"sound.q044","A machine measures 100 dB at 5 metres. Using level(d₂) = level(d₁) − 20 × log₁₀(d₂ ÷ d₁), what does it measure at 20 metres, to the nearest whole decibel?",{"kind":218,"answer":656,"tolerance":5,"unit":647},88,[658,659],"The distance ratio is 20 ÷ 5 = 4.","20 × log₁₀(4) ≈ 12.","Distance ratio = 4. Drop = 20 × log₁₀(4) ≈ 12.04 dB. Level at 20 m = 100 − 12.04 ≈ **88 dB**.",[566,662,307],"distance",{"id":664,"section":31,"level":49,"prompt":665,"check":666,"hints":677,"solution":678,"skills":679},"sound.q045","Which part of the ear is the thin skin that arriving sound pushes in and out?",{"kind":52,"options":667,"correct":676},[668,670,672,674],{"id":55,"label":669},"The pinna",{"id":58,"label":671},"The eardrum",{"id":61,"label":673},"The cochlea",{"id":64,"label":675},"The auditory nerve",[58],[],"The **eardrum** (tympanic membrane) is the thin, tight skin at the end of the ear canal that arriving sound pushes.",[680],"ear anatomy",{"id":682,"section":31,"level":49,"prompt":683,"check":684,"hints":695,"solution":696,"skills":697},"sound.q046","About what range of frequencies can a young, healthy human ear hear?",{"kind":52,"options":685,"correct":694},[686,688,690,692],{"id":55,"label":687},"0 Hz to 20 Hz",{"id":58,"label":689},"20 Hz to 20,000 Hz",{"id":61,"label":691},"2,000 Hz to 200,000 Hz",{"id":64,"label":693},"1 Hz to 100 Hz",[58],[],"Young human hearing spans roughly **20 Hz to 20,000 Hz (20 kHz)**, about ten octaves. It narrows with age, usually from the top down.",[698],"hearing range",{"id":700,"section":31,"level":91,"prompt":701,"check":702,"hints":713,"solution":714,"skills":715},"sound.q047","Put these ear parts in the correct order that an arriving sound passes through them.",{"kind":52,"options":703,"correct":712},[704,706,708,710],{"id":55,"label":705},"Cochlea, eardrum, ossicles, pinna",{"id":58,"label":707},"Pinna, eardrum, ossicles, cochlea",{"id":61,"label":709},"Ossicles, pinna, cochlea, eardrum",{"id":64,"label":711},"Eardrum, pinna, cochlea, ossicles",[58],[],"The path is: **pinna** (gathers sound) → **eardrum** (moves) → **ossicles** (three tiny bones, amplify) → **cochlea** (turns movement into nerve signals).",[680],{"id":717,"section":31,"level":91,"prompt":718,"check":719,"hints":727,"solution":728,"skills":729},"sound.q048","Sound above 20,000 Hz, too high for human hearing, is called",{"kind":52,"options":720,"correct":726},[721,723,724,725],{"id":55,"label":722},"infrasound",{"id":58,"label":412},{"id":61,"label":35},{"id":64,"label":394},[58],[],"**Ultrasound** is sound above 20,000 Hz: too high for human ears, but used by bats, dolphins and medical scanners.",[412],{"id":731,"section":31,"level":91,"prompt":732,"check":733,"hints":741,"solution":742,"skills":743},"sound.q049","Sound below 20 Hz, too low for human hearing, is called",{"kind":52,"options":734,"correct":740},[735,736,737,738],{"id":55,"label":722},{"id":58,"label":412},{"id":61,"label":551},{"id":64,"label":739},"timbre",[55],[],"**Infrasound** is sound below 20 Hz: too low for human ears, though elephants and whales use it for long-distance calls.",[722],{"id":745,"section":31,"level":91,"prompt":746,"check":747,"hints":751,"solution":753,"skills":754},"sound.q050","What do we call the microscopic cells inside the cochlea that turn movement into nerve signals, and which never grow back once badly damaged by loud noise?",{"kind":131,"accept":748},[749,750],"hair cells","hair cell",[752],"There are about 16,000 of them per ear.","They are called **hair cells**. Loud noise can bend or break them permanently, since they do not regrow, which is why hearing damage from noise is usually permanent.",[749,640],{"id":756,"section":31,"level":141,"prompt":757,"check":758,"hints":769,"solution":770,"skills":771},"sound.q051","The three tiny bones of the middle ear (hammer, anvil, stirrup) mainly serve to",{"kind":52,"options":759,"correct":768},[760,762,764,766],{"id":55,"label":761},"protect the eardrum from all sound",{"id":58,"label":763},"concentrate and strengthen the eardrum's movement onto the smaller oval window",{"id":61,"label":765},"produce the sound of a heartbeat",{"id":64,"label":767},"clean wax out of the ear canal",[58],[],"Sound arrives easily in air but must move liquid inside the cochlea, which is much harder to shift. The three bones act as a lever, concentrating the eardrum's movement to give roughly a **twenty-fold** pressure boost.",[772],"middle ear",{"id":774,"section":31,"level":141,"prompt":775,"check":776,"hints":778,"solution":780,"skills":781},"sound.q052","The middle ear's pressure gain, from eardrum area divided by stapes footplate area times a lever ratio, works out to about 22 times. Using 20 × log₁₀(gain), what is this gain in decibels, to the nearest whole number?",{"kind":218,"answer":777,"tolerance":5,"unit":647},27,[779],"log₁₀(22) is about 1.34.","20 × log₁₀(22) ≈ 20 × 1.342 ≈ **27 dB**: the middle ear's roughly twenty-times pressure boost, expressed on the decibel scale.",[772,566],{"id":783,"section":31,"level":178,"prompt":784,"check":785,"hints":796,"solution":797,"skills":798},"sound.q053","A bat calls at about 100,000 Hz, giving a wavelength in air of about 3.4 mm, small enough to reveal a flying insect. This shows that a wave",{"kind":52,"options":786,"correct":795},[787,789,791,793],{"id":55,"label":788},"can reveal detail smaller than its own wavelength easily",{"id":58,"label":790},"can only clearly reveal features about as large as its own wavelength or bigger",{"id":61,"label":792},"always travels faster at higher frequency",{"id":64,"label":794},"cannot be used for detecting small objects at all",[58],[],"A wave can only clearly reveal detail **about as large as its own wavelength**, or bigger; smaller features simply blur past it. A high frequency gives a short wavelength, which is why bats and medical scanners use high frequencies to see fine detail.",[412,467],{"id":800,"section":35,"level":49,"prompt":801,"check":802,"hints":813,"solution":814,"skills":815},"sound.q054","Resonance happens when an object is pushed",{"kind":52,"options":803,"correct":812},[804,806,808,810],{"id":55,"label":805},"as hard as possible, regardless of timing",{"id":58,"label":807},"repeatedly at or near its own natural frequency",{"id":61,"label":809},"only once, very gently",{"id":64,"label":811},"at a frequency far from its own",[58],[],"**Resonance** builds up when repeated pushes arrive in step with an object's own **natural frequency**, so each push adds to the last.",[35],{"id":817,"section":35,"level":91,"prompt":818,"check":819,"hints":830,"solution":831,"skills":832},"sound.q055","A sitar's sympathetic strings, which nobody touches directly, vibrate mainly by",{"kind":52,"options":820,"correct":829},[821,823,825,827],{"id":55,"label":822},"friction with the air",{"id":58,"label":824},"resonance, when a played note matches their own tuning",{"id":61,"label":826},"electricity stored in the strings",{"id":64,"label":828},"the heat of the player's hand",[58],[],"Each sympathetic string is tuned to a particular note. It rings by **resonance** only when that matching note is played nearby, adding a shimmering halo to the sound.",[35,88],{"id":834,"section":35,"level":91,"prompt":835,"check":836,"hints":847,"solution":848,"skills":849},"sound.q056","In the four-family Indian classification of instruments, a tabla belongs to which family?",{"kind":52,"options":837,"correct":846},[838,840,842,844],{"id":55,"label":839},"Tat (stringed)",{"id":58,"label":841},"Sushir (blown)",{"id":61,"label":843},"Avanaddh (covered with skin)",{"id":64,"label":845},"Ghan (solid)",[61],[],"A tabla is a drum with a stretched skin, placing it in the **avanaddh** family. Sitar and veena are tat (stringed); bansuri and shehnai are sushir (blown); ghatam and manjira are ghan (solid).",[88,850],"classification",{"id":852,"section":35,"level":91,"prompt":853,"check":854,"hints":865,"solution":866,"skills":867},"sound.q057","A ghatam makes its sound because",{"kind":52,"options":855,"correct":864},[856,858,860,862],{"id":55,"label":857},"a skin stretched over it vibrates",{"id":58,"label":859},"the solid clay pot itself rings when struck",{"id":61,"label":861},"a string inside it vibrates",{"id":64,"label":863},"air is blown across its opening like a flute",[58],[],"A ghatam has no skin and no strings: the **baked clay itself** flexes and springs back when struck, ringing at its own natural frequency.",[88,35],{"id":869,"section":35,"level":141,"prompt":870,"check":871,"hints":874,"solution":876,"skills":877},"sound.q058","Using L = v ÷ (4f) for a closed resonance tube, what length, in metres, resonates with a 200 Hz tuning fork? Give your answer to three decimal places.",{"kind":218,"answer":872,"tolerance":873,"unit":221},0.429,0.005,[875],"Divide 343 by (4 × 200).","L = 343 ÷ (4 × 200) = 343 ÷ 800 = **0.429 m**.",[35,496],{"id":879,"section":35,"level":141,"prompt":880,"check":881,"hints":883,"solution":885,"skills":886},"sound.q059","Using the same formula, what length, in metres, resonates with a 320 Hz tuning fork? Give your answer to three decimal places.",{"kind":218,"answer":882,"tolerance":873,"unit":221},0.268,[884],"Divide 343 by (4 × 320).","L = 343 ÷ (4 × 320) = 343 ÷ 1,280 = **0.268 m**.",[35,496],{"id":888,"section":35,"level":178,"prompt":889,"check":890,"hints":900,"solution":902,"skills":903},"sound.q060","An open pipe's fundamental is 220 Hz. Which of these frequencies is NOT one of its harmonics?",{"kind":52,"options":891,"correct":899},[892,893,895,897],{"id":55,"label":507},{"id":58,"label":894},"660 Hz",{"id":61,"label":896},"770 Hz",{"id":64,"label":898},"880 Hz",[61],[901],"An open pipe's harmonics are all whole-number multiples of the fundamental: ×1, ×2, ×3, ×4...","220 × 2 = 440, 220 × 3 = 660, 220 × 4 = 880: all whole-number multiples. 770 is **not** a whole-number multiple of 220 (770 ÷ 220 = 3.5), so it is not one of this pipe's harmonics.",[904,35],"harmonics",{"id":906,"section":39,"level":49,"prompt":907,"check":908,"hints":918,"solution":919,"skills":920},"sound.q061","As an ambulance with a siren approaches you, the pitch you hear",{"kind":52,"options":909,"correct":917},[910,912,914,915],{"id":55,"label":911},"rises",{"id":58,"label":913},"falls",{"id":61,"label":116},{"id":64,"label":916},"disappears",[55],[],"An approaching source compresses its sound waves ahead of it, so more wave crests reach you each second: a **higher** heard pitch. This is the Doppler effect.",[39],{"id":922,"section":39,"level":91,"prompt":923,"check":924,"hints":935,"solution":936,"skills":937},"sound.q062","A rider sitting right next to their own motorbike horn, while the bike is moving fast, hears",{"kind":52,"options":925,"correct":934},[926,928,930,932],{"id":55,"label":927},"the same shift a bystander would hear",{"id":58,"label":929},"the horn's true, unshifted frequency",{"id":61,"label":931},"no sound at all",{"id":64,"label":933},"only a falling pitch, never rising",[58],[],"The Doppler effect depends on **relative motion** between source and listener. The rider is not moving relative to their own horn, so they hear its true, unshifted note.",[39],{"id":939,"section":39,"level":91,"prompt":940,"check":941,"hints":943,"solution":945,"skills":946},"sound.q063","A source sounds at 250 Hz and approaches at 50 km\u002Fh. Using f' = f × v ÷ (v − vₛ) with v = 343 m\u002Fs, what frequency is heard? (First convert 50 km\u002Fh to m\u002Fs.) Give your answer to one decimal place.",{"kind":218,"answer":942,"tolerance":343,"unit":473},260.6,[944],"50 km\u002Fh = 50,000 ÷ 3,600 m\u002Fs ≈ 13.89 m\u002Fs.","50 km\u002Fh ≈ 13.89 m\u002Fs. f' = 250 × 343 ÷ (343 − 13.89) = 250 × 343 ÷ 329.11 ≈ **260.6 Hz**.",[39,307],{"id":948,"section":39,"level":91,"prompt":949,"check":950,"hints":952,"solution":954,"skills":955},"sound.q064","Using the same source and speed but receding instead (f' = f × v ÷ (v + vₛ)), what frequency is heard? Give your answer to one decimal place.",{"kind":218,"answer":951,"tolerance":343,"unit":473},240.3,[953],"Add the speed to 343 this time instead of subtracting.","f' = 250 × 343 ÷ (343 + 13.89) = 250 × 343 ÷ 356.89 ≈ **240.3 Hz**.",[39,307],{"id":957,"section":39,"level":141,"prompt":958,"check":959,"hints":970,"solution":971,"skills":972},"sound.q065","A recorded voice usually sounds different from how the speaker hears their own voice while speaking, mainly because",{"kind":52,"options":960,"correct":969},[961,963,965,967],{"id":55,"label":962},"microphones always distort pitch",{"id":58,"label":964},"the speaker also hears their own voice through bone conduction, which a microphone cannot pick up",{"id":61,"label":966},"recordings play back too quietly",{"id":64,"label":968},"the speaker's ears work differently from everyone else's",[58],[],"While speaking, sound reaches your own ears both through the air and through **bone conduction** (vibration through your skull), which adds extra bass. A microphone only captures the air-conducted sound, which is what everyone else already hears.",[973],"bone conduction",{"id":975,"section":39,"level":141,"prompt":976,"check":977,"hints":979,"solution":981,"skills":982},"sound.q066","A recording engineer wants to sample audio faithfully up to 18,000 Hz. Using the Nyquist-Shannon rule (sample at more than twice the highest frequency), what is the minimum sampling rate, in hertz?",{"kind":218,"answer":978,"tolerance":220,"unit":473},36000,[980],"Double the highest frequency.","2 × 18,000 = **36,000 Hz** is the bare minimum; a real system would use a rate somewhat higher for a safety margin.",[983,984],"sampling","nyquist",{"id":986,"section":39,"level":141,"prompt":987,"check":988,"hints":990,"solution":992,"skills":993},"sound.q067","A seismograph records a P wave, then the S wave 8 seconds later. Using distance (km) = 8.4 × the time gap in seconds, how far away, in kilometres, was the earthquake?",{"kind":218,"answer":989,"tolerance":5,"unit":252},67.2,[991],"Multiply 8.4 by 8.","8.4 × 8 = **67.2 km**, using the same style of reasoning as the flash-to-thunder rule, but for P and S waves underground.",[994,307],"earthquake waves",{"id":996,"section":39,"level":178,"prompt":997,"check":998,"hints":1000,"solution":1002,"skills":1003},"sound.q068","A train horn sounds at 600 Hz and approaches at 90 km\u002Fh. Using f' = f × v ÷ (v − vₛ) with v = 343 m\u002Fs, what frequency is heard? (First convert 90 km\u002Fh to m\u002Fs exactly.) Give your answer to one decimal place.",{"kind":218,"answer":999,"tolerance":343,"unit":473},647.2,[1001],"90 km\u002Fh = 90,000 ÷ 3,600 = exactly 25 m\u002Fs.","90 km\u002Fh = 25 m\u002Fs exactly. f' = 600 × 343 ÷ (343 − 25) = 600 × 343 ÷ 318 ≈ **647.2 Hz**.",[39,307],{"id":1005,"section":43,"level":49,"prompt":1006,"check":1007,"hints":1018,"solution":1019,"skills":1020},"sound.q069","What is the main difference between musical sound and noise?",{"kind":52,"options":1008,"correct":1017},[1009,1011,1013,1015],{"id":55,"label":1010},"Musical sound is always louder",{"id":58,"label":1012},"Musical sound repeats regularly and has a definite pitch; noise does not",{"id":61,"label":1014},"Noise cannot be heard by humans",{"id":64,"label":1016},"There is no real difference",[58],[],"**Musical sound** is ordered, repeating vibration with a clear pitch. **Noise** is irregular vibration with no definite pitch, though the line between them is not always sharp.",[1021],"noise vs music",{"id":1023,"section":43,"level":49,"prompt":1024,"check":1025,"hints":1036,"solution":1037,"skills":1038},"sound.q070","Which of these is the strictest daytime noise limit under India's zone rules?",{"kind":52,"options":1026,"correct":1035},[1027,1029,1031,1033],{"id":55,"label":1028},"Industrial zone",{"id":58,"label":1030},"Commercial zone",{"id":61,"label":1032},"Residential zone",{"id":64,"label":1034},"Silence zone",[64],[],"The **silence zone** (near hospitals, schools and courts) has the strictest limit, 50 dB by day, stricter than residential, commercial or industrial zones.",[621],{"id":1040,"section":43,"level":91,"prompt":1041,"check":1042,"hints":1053,"solution":1054,"skills":1055},"sound.q071","A basic dynamic microphone turns sound into an electric current using",{"kind":52,"options":1043,"correct":1052},[1044,1046,1048,1050],{"id":55,"label":1045},"a small battery inside it",{"id":58,"label":1047},"a coil moving through a magnet's field, induced by a moving diaphragm",{"id":61,"label":1049},"sunlight hitting the diaphragm",{"id":64,"label":1051},"chemical reactions with air",[58],[],"Arriving sound moves a diaphragm, which moves an attached **coil through a magnet's field**, inducing a current, the same principle a generator uses.",[1056,1057],"microphones","electricity",{"id":1059,"section":43,"level":91,"prompt":1060,"check":1061,"hints":1072,"solution":1073,"skills":1074},"sound.q072","A loudspeaker converts an electric current back into sound mainly by",{"kind":52,"options":1062,"correct":1071},[1063,1065,1067,1069],{"id":55,"label":1064},"heating the air directly",{"id":58,"label":1066},"using the current to push a coil and cone inside a magnet, moving the air",{"id":61,"label":1068},"storing the current as light",{"id":64,"label":1070},"spinning a small fan",[58],[],"A current through the speaker's coil, sitting in a magnet's field, creates a force that pushes the coil and its attached **cone**, which shoves the air into a sound wave.",[1075,1057],"speakers",{"id":1077,"section":43,"level":91,"prompt":1078,"check":1079,"hints":1081,"solution":1083,"skills":1084},"sound.q073","A machine measures 90 dB at 1 metre. Using level(d₂) = level(d₁) − 20 × log₁₀(d₂ ÷ d₁), what does it measure at 4 metres, to the nearest whole decibel?",{"kind":218,"answer":1080,"tolerance":5,"unit":647},78,[1082,659],"Distance ratio = 4 ÷ 1 = 4.","Drop = 20 × log₁₀(4) ≈ 12.04 dB. Level at 4 m = 90 − 12.04 ≈ **78 dB**.",[566,662],{"id":1086,"section":43,"level":141,"prompt":1087,"check":1088,"hints":1099,"solution":1100,"skills":1101},"sound.q074","Standing further back from a firecracker reduces the loudness you experience mainly because",{"kind":52,"options":1089,"correct":1098},[1090,1092,1094,1096],{"id":55,"label":1091},"sound level falls with distance, roughly 6 dB for every doubling",{"id":58,"label":1093},"sound cannot travel more than a few metres",{"id":61,"label":1095},"firecrackers get quieter the longer they burn",{"id":64,"label":1097},"distance has no real effect on loudness",[55],[],"Sound level falls with distance, roughly **6 dB for every doubling** of distance from a small source in open air, which is why stepping back genuinely helps, though very loud sources can still be dangerous even from well back.",[566,662,640],{"id":1103,"section":43,"level":141,"prompt":1104,"check":1105,"hints":1116,"solution":1117,"skills":1118},"sound.q075","A recording studio's vocal booth is built to be almost \"dead\" acoustically. This means it is designed for",{"kind":52,"options":1106,"correct":1115},[1107,1109,1111,1113],{"id":55,"label":1108},"a very long reverberation time",{"id":58,"label":1110},"a very short reverberation time, so little room sound is captured",{"id":61,"label":1112},"the loudest possible echo",{"id":64,"label":1114},"no sound insulation at all",[58],[],"A vocal booth uses soft, absorbing surfaces to keep the **reverberation time very short**, capturing a clean voice with minimal added room sound, unlike a large stone hall built for a longer, richer reverberation.",[394,1119],"recording",{"id":1121,"section":43,"level":178,"prompt":1122,"check":1123,"hints":1125,"solution":1127,"skills":1128},"sound.q076","Two different machines measure 65 dB and 70 dB alone, at the same spot. Using L = 10 × log₁₀(10^(L1÷10) + 10^(L2÷10)), what is the combined level, to one decimal place?",{"kind":218,"answer":1124,"tolerance":646,"unit":647},71.2,[1126],"Convert each to an energy ratio, add, then convert back.","10^6.5 + 10^7 ≈ 3,162,278 + 10,000,000 = 13,162,278. 10 × log₁₀(13,162,278) ≈ **71.2 dB**, only a little above the louder 70 dB machine alone.",[566,307],[1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141],"sound-ncert-class9-sound","sound-hyperphysics-speed","sound-hyperphysics-ear","sound-nidcd-hearing","sound-nidcd-noise","sound-cpcb-noise","sound-britannica-doppler","sound-noaa-sonar","sound-wikipedia-instruments","sound-wikipedia-bone-conduction","sound-wikipedia-44100hz","sound-usgs-earthquake-locate","needs_review",{"generatedBy":1144,"notes":1145},"claude-code","Draft generated locally; pending owner review. Every numeric answer computed and asserted in scratchpad\u002Fsound\u002Fnumbers.py and gen_bank.py.","8572bc86aa5880aa4687f6dcd5372b6dfe60d1859966a267c178cdfa939753e6",{"logic:questions":1148,"source:sound-britannica-doppler":1149,"source:sound-cpcb-noise":1150,"source:sound-hyperphysics-ear":1151,"source:sound-hyperphysics-speed":1152,"source:sound-ncert-class9-sound":1153,"source:sound-nidcd-hearing":1154,"source:sound-nidcd-noise":1155,"source:sound-noaa-sonar":1156,"source:sound-usgs-earthquake-locate":1157,"source:sound-wikipedia-44100hz":1158,"source:sound-wikipedia-bone-conduction":1159,"source:sound-wikipedia-instruments":1160},"e7fd7c240a65bea1bff6277f7af7cca65e2c7fcb13c6d756cb943d53f3cbc948","838644206b59946eaed329bdfe25d227ac6dbb22279805052fee24175ed3ce31","278297753fb9417bb45ce52bcbba4e42ccba48426815813568968b0ffaa42b34","0a3d2c27986cca40d06b5de949d3c7a13272672e9766ecf33e53ec27ee28c886","4cb248d8beea032b112212f11d2a3d10751a3a68da1b26d2ef93b11835467932","615e6ca7b7252ccb2523eea00746ef69215849397defe43c853a9fcb617799dd","562aa906d72517f7a88b5d3bae2937ed3678a02844460b91738fc93e493f3490","6c2548bc22d1e37e553f1f05a7b1c919c097e49ad319523b186e766828b576cd","89db468fdabca49aa3be9a157e9e0767aa5bb8e500bc451e3b1137895f11bb97","b2c9464b8e51c98308ebd63e76a062662ba23f7c7150ac64cc555216cf2ffab8","85166e3b268f56304a2070992c53f631f7e9fa6a0b1864bba5770b13c2471743","1c161fa64b415c06c85cc03facf17983594bcde1c6e94c2470c385ea3f36a7fc","0b24a438b7c5bb6e98dad1043334a28d32ba3aa4ef1eca60660933b537c66d0a","preview-7e1cbbcc4f",1789899599989]