What is the evidence that sound travels as a wave?r)j lu(.mxo/ o

What is the evidenceb by/0 q+rd:k2- m5veph e+elk that sound is a form of energy?

Children sometimes play wi0+z5 yad hmul9pvg345e* dvn ath a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks inp dl4a yvz5g*a+neh59 m30vu dto one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expec9f r;wz,i h,czt the frequency or wavelength to change?hfczr9w i z,;,

What evidence can you give that the speed of soun3eb*h e)su;zo-n e3b nd in air does not depend significantly on frequu-sz h;)ee 3nnbbe3*o ency?

The voice of a person who has inhaled helt a7dtl3v;ag: ium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch fb2 ) c)nxaoy1of organ pipes?

Explain how a tube might be uq(xk i7l,ex,osed as a filter to reduce the amplitude of sounds in various frequency ranges. (An example kiexl,q( 7 xo,is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move9l xc ed2g49 -bo0vbhh up the fingerboard towaro9gxdeh4l9 vchbb 0-2d the bridge?

A noisy truck approaches you from behind a buildinghg3 m)y5ihm8z. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 onyzim3hm 8gh5) diffraction.]

Standing waves can be said to 562.g 5aucfnww l0m cvbe due to “interference in space,” whereas beats can be said to be due to “interference in timcm na2w065w.lc5gfu ve.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweredy)te7go3nk v4s79scb6 ffdi ,xc-o5g , would the points D and C (where destructive and constructive interference occur) move6e- x bot f7gndk cs3ys9gcv75),4foi farther apart or closer together?

Traditional methods of protecting the heargbteup(ddj2 +/d-n/ ring of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technologgtdbe j/-pn d2+ur d/(y, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31.wassfek3+6h 4 Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (hsa ewf+64sk 3b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directivn5a,pt-v ebk e 6-ae5on, with the same velocit6 t-v5ne5eaek va -pb,y? Explain.

If a wind is blowing, will this alter the frequency of the sound heard b/2 2q81zxjsei4ei .ok zg5mauu8zg0v y a person at rest with respect to the source? Is the wavele z1ui z8g uxms2j /8gevqi24 .okz5e0angth or velocity changed?

Figure 12–32 shows various 3+wyu),vayt n,g1 e uopositions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through Ee3ungw,tv,o y+u a )y1, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listen44f0 ,q fi-d61a k0veo diwyswing for the echo of her shout reflecti,o6 sad4w-dqf ew0k1v0y f 4ied by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $\times {10}^2$m

  A sailor strikes the s84j 4 y9lvqdatr*f, ntide of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s latt*4t, ay 9d8nvl4rjqfer. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $\times {10}^3$m

  (a) Calculate the wavel/ 2snzv71f;z-rcovii aslh5( 2o 4i igengths in air at 20 ${}^{\circ }$ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. ${\lambda }_{20Hz}$ =    m ${\lambda }_{20kHz}$ =    $\times {10}^{-2}$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $\times {10}^{-5}$m

  An ocean fishing boat is drifting jumu *quv*x+r 8bxy0 uu3st above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) uvrqyu8x *0b + u*3xumby the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikz4kwt dx ,ov jl )3b.(-uveht7ing the water below is heard 3.5 s later. How high is the cliw(hu.3z ojx vkdbt4tv)l- ,e7 ff?    m

  A person, with his ear to the ground, sees a huge stone ste2q)ku qf4t,f q-o tc-rike the concrete pavement. A moment later two sounds are heard from thefu,2 -kqocqf- tet4 )q impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $\times {10}^2$m

  Calculate the percent error /umnotxr.*z /phc v :*made over one mile of distance by the “5-second rule” for estimating the distance from a lightning ouh v.*xz pnm/c:t/ r*strike if the temperature is (a) 30 ${}^{\circ }$ C, $\approx$    % (b) 10 ${}^{\circ }$ C$\approx$    %.

  What is the intensity of a so znd *wgz rd/u2 -jcu6r2.zt8zund at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $\times {10}^{-10}$W/$m^2$

  What is the sound levey p3pcfg96)rvl of a sound whose intensity is $2\times {10}^{-6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 bt7n8 vr(1qo edB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.] en7 q(8ro1tv b   dB

  A person standing a certain distance from an airplane with four equally noisdn )yh (m;h-(7rifj 0xxgom*by jet engines is exp )mf -ihx7rg(dynjxm; (o*b0heriencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratikkptw ivpd;2z; ) fo0)gf;ka /o of 58 dB, whereas for a CD player it is 95 dB. What is o0dtv pa;kf2kpzw)g;/k ;)ifthe ratio of intensities of the signal and the background noise for each device? 58 dB =    $\times {10}^5$ dB =    $\times {10}^9$

  (a) Estimate the power output of sound from a person spe9ixnz 9t3meex) a cip:gd)4x;aking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on txi9 4 gde:;a3x )9em xpizc)nthe mouth. $\approx$    $\times {10}^{-6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $\times {10}^7$people

  A 50-dB sound wave strikes an eardrum 1ap) (uup40g svii:(d n + 2m4wfuxb+few5yggwhose area is $5\times {10}^{-5}{m}^2$ (a) How much energy is absorbed by the eardrum per second?    $\times {10}^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $\times {10}^3$yr

  Expensive amplifier A is rated at 250 W, while the mor 2ze.s6ps. r: wwior5qe modest amplifier B is rated at 40 W. (a) Estimate the sound .6zewiro:s wp.s2 qr5 level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dBpl-ja 1- oqm/d meter registered 130 dB when placed 2.8 m in front of a loudspeaker on tomdp -ajql/ 1-he stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $\times {10}^2$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $\times {10}^2$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What tpw9h oi:8jo9 is the ratio of the amplitudes of two souh:ipjoo8 w t99nds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will-olyn+ e.zvev0:zx6h5lp+3 dkk jgp. the intensity increase? Increase by z3pz6l:k d-50y+kx.pvjoe v.l egn +ha factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hasj -o;7a rujyx6)ddn/-ou hj-g twice the frequency of the other. What is the ratio of theirdn7;yrj/ 6 - h)uxuo- -djgajo intensities?   

  What would be the sound ls e iz c*rnyyq+ v;t(7b5ts2a8evel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300s52*qsy ne7ti rc8v( y;z+a tb Hz?    dB

  A 6000-Hz tone must have what sound level to 8w;, yiwdeqif7io -p8 seem as loud as a 100-Hz tone that has a 50-dB sou,y8i8w7;i q-pefdowi nd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequ,l; d6id x,y7u vdgvo6encies that an ear can detect when the soun;7v xg6didloy 6,u,dv d level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lxgx6pg x;6c9jho hrcc34kx (k:81t ukevels. What is the ratio of highest to lowest in oghxcuh ct8x :rx (ck613xk;k4g96jp tensity at
(a) 100 Hz,$\times {10}^a$ a =   
(b) 5000 Hz? $\times {10}^a$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. T l nh8cs p::irupeb:p(6yg 0.nhe length of the vibrating portion is 32 cm, a0 p .phcb8peginnr:s ::(yu 6lnd it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firs 0yidy h1:m* phd.mwm7c;h- qot three audible overtidy;oc*h-m7h pqy m.: hmd0 w1ones if the pipe is
(a) closed at one end, $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz $f_7$ =    Hz
(b) open at both ends?$f_1$ =    Hz $f_2$ =    Hz $f_3$ =    Hz $f_4$ =    Hz

  (a) What resonant frequencyva e-iv6n hw3eey8:nip /4:ahy6 fk .h would you expect from blowing across the top of an emvviw 4nh6 p. i:a -/fky6ye3he8enha :pty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of hu xztjn3olde9zkmce l*8u/) f25mr j *9rxo3f 0man hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requiret8zr0r3n cezl j o5fme x)2j xfud 9m/3*l9k*od? $L_{20Hz}$ =    m $L_{20kHz}$ =    $\times {10}^{-3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What willm 3d7;hq s9i9(o6 hwia xgy)jd be its fundamental frequency if it is fingered at a length of only 60% of its originamodxjqs6;h y9(i h 3g9 dw7)ial length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plxg+jp8j :z .laay E above middle C (330j. +zagp8: jlx Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length o()cc f6:z og ;qnj8pt8q, y5txjrat0t f an open organ pipe that emits middle C (262 Hz) whentt cpqcoa, tfn)0yj5 6 j8gx8; :qtz(r the temperature is 21 ${}^{\circ }$ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 ;qrw vp(kosy2xj9r:8 ${}^{\circ }$ C. By what percent will the frequency be off at 5.0 ${}^{\circ }$ C?    %

  How far from the mouthpiece of t7izi v8,qe*dlhe flute in Example 12–10 should the hole be that must be uncovered to play D above middle v,l7 ze8i*diqC at 294 Hz?    m

  (a) At T = 20 ${}^{\circ }$C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, .w c)i, i9kb)kl:m, m7(f5jnnarrp jyand 616 Hz, but not at any other frequencie k w() r,m) abf7. 5rilc,pmjkyi:9njns in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is op ibfy kvqm)ldks 3+wxc+ +2a+z-4r lh.en at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. y.+hrfcdwzali+ 3kk) ml-x+v4b 2sq+What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $\times {10}^2$ m/s

  A pipe in air at 20 shj k8 *d(bbc-${}^{\circ }$ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-lo ,og4njj;1vew3k ii0m ng organ pipe ,4jonwik ;m ive103gjat 20 ${}^{\circ }$ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside and 1txjlv y: 7i .nu)e0ugis closed at the other end by the eardrum. Estimate the frequencieive0g.)tn :ly1u 7ujxs (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, gtw t1w g7y6.pone of which is sounding 440 Hz. How far off in frequency is the gw .ywtgt 716pother string? ±    Hz

  What is the beat freq(-fxdj vt3j*j9+g zlv uency if middle C (262 Hz) and $C^{＃}$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand ;5r;/txdk;xi 1znq sgX) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 x i;sqrt1xzg;d5k ;/ nHz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sojwx bnusa*we l3 pa():bxp.+1 unded with a 350-Hz tuning fork and 9 beats/s when sounded with a 3*ujnw b3(x:x wabl+a.e1p)p s55-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned t2rx2dko , gz(azi4x,uo the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played toadx2gku,z2 z xi4 o,r(gether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fluy m(fe4iuy -1k y b:34h9cod2j;hadmetes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25ym:e ea4mo4d hd9u y2c1-k ;( fyjh3bi.0 ${}^{\circ }$ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 H *5plm)injjp:g) fnh 8z; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, thnlmj8ih :np* )jp)g5f e beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A peo/;,qilqu x 0l4w5hnpi2c2uh8 8l r ftrson stands 3.00 m from one speaker and 3.50 m from the other.rx08lf228opn ,t5hwi iqc;ul q hlu4/
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 ${}^{\circ }$C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be wys 7(y0kpuw)qi c( h5vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the othe qypiuwsy)kch57( (0 wr ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavele,j 9g vx/ia 2j(ql7ad:t*r ogjngths 2.64 m and 2.76 m in air. How many beats per second will be 2jq gijgla(r9 jxa do:*,v7t/heard? (Assume T = 20 ${}^{\circ }$C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’p sd80 gqikt5,s siren is 1550 Hz when at rest. What freg,iq5sd8 ktp0 quency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose lmg +*ceo7 0h( ef,f*cq tj 8zhf4x)vbsiren emits at 1550 Hxg fqj8 *t7vm,l*( 0hefz f)4o bchce+z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcrso7 x(ils h17e is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are th xi 7rhl71ss(oey close? $f_{sourcemovine}^{\prime }$    Hz
$f_{observemovine}^{\prime }$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f_{sourcemovine}^{\prime }$    $\times {10}^3$Hz
$f_{observermovine}^{\prime }$    $\times {10}^3$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f_{sourcemovine}^{\prime }$    $\times {10}^3$Hz
$f_{observermovine}^{\prime }$    $\times {10}^3$Hz

  Two automobiles are equipped witu*nqy axq- c/o jhc;2 )6xle8dh the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is q 6jadc*8c no-eq u;/hyx)lx2 the frequency the horns emit? Assume T = 20 ${}^{\circ }$C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives thefxc6q;gh o,bpn/w*/wda; fw, m returned from an obj wwfd,gfnao;b/qwc*ph ,x ;/ 6ect moving directly away from it at 25 m/s What is the received sound frequency?    $\times {10}^4$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, t6n orap2/ mks-he bat emits an ultrasonic sound wave with frequepr/2km6snoa - ncy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $\times {10}^4$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat t,yn(wu 1 ay0nprain car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approacynyp ,(nu0aw1 hed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultra jcvzc-2)fd7asound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tis- dzv27)cjcfa sue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequen mjpas2 dsr 6k9dz3h*o7llo/h;/qri 6cy $2.25\times {10}^6$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54\times {10}^3$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emitiv ,ledn )wpgt174lzxph5-+f bk4 4hus sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear win5bxtkl de p lv1,f4 4g4+zuhp-h)7who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 ${}^{\circ }$C

  How fast is an object movi )ter x ndtyen*) ;qo(khn)x4)ng on land if its speed at 20 ${}^{\circ }$C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 woiy* m8(j/nw ao cgz*:here the speed of sound is 310 m/s (a) What is the angle the shock wave makes witmjn *oo8i(wyg:z*/ cah the direction of the airplane’s motion?    ${}^{\circ }$
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed ow*x( zik1yw1zg yz m.p 4g3lpf+,tv 4cf sound is only x4+.ppm3zcw1*1z lygy4(gwvt, fkizabout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    ${}^{\circ }$

  A meteorite traveling 8500 m/s strikes the sgsoihqyf4 bmt 3-. k /x5u;j0ocean. Determine the shock wave angle it producesoif bjq0sk.u xt 4s5/y- h3;mg
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    ${}^{\circ }$
Assume T = 20 ${}^{\circ }$C

Show that the angle s69vv+ mm;bm y$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheadmz+7 coq/v gb8 xd +ki5lt7:eh and see a plane exactly 1.5 km above the ground flying faster than 85qe 7iv7b/mc+kl:zd+toxh gthe speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    ${}^{\circ }$
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound 0yn.vj)k3 vgj pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fregjy 30kv).vnjsh water)?    s

  Approximately how many octaves ar;1dpu:bcvy* .qzgz(wg +*klte there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sgp90(p7+ d8stzq yw maymphony. It consists of many plastic pipes of various lengths, which are op yagdp9swm (p+ tz78q0en on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresuy ejcx /aef3;hz0-( rhold of human hearing (0 dB). What will be the soune0a3(czy-xrefj u/ h;d level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an hjh8000yfjy k t7e) f;(ohrmv82-dB sound and an 87-dB sound are heard yrot(feh0 k y h0m7; jv0)fhj8simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the ope x/7mfj,0dfmo0aiy z,n, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equm0d0ai,m, f/f7 z jxyoally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops b +e y3jwo3bx,5l,mlqby 10 dB a ,+ lex,bl33ybowjqm5 t 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. Aerm42gzlv;62m jp- n5ldw1s0v upe q 6ssume that the sound level of a jet airplane e vq;2w56ul jnm2 ls01pgzr mpe6ved- 4ngine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the 4e f+ yen/zpu+t.4icj gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frsze9upe 9s:l6wms v /(equency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_A$ =    ${\mu }_A$
$f_B$ =    ${\mu }_A$
$f_C$ =    ${\mu }_A$

  The A string of a violin is 32 cjw;j89 gc lb4wm long between fixed points with a fundamental frequency of 440 Hz and a mas4jcw; glb8wj 9s per unit length of $6.1\times {10}^{-4}$ kg/m
(a) What are the wave speed and tension in the string?    $\times {10}^2$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled k uyb(q6 5n9jswith water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at yk(u nj9b6q5s 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2 ;s h6l9hwfoi7,bp2t u8o7 he*f sovf:.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fund2p*sb h8et:oh9f,76i7;owsflvf uoh amental mode) with the third harmonic in the tube?    $\times {10}^2$ N

A highway overpass was observed to resonate as if rou3y 29uv4rvm)6jone full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sourceh4y-, wi4 py;rqieq w:s. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and q:4-4q;y p irwhyw,ei finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-msmln-;r 8xpt 2u52ae* -ryoeeu.ye) Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is theroetm8nu-es*py.5e x l-uam2;e2y) r speed of the moving train?   m/s

  The frequency of a steam train whistle avx00 h7ghr6i os it approaches you is 538 Hz. After it passesxhg6 h70r0ovi you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeninnfb7ol71irdlp+ .7*xq6si , n.l rnms4v xo6j g to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drop x77.6b1 m,o+lr 4sf r* pivndon6nxq.li7sjls by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz.ythz du k-7fy1 kwm:i33tpf -foq2(h9 The shorter one is 2fq-t-23kh:d ftzo 7wy k13 i ym9pufh(.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of w7 g-brf:0gj:cdkj0f a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, kwrb- j:0:j 7 f0gfgdcin front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flo)cbmdx f n*u p7ng7;r4w in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along tb*xnfp mn7rd7u;gc4)he flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54\times {10}^3$ m/s   $\times {10}^3$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward t9ruxuha x8*) sv5nmfny6e:j 9he bat at speed 5 m/s The bat emits arx * 96sn)8jmf5ahye9nv:xuu sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulswk imls82 l7j/es as it approaches a moth. The pulses are approximately7 jk28wm i/lsl 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villau0a,b-g x 0glkge to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonatbgglx, au0k-0ing. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised 2 di )/n(lhfotby the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this roon d/(2ihft l)om.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” il7r+uz hf1gs 18k(apf of9ao0 nvolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a littleu(fg97fo8h0p s l+ra1zfk a1 o practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $\times {10}^3$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 ${}^{\circ }$ C?    m

  The intensity at the threshold of hearing for the human eyqhc:gh(nv 0 11/p3+zs c anesar at a frequency of about 11 pcz hy+e:shg3v/ n1n 0csa(q000 Hz is $I_0$ = $1\times {10}^{12}W/m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1W/m^2$ corresponding to an increase of intensity by a factor of ${10}^{12}$ By what factor does the displacement amplitude, A, vary? 10${}^a$ a =