What is the evidence that sound travels a9zk d9jewco5+ s a wave?

What is the evidence that sound is x3lrbc7c 5 lqf 40q2d7as; tufa form of energy?

Children sometimes play with a homemade “telephone” by attaching a strxikl)t;+urlb/u 2d2:r mgwg/ing to the bottoms of two paper cups. When the string is stretched and a child speaks into li2du/2k)xtwbl/;rrg g: m+u 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 expect the fje ;hlx8 (j*dbrequency or wavelengtj;*l ( exb8jhdh to change?

What evidence can you give that the speed omp5g4/4n +lk+ya qso tf sound in air does not depend significantly oagqynp+km4 st+ /l54on frequency?

The voice of a person who has inhaled helium z3a3 bblm- l :8yjzvn7sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pg g*8h ,iwl.ywipes?

Explain how a tube might beqf vqoj:r ac4zvqa 11f/-p m74q:pv6j used as a filter to reduce the amplitude of sounds in various frequency rangesmr:fa4fz64 :p qv 7vqc11o-qjvpq/ja . (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–3 vx7e*2fkbi-bv y1:gehq)1w j;umc/u 0) spaced closer together as you move up the fingerboard toward the brid1/v:kwf 2yi)eqbmbhv*e u-cu1 ; g 7xjge?

A noisy truck approa - 7zm:fjizl ;gs2fc81zcji m7ches you from behind a building. 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.z1-2 zf77:8ccimf jl;jgismz Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sairm) 5hjsy ov3)d to be due to “interference in space,” whereas beats can be said to be due to “interference in time.symjv 3o)5hr )” Explain.

In Fig. 12–16, if the frequency of :2wcdi01juk nwl dje64r. vx5 the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther nl1e54w.crvd6d :ku wj2ixj 0 apart or closer together?

Traditional methods of prot g/uqjzem8e5 aj s) u972u4j5sp+o r7z;kcoyxecting the hearing 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 technology, headphones are worn that do not block the ambiensej7a8+cg7z o2sk)u/o4exy ujuj5;mq 9r p z5t 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 Fi-nv3ot(ze1:d vyy2cu g. 12–31. 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 (b), are the v (e-n3tdco:zvu yy 12two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer movego2yf6: c/bmu in the same direction, with tbm:cu y/ofg2 6he same velocity? Explain.

If a wind is blowing, will this alter the frequency zcsj09sdop*c;f8 8tbqo;i2qj n71 jbof the sound heard by a person at rest with respectq s2sfo 89;cin 8jjz*q1 dbbt 0cj7o;p to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor bo r8v h(29 bw:lfq7fet9r ya/is blowing a whistle in front of the child on the ground. At which position, A through E, will the ch9 rfe(/:v2wo8ql h9bft7yr b aild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the len gq(ni-fam26x gth of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimai-g xfqn m2a(6te the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of m5mj8rsk ah,9v nt:1lhis ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at jkmlthr5m s :,v89na1this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aihpk ;nm257 yijr at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a fogmcguj bkgi((3(t-u 6c gy day. Without warning, an engine backfire occurs on another boat j-ibg 3c(umcgu(t6(k1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splas5a -tb4wlf rz. , -2r0*fmhvlwjr)dl wh it makes when striking the water below isamw)frrd -*wr -w4.tfzj25l0lv,hbl heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge s:8dj9idp .p/+(pk5hmekfdi otone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.(+fp:dj 5/pi.om9ehk dd kp8i1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-sec6 .o nvub6a*jjezh3h1ond rule” for estimating the distance from a lightning strike if the temperatuvzj 6nao31hbe *h6.jure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 12e l-bu p ./r)vz5h3nlj0 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound wjvy6 skvg*o m0z hwn75;x67vz hose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired siqx78pz l0x6qa-crr rze*5hr+multaneously at a certain place, what will be the sound level ifp*-z 70xlr6ar5cr+r zq8x hqe only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equallyh n,3vjb:7jfz noisy jet engines is experiencing a sound level borderin,3j bz:vnf 7jhg 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 hadw.t 5n ,;llfmy065p ltlxw p:ve a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitl0xt :, 5ltp.npm;yf5lwdw6 l ies of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking inc9p n l-irl*eswk:;/t normal conversation. Use Table 12–2. Assume the sound spreads /w9 ; s:kit-ne*lcpl rroughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -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$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area i+xf 3uom)*bhqs $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, g+/g wmuq3wy.ij 3f6p while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would e3 /u.gwq3wij+gf 6y pmxpect 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 dB meter registered 130 dB when placed 2.8 m in frol;;k ni8g xj6fnt of a loudgk in;lfjx 6;8speaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference d rmx7z- b.rw(in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levr w.7rb-xm zd(els differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inp x;5ck .yjmy*tensity *ypk5x.mc jy; increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudea hb 6x3jc df8atr;44eqew cp0: e.z/qs, but one has twice the frequency of the cq/tw.x3 e 8re4p4zahd;f0j:acebq6 other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thar20sfmk5 m v:c omljng(1:9x gt corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 H :g vkmf2mon(5 sg1jlx:09rcm z?    dB

  A 6000-Hz tone must have what s jrqs.ws dtgy2z.)f7kjonf/m5k+1 m)b.n+eround level to seem as loud as a 100-Hz tone that has a/sr zo2 nnfs mg1q..7rjw kdjm5bt fe ++k)y.) 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can ds .l-61m dzkhketect when the sounkz -1.dslh6mk d level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lj -o)ftdsl1/hevels. What is the ratio of highest to lowest intenhltdf) /-osj1sity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fund51vsqd tjq 51q)e 6outamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension musev5 qu 16ot)j51q dqstt the string be placed?    N

  An organ pipe is 112 cm long. k nybah+e0gp1 l)u0u y(bk66 fWhat are the fundamental and first three audible overtones if the pipe n0 1lyub gk6 +e)uak( ybfhp60is
(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 frequency would you expect from blowing across the tpa .)jnk-tx6j-c7lwx7 k y my3op of an empty soda bottle that is k. nx)-6pwmxjtl7 yj k3c7 -ay18 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 pipesh2h2 5gkhxk;b ofs 9j; spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requx shok25h f;;2hg9bj kired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Whb)fa,;psxz6 yn md f+z 5/lbq9at will be its fundamental frequency if it is fingered at a length of only 60% of its ori nbxz)l/,dpf6 afmq+sybz 5;9ginal length?   Hz

  An unfingered guitar string is 0.73 m lonuu*u d-gq/hgxw5/ ui s i41u(mg and is tuned to play E above middle C (330* h-ud/smw 5(iuu x4uggi/q1u 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 of an open organ pipei46jvpr51yn:ccy( h t3yq ;xc that emits middle C (262 Hz) when the temperature isyy3pcjt6c:5 4cvyq rhi x(; 1n 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 9bf z)pm:u y0rat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thun .: va tr )ggna(-*(stel-ez4 ezp+we flute in Example 12–10 should the hole be that must be uncovered to play D abovg+-ge tua4(n vz:l).(e *rt wa-senp ze middle C 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 rezdey9iknc;*s3 .6 lw vsonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a yeivcw. ;nsz6dl93* k 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 open at both ends. It resonates at two sucu.lj ;u0blfx( pp ;dd1cessive harmonics of frequencies 275 uu.pd1pxfjb0ll d( ;;Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 x1bg5no oz1:7 a1t gnd$^{\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-gfoc 1ljw )od ;6l)ud d--8ceslong organ pipe at 1g s;6clo-8dowej) l )dd-fcu 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lof;0a3v wkti7 bng. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (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. 127k;b0vw t3 ifa–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, one krzmjt8 a e6 5;:0 d-fxo6y5ev salgk(of which is sounding 440 Hz. How far off in frequency is the other st5msfl(are6z0vy a tkd ;5ex og6-k8 j:ring? ±    Hz

  What is the beat frequency if middle 8zu x5a2x7n)z 3flcd0 fa 5kc(igsa5d 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 opt ef0/ce /guzyo) +t8merates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimgf/yte+)c tzo80eu/m ate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuningo *trk z,+ned3;o1gsr fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasonist+ 3,rg*1dzeo;nrokng.    Hz

  Two violin strings are tuned to the same f/ey( ublmas /ep0m: v )wl 6w.-qkn,ucrequency, 294 Hz. The tension in one string is then decre6e(// k0pc-ly l :wwq.vmab)uue,nsmased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identx t j9*b y3lsb qw,2yue-5ac1aical flutes each try to play middle C (262 Hz), but o5e bj twyl 39yu*, asqcx12ab-ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whe* ne e(h-wcdz5n A and B are soundedw*-en zeh c(5d together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the 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 person stands 3.00 m from onipu rtap6gb15 ;* /tqee speaker and 3.50 m from rp ;tit u 6be1pq/5ag*the other.
(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 vibrating at 132 Hz, but a piano tuner hear8ay8 h1kh ,gqn48z66dd ye cxrs e ,y4h6h18drn8xz g d86cqkyathree 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 other ?   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 wavelengths 2.64 m and 2.76 m in air. How manyvbmso-)hx w08 beats per second will be heards0)w8b ovhm- x? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ofcabr;o z25 a3 ow:t6rt a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed 5z3:ra;btac6 too2wrof 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 sirez 86 r7acmnd7jn emits at 1550 Hz moves at a speed of 32amr7d 786zjn c m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hzky f0)s q pywsu5y+f31h5eli ( source is moving toward you at 15 m/s versus you moving towu 0lwk)p1s5q+y if5 seyfyh( 3ard it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn.fc vnwt-y/o.7 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 the ftv- fn7.ywco /requency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 6*ygb o8,p*5urxg.,sl o m c+gnzjiq-50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the re cp* ,g o*5z 8 jgqrb.x,+6luoisy-gmnceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ultrf6( vboi am1* kjqf3g.asonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wav6qg3 j m(v b.faifo1k*e?    $ \times10^{4}$ Hz

  In one of the original Doppler experime0kaiwv 6b (b6hnts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at resthb k vi60(wa6b in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measbob)r-* 9g)sy u7 y7hpvgl7 hture blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue 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 f7ps7 hrov*uyg) 9bhy)l -g7 btrom the sound source?   Hz

  The Doppler effect using ulm.xn phi j6f-r9:6s krtrasonic waves of frequency $2.25 \times10^{ 6}$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 $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity irv7(;+s-ditkooj z4 bs 12 m/s from the north, what frequency will observers hear whoo; j-vkb+7z 4siod(rt 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 moving on land if its2ep;lr,wv z (b 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.su6i-tvak/ xr6x9se(y y 0f18bat7l o 3 where the speed of sound is 310 m/s (a) What is the angle 9la 6r7 u8e(s6a tikft0x/x1s-yvbyo the shock wave makes with 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 atow *;*ypice.guv1n74 sc1br emosphere of a planet where the speed of sound is only 1vw.re;pc4 b*u gic*1 e7snoy about 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 striy humqel;ke(xj*7i t( / 6b-qlkes the ocean. Determine the shock wave angle itx;e6 llyku /i(-7*j hqbmteq( produces
(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 + ek amchvt1t 2kk;/ txir,:ffvc+c+* $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ove36x4h zlzwu xxb0 ,n7crhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal dwx7zn0b 6xz 4cxl,3uh istance 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 pulsdyq l 2- h:*el;6 un ,(qzs.d7djhfniwes downward from the bottom of the boat, and tyjd wi nh-l:e;q7zu6. ls2,fn* dd(hqhen detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octavozu2ju 3z ez19es are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display ca yyk+ 2o,pnno+8yf1pslled a sewer pipe symphony. It consists of many plastic pipes of various lengths, whiy kyp,1fpyo ns2+o +n8ch are open 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 closr/21yv9ck2+b baif ase to the threshold of human hearing (22+ aybsa/9 frvbik1c 0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB 94jj tx0mn , *wxuchyis-32ac sound are heard simultam cwis,jjx 204yc*-xnu93 h taneously?    dB

  The sound level 12.0 m from a loudspeake5vdo9d9i,g xqbuf +/dto +r j-r, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?fov ,/9i trjxdg-bu5 o+dq9+d    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power npjm60 xy z 0ugsc3*rl1d5nc5output drops by 10 dBg6150cl z mdnx0*3yn c5jrusp at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deu 1zw3*zo6p9g jfkn) i;2z8xv zuw,vivices over their ears. Assume that the sound level of a jet airplane engine, 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 v86zpnz g,uf);9* zi wozk 31u 2xiwvjintercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems0a(x6;3kfvzj efy9 fu, the 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 jz dpz7bb1apfs.o w.07, 6nwga frequency 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 cm long between fixedcr7dox+ l0 x+fdz9j)t points with a fundamental frequency of 4j )79xdxr+ z0+flodt c40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{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 abovencwohy 1z1+ (. pu7s8he pjpp( a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so.o ny11(hsh +wu 8ppjzp7epc(, 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 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube -qb*l j+)jxw tthat 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 fundamental mod)+q * xwjb-ltje) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop (a d(nxkxm f55($\frac{1}{2}\lambda$) 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 sources. The uzv)40a xgxsx+6zqy3e*yt 6g sound is loudest at points equi *qts0 yg)yezzx3vu axg +46x6distant from the two sources. To determine exactly what the frequency is, the person moves about and 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-Hz whistles. One train is statixbpod9 bjbm)hbp5q: 66sfu 84 onary. The conductor on the stationary train hears o5u 8pphd9 b664fbqjmxbb) s: a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 539u/,f)ks r ojs8 Hz. After it passes you, its frequency is measured as 486ouj9kfsr )s ,/ Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars v:y, a,mdtmi o*.lk3x just by listening to the diff iv3l:k, .,d*amoxmyt erence in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops 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 z guj3w*ddc*5gu z-jcai2 *p+a beat frequency of 11 Hz. The shortiu*pz *2j-gduc3gwz5cd*+j a er one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it at8w)dhsca;1moves 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, in front of ttwa1 hdasc )8;he 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 flow in the aorta is3(,r3mq thtf2tf3 h2w1 lnf6rfh r1o2z e2but normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the redmh(f 6wrh3etrf 2t 2 3 b22z1u1nqtr,ohflt3f blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/bme a(s nk:37us while the moth is flying toward the bat at speed 5 m/s The bnebua( 3smk :7at emits a 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 pulseso mtr fpt0(*9y as it approaches a moth. The pulses are approximately mo0yt * p(rt9f70.0 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 Alpin+sr;nc5q6x -b,pwcapd kb tao.i p-* 1e village 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 resonating. 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 oped;kct,ar s.c bpi*nbq61+wp5-a-o p xn tube.

  Room acoustics for stereo listening can be compromised by thw7nv/d* gik e1ojh k-3e presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a lwk* /j17-hnk edvio 3giving room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” in l bj ve2ce4ac pxt)q)+x snf.na7)7x6g-ip/ mvolves a long, slender aluminum rod held in the hand near c7qbl ))xn/p)xajm7 e4c-pei2ngv .fs +t6xa the rod’s midpoint. The rod is stroked with the other hand. With a little 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?    $ \times10^{ 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 ear at a frequency of a w/i91ducrt ox3p 63eabout 1000 oa3r91 ex tid63pc wu/Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Macha -0tuztmbb w 3g40b4n-az;bn 2.0. An observer on the ground hears the sonic boom 1.5 min afteztntmb-44u 0bb;b3-n0 wzag ar the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat gejk,s8j-a(qudnt3 n c.n 8(ois 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h