What is the evidence that souoc)h282ejhyye,tw )o- kbd )hnd travels as a wave?

What is the evidence that sound is a form of mhewi4 8qxwzf;hu.6 l c,r70henergy?

Children sometimes play with a homemade “telephone” by attaching a string t)vahipm)/h+ k d8jx-, rtmkv5o the bottoms of two paper cups. When the string is stretched and a child speaks into ohvph-+,xir kmvjt/58 kdm)a) ne 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 frequ )4 g.ryubqhkd)gj94dency or wavelengg r)9g.hqd4)yd uj4k bth to change?

What evidence can you give that the speed of sound in air doe/h0 cks4qns h8s not depend significantly on frh80kqhc s/ ns4equency?

The voice of a person who has inhaled helium sounds very high-pitc v5*e--wjxc(ly obu/ fhed. Why?

How will the air tempy,jw+zn w fjh8+g/9hmerature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sound5hez-e00/hkik ys m+ss in various frez5 m /+hess0yk-0 hikequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) space9vj)jno k.9ct5aat)w enyc7;xq9 9o )fgo.v nd closer together as you move up the fingerboard toward the.99vj7n)kteajq))5. cn f w9yoog ctnv9a; ox bridge?

A noisy truck approaches you from behind a building. Initiallv,j5esl-y8t 9f)jj x (e5a yaay 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 noisav ( e8yj jsy-5)ax,59jfelt ae. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” 8h ):tu :vpiu69habaok( if3 jwhereas beats can be said to be due to “interference in tij(: 3h auo)8hatf 6up:bk9ivime.” Explain.

In Fig. 12–16, if the frequency of the speakers were low+*hpry,di8iim.v72p l rkfcp;gdq1n w4 ij)0 ered, would the points D and C (where destructivev.f1 7j*w+ikqlp ihr;,y)ii 0dcdnmrp4 g p82 and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hea5 yhlbg0i 1 lp axat-2qs+p.x-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 rx0yt-i 5hgp1pq +2xslla .b-aelatively new technology, 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 Figcv+i(gv, :l 8pt : +bt//ulo xd9lxmkw. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different freqp v(, llu ttc:++9:i/okx dgm8/xvbw luencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in th.om)1b,rmg qk4 rmjb .e same direction, jq,gbm.4krr .1b mom)with the same velocity? Explain.

If a wind is blowing, will this alter th0vu( ryiwkqfe1 l .36ce frequency of the sound heard by a person at rest with i(ryvcf.lk 0qu136ewrespect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in+izv v2xyar;gi,82phzu( d6 p motion on a swing. A monitor is blowing a whiu6xirvz(;z2paidg, 2p8y hv+ stle in front of the child on the ground. At which position, A through E, 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 listening for the echo of her shout6himx;m ys3+ v reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the l+s ix3mh;m y6vake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sid7cbg8pp;kh*9 neb6 iezfb2p- e of his 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 this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significante 2*gf pi;bcpehbnb 9k-87zp6ly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths mu5ua *efmtv)w8 5qe4in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \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 tuma . t2dwk6wtf.3hx81m a9gqt na on a foggy day. Without warning fxm182 m 3akw.6ht.t9watqgd, an engine backfire occurs on another boat 1.0 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 clicqbi9pe0 g8j li k,b(9ff. The splash it makes when striking the water below is heard 3.5 s l,98bj gi(9cpk eb0qi later. How high is the cliff?    m

  A person, with his ear toa q5b.oiad10oh g;db4b v b+b, the ground, sees a huge stone strike the concrete pavement. A mom ah.1v,ib;bboqa40b+d dbgo5ent later two sounds are heard from the 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.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by f:pi1k/j0et)dlf;tz -z m4o sthe “5-second rule” for estimating the distance from a lightning strike if the temperature is (4-z:0km ) /zjfotei lfpd;1tsa) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levl e.9d:gyp.q :npkxt6el of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leve -cs:am k38gsjs5r3 zs(uyl1ql of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produmoe kk9fcp 3f*vwz (ek :1f,9wkk2g/hce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sokz,p9ew:m2eh k f gkv9f *3ckwk( /1found level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jeb*wb 7k k:hmn/a3r4d lt engines is experiencing a sokwrkd:*b/a7l4hmnb3 und 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 rati az *b-f.fi2suvy0zwbq 3v x22o of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each deuz byvf2 -iz0bsfv2aq*w x2.3vice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a per5 keh-v,r gj*bw.v2aason speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered e*.haj rwav gb2v5,k -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 ar4xfd s,-6fw h6m i9ywmea is $5 \times10^{ -5} m^2$ (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 bq--6omcy6j ut xk-3erated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a t 3cmu- eqjkbo-x66- ypoint 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 de5f .3rbp k2ldB when placed 2.8 m in front of a loudspe kd2b .p3rlf5eaker 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 in sound levexo r+ mob:,+7liz btj8l of 2.0 dB. What is the ratio of the amplitudes of two sounds wh8jxmblbz+t+ ,7i roo: ose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of dth 7*uflkexnsb1ro)7 vgbp*+a4 u* ;a sound wave is tripled, (a) by what factor will the intensity incrn+o*h)*d7be uv*k su1t7pgrf 4bl;xaease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, n4ua-ie5q,ta +s ;whobut one has twice the frequency of the other. What is the ratio of their intei a4;e- o+uwtna, s5qhnsities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds tonq 3 49zrfh 1t:keeyr8hmhj/-er2 5gj+fru( y a displacement amplitude of vibrating air molecules5reqf :ke/rn+tmu1jy4ghehf zr92 -y8 3j(hr of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sou9njm aueht9poa,s 5/6flc d+d t)zh() nd level to seem as loud as a 100-Hz tone that has a 50-dB sof mh)duje,t p a a(/ntdco59+)96lszhund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear canqwa io-r: +rgpi9 ayy-sf9d)3 detect when the sound lesiy9y-o +r)rqwaag9d-f pi :3vel is 30 dB? (See Fig. 12–6.)

  Your auditory system cawds7d (n+6pnn22vsrv n accommodate a huge range of sound levels. What is the ratio of highes(sdr67 n22nvp+n d wsvt to lowest intensity 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 fundamental freqxbc( ab3 b(i4g,py -szuency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tenpb3-a ( y zbgxi4bs(,csion must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threj ,wjgd+0 p3wisf62a ceuh8x1e audible ove8 23d,sa pjx0gh w1+c6wef ijurtones 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 freoa:9 9r;: mtpk26zw- zfjwnr *wqsz k*quency would you expect from blowing across the top of an empty wn9w:qt p9;2z kao -zr *m6kf:sjz*wr 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 spannin h cq984/jalzxg the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes reqzcq hj9l4a8/ xuired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hasf)/y d7bno:pgu.bh7n a frequency of 540 Hz as its third harmonic. What will be its fundag):/ bnpu .oyhdn7b7fmental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunedk l(bvq;3km+t to play E above middle C (3303k;tkv (mb+lq 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 pipe that emits middle Ch *eyff*3pkx+ i 3tqp. (262 Hz) when the temperature is 23k**. pxqpih3yfetf+1 $^{\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 (t)cvj 6 ,binrat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiwlq8ul( pgn/q d 0r4j1ece of the flute in Example 12–10 should the hole be tha(wd 0gl/8u4qln rpjq1t must be uncovered to play D above 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 resonate at 264 Hz, 440 Hz, and 616 fp, :otouoomf4i :6p l1v6qd7Hz, but not at any other frequencies in between. (a) o::6ftfo7o,u4q m l1pvdi 6opShow 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 open at both ends. It resonates at two sy 05 afmhio6t 4y8inwjfijk bfc1,6(( uccessive harmonics of frequencies 275 Hzw0 h1iyk6jff( ci(na5o j4f ibym8,t6 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 *n-+ pzp)f l6l gxf8ij$^{\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 presentsl0.gtcn fmvzzi.j8f n*/ ufw01yu 09 within the audible range for a 2.14-m-long organ pipe z c0f1styn/f0gu98*.fzlm. inwu0 v j at 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 andx 1 i 7oavaeg (5kozajmx006-h is closed at the other end by the eardrum. Estimateijov5a-kz gx h7(ma ex0o106a 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. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one bea. wa- vk9rlkv:t every 2.0 s when trying to adjust two strings, one of which is sow k.l-v:vr9a kunding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262cien5 * h l+t cxw9;y0.x(cvnz 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 X) opera(ak3 5fnyt 4o0dfan4y27gk45 palmmo tes at an unknown frequency. If neither whistle can be heard by humans when played sept gky 7np3(kmf5 ldna4 a 4m2ooy0f5a4arately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork .t q)zxw3ph-w and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vt-3qwzw)x h.pibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the samlah rff5l*ny xkn ;v:7 ;;h3tre frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will bx; 37*t l:ynnkhh5ff;rlar;ve 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 identical flutelruco7.d1d ,qp6 1 ndzteh. ;as each try to play middle C (262 7 n;lh tdcdqu6r,o.zad .e1p1Hz), but one 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 7syc* trs;j:v a i,a(a441 Hz; when A and B are sounded 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 frequenciecs r*a:;vs7,jtai ay( s 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. Aqgjhpqh ,f ,p0hkkojn+b; 0q i+ 7ct.3 person stands 3.00 m from one speaker and 3.50 m from the othercojhn gkkqihh++0j b3.; t,,q pq0p7f.
(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 areg cp4tv(w3kj5 s(pcp 1 supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) j1 pc 5s(kt(cvpgw4 3pIf 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 sounduuksbdcw 5.6w dad0 ,2 of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume Tc, .s2d wu5w6 k0buadd = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sire0ugn;q3kl )e/ m cbzj9n is 1550 Hz when at rest. What frequency do you detect if )egbjm nk0qu;/ z9c 3lyou move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still.)w x(5n, ksabfc 7rkq1 What frequency do you detect if a fire engine whose siren emits at 1a1nfwrxb)q c s7(k,k 5550 Hz 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 source is moving ton rvchg+q1w rtz4x -ynfh+67q *.wq*sward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exaw6 yq47zg-rqnh*+ cnhfx1t.w s r*vq+ctly 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 witha35anbec 2txb zhe9c1 z4 7vhd4/ dtv0 the same single frequency horn. When one is at rest and the other is moving toward thhdhtecv t 2a4 19bz3dnv5 a ze4b70/xce first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is 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 receives289kzz;9nvsj zwok qsib.-i twsc4:z nm,: 4h them returned from an object moving directly away from it at 25 m/s What is the received sound freq2nbzz4 sk niwcv9;:: j4q.ssm ioh ,tzz9 w8-kuency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fh5rif 5 /rznpx,uj,i2fh pe07 lies, the bat emits an ultrasonic sound wave wnpr,ripj 5eu0i,f2zhx 7 5fh/ith frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Do14 aa9rc. 1tryyasue9ppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identi aat1re9.14asyru9y ccal tuba played the same tone while at rest 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 wavefe l m-:cuw mzkj6g-*+s to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, w-k6 mcufj-:m elzg +*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 from the sound source?   Hz

  The Doppler effect using ultrasonic waves of iurmh 5ri2n.kj8(3nd mpa.z 2frequency $2.25 \times10^{ 6}$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 winsubf 3 vg*3ftw:kpo9n0gty r4rq9 t3v0oz,m-d velocity is 12 m/s from the north, w030kq f-3 9trp3stguo*,wyobvr9v4m ngf:zthat frequency will observers hear who 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 its:p+)eb1p re ge 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/ rv z1tc4zbpmk ;hd-b ,.zs1b3 a:evc 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wavbzc .p-av sk;4dtb z/b 3h:cvm ,r1ze1e 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 atmosphere eos8ew:*bz -y g2eti2 qi7z7hs6 en:iof a planet where the speed of sound is on: e7nes6 o i8tq:2i-ee 7b* wzszgh2yily 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 strikes the ocean. Determine the shock wave an9ynq8g0 k* 91v pkcpj( mnlet1gle it pyg8 k ce m* pnnk1v99(0j1tqlproduces
(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 vsovk9ze.u c;:4j5ms $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grourhkm ,+2prsv1c.8udu 4dgb r) nd flying faster than the speed of sound. By the time you hear the sonic boom,d pu4b82d,1u.)c rr rs+vh gkm 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 sen2m6;1bo kxkqj ds 20,000-Hz sound 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 ;q j2 km6x1bokthe minimum time between pulses (in fresh water)?    s

  Approximately how many octav ozw 5s tvhc 1+jd0gq/hseq;pui:s:- 2es are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consistin(bjb*7u8c j6n f: fos of many plastic pipes of various lengths, bno bji( c*f u:n86j7fwhich 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 close to the -oil43la7 t(ubl+ pi tthreshold of human hearing (0 dB). What will be the sound level ot+ -u bplia37t4 ill(of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound area5fy0zrt6 rb,xl09 7 o 2inhzm heard simultaneouslyifx z0trh0 r67a 52,mon9zlby?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opesmri/ybkd) ..5 vp;pjt fv8y( n, is 105 dB. What is the acoustic power output (W) of the spe8 i 5vrdf(b)pj.yt;k yv/ps.maker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Tfn sbhr-,hk0; he power output drops by 10 dB at 15 kHz. What is the ,b-0 nr;hhf skpower output in watts at 15 kHz?    dB

  Workers around jet aircraft tyhw4vzf 4h8h6abk *ch 7qk3 r/apically wear protective devices 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 averazr3/64whk7f q4c h*bkvah ah 8ge 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 :9aia1 ohx4(jfrzk 8n, 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 violi( wt/n0 k572otvyazkwn is tuned to a 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 betw .eo rq425hflween fixed points with a fundamental frequency of 440 Hz and a mass4r2wlfoqe5. h 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 v b60t6o g.mz wkke2z7eibration above a vertical open tube filled with 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 0.395 m. What is the frequence 0kzw.ek6 mo2tgb76zy of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube zb fpeuc u.32fm)iz n7 lx ,t8-1m,amwthat is open at one end and also 75 cm long. How much tension should be in the string in,e,.wz f )plzum-8mux1fab3 cm 72itf it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reson q fyv*(;i 9qxq9,qtmhate as one 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 purl ux+m/tx0 u,r0m:tw je tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two u u,tx:/0+mxwr0l mtjsources. 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 stationary. The conductor onoh*y7 e zr0t5ts/5kns the stationary train heso5s e7 trh/z05tny*kars 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 85bf.-gzfyx hx*kzh 3538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant 5zf8*z b3xky.xg-h hfvelocity)?    m/s

  At a race track, you can estimate+ ,-mxbgxskx) the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certai+xkx mb g)s,x-n 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 tvn+;q4d.c yc ruta/ 7rogether, produce a beat frequency of 11 Hz. The shorqc r/v7crtya4un+;.d ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as itsd 2d50t3uhw 2gf)j :id6)ua.pehyuz moves past a stationary observer at 10 m/s as shown in zd)t3e.5 sd w 22fa6)y: 0uhudg hpijuFig. 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 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 flow in the aorta is normally about 0.32 m/s26;vpi ,ypc gi6 zqj/v4o4zod what beat frequency would you expect if 5.50-2z qpo6dvi,pz o4;6 cyj/ iv4gMHz ultrasound waves were directed along the flow and reflected from the red 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/s while the moth is flying toward the 5 xq*u-d2b l .;y2vbi fekbki7bat at spe*bflb 752;iy2 veqk- udkbx. ied 5 m/s The bat 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 pulses as it approacw8g5-bn bwz(ji: zoc (hes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detew 8:-n5zwgbco( jb iz(cted by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38)7gdov o255 qt,sf3j . jo8pvdm was once used to send signals from one Alpine 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 r, v .pjt7dd2qv55 j8gof3omosesonating. 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 compro6qby; u z h14zngrxjb+:5)mn fmised by 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, +b4b; nxyn6)r51z u fgq:mjhzand 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 ronj*hh 7 ps znecmu:;.1ds,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or eh ;ps:j em*u 71n.nzchmit 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 qg2.8/agfqpr6 bnmt ,threshold of hearing for the human ear at a frequency of about 1000 fabnr/ tg,pq 8 2qg6m.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 Mt9 cv py.;n1suync; 4lach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly ovtyn4.vu n p; yc9s1;clerhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1 6gm1fhtwgo qq1p+y nn(g85*m5 $^{\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