What is the evidence that sound travel* qa0a).xrkxws as a wave?

What is the evidence that sound is a form of enema7o6-ue3x burr ef(+ rgy?

Children sometimes play with a homem p9(waqs/z--ef6jfdou t4 1/zf wv:yzade “telephone” by attaching a string to the bottoms of two paper cups. When the s(w wu za4/9 o1svj edftzf/-q-:6yzf ptring is stretched and a child speaks into 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 frufh ( cwxt7 5*yw)pey,equency or wavelength to c,f) c* hxteyw(5yw p7uhange?

What evidence can you give that6;qcd ig1atm8i7 /lzt the speed of sound in air does not depend signifi76lmtctz q1 /i a8dgi;cantly on frequency?

The voice of a person who has inhaled helium sounds very high-6b+h cuqvnlvft ) s*,3m9w jw7pitched. Why?

How will the air tempera a62jf7 m,vnvdo2ayn 9ture in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filtervt.b4bat,/x r to reduce the amplitude of sounds in various frequenct/rbvb x.t a,4y ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1 ,f61 u w-+milprw /dm+i:etjg2–30) spaced closer together as you move up the fingerboard 1l-wg j ,rm+edm+put fii6w:/toward the bridge?

A noisy truck approaches you fr+dr 9 jylyamxy*-3bm;td6 e*oom 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. Explain. [Hint: See Section 11m 3-a+j6ryde*t ym9x; y old*b–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beat ren/+ f2zvbeo32.bhos can 2fre/3nohev2. bb +ozbe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the ;xil 3 k 1epj-ebso 8qw.77untpoints Du 7lp xesoni w3t;18.jq kb7-e and C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wob ncmw m 07muroya)0*;f+qt ,rrk 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 ambient noise. Instead, a device is used which detects the,y ;mmq)0w+7orf abrtn0uc* m 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 (fk5be /fm6 xdshown in Fig. 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 th 6bkm /(5dfxfee two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sawme d:s:4, pz,1hhzr gme direction, with the same veloc:dz sr:hh, ,ewzg1p4m ity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a perssb 1. qn,9i93r kmesqson ae9nss,qqk s m3.ir9b1t rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions 5g()alz9zj2k0fms4/n t 9xvhqai8 fo 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 E, will the child hear the highest frequency for the sound of tfak gi mz)n2zq h(f o9t0/8jlsx59v4a he whistle? Explain your reasoning.

  A hiker determines the lengj jb*,pkwi6v 5 1vlg7g,v4+dqmhx0 yp th 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. Estimate the length of1p7v4q,jhl0 g6 x wi*b+,mkdjv5 vgy p the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below tgrtgqw3e,*n hxpj,)65r n th+he 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 soune,5ggn3q *px6n rhrhjt w+,t )d in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2rg;u7nbty: -v/) sxn8i ryk p0ta5w;d0 $^{\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 ey sup-mu,3:w of tuna on a foggy day. Without warn:we3-y up, usming, 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 cliff. The splash it makes when blz m* bpgp 62 zrfqk9z(i:0(gstriking the water below is heard 3.5 s later. How high is the c*bz f02l (:kirbm(z gp gz9q6pliff?    m

  A person, with his ear h4t: yg3uf - wc5krfg.to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the con3 fy. g-cguhwr:4f 5tkcrete, 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 o,upzsxmb -yzf/u s8; q.p;k)f ver one mile of distance by the “5-second rule” for estimating the distance from a lightni-ymzu/x ;quf),s.ps8 pf;zk bng strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the s74qbk 39qsta pain level 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 level of a sound whose intensigx(k*tu f9af.,(gn/zbd *zt nty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level o +qcex6h2oz/v f 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]e2 oq/vhx+c z6    dB

  A person standing a certain distance from an airplane with four equally +b6)t3in c5t madyh.ml: nt7f noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down alltlmni:. 7ndcm t 6fa ty+)5bh3 but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio og+ka3h jl1g5 r inqut(d0d8k -f 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background dtu+18(0di jkngag 3rh q-5lknoise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frox qr,vh1vpgct 4 :1lgexi) +af*jz,l p;p/*skm a person speaking in normal conversahq4l x/r,p1v: cejl;k + pi*z) tav1fx ggs*,ption. Use Table 12–2. Assume the sound spreads roughly 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 eardr8r3tr(wsnwe 22n.htq i 0huq (um whose area 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 rated at 250 W, while the more modest ampln9nvctq2mr /h+dxl zr( +8 za(ifier B is rated at 40 W. t92d+ z(xrcr m(an+q h8zv/ln(a) Estimate the sound 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 dB meter registered 130 dB when placed 2.8 m in front of a qe9jesa o; *l4loudspeaker o sea9loj*4 e;qn 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 ik ,ser3;7 jhzywu5 y .gl8nb.mn sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whosuh b w5y 38n7lgzs.;m, .rykeje 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 t5-e. zblx cef2iybm8 ,he intensity increase? fbm .-l8,by5eic ezx2Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes;(8 y lztd r4rfx(uq4w, but one has twice the frequency of the wlut(x4r;q 4z (r 8dfyother. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in m0 o +v/gkz0qk)nxmx q no;+9iair that corresponds to a displacement amplitude q xozg+knk qm 0;i/ xmo)v+0n9of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud ain,x f91h1 ulzs a 100-Hz tone that has a 50-dB sound lunl 1if1z9x ,hevel? (See Fig. 12–6.)    dB

What are the lowest and highest freu-qu-a( porgv7s0 yy o8gun,:quencies that an ear can detect when the sound level g0-gu(-8u:y no avy uqos7pr, is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lev9ar/eh*p:rr78( zkingzw np9 . b2fseels. What is the ratio of highest to lowest ina*s8z(p: np7wbn/ 9zerir 9erh .f g2ktensity 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 frequency of 440 -c (gf2ixp+9l u+blma Hz. The length of the vibrating portion ib + (9l+2xiculfap- mgs 32 cm, and 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 fundamen-g j *sieee:9xs+a5: wwim/vjtal and first three audible overtones sew/w:jmjee5 s+ -:a9x*iigvif 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 frequency would you mds3 z u,mlu; .:r:h/hyd-q idb1f)onexpect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wasf yu1b-d mz dil ;:hmsu)d,:nhr/oq3. 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 otp/spw k/:a80kyx6qt pen-tube pipes spanning the range of human hearing (20w8xqy kk6 /s:0 pa/ttp Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenc u(v79xxph+ xs w (no lwc1vc9y:0t,wmy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is finge1:nsc,ph7wo+wmtlc wx v09(9 xv uy(xred at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7g+s lyex8un2. 3 m long and is tuned to play E above middle C (330 Hz)nu8 2sgye.+lx .
(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 lenqook1 kcuvw h ec/k(,2t16 t,xgth of an open organ pipe that emits middle C (262 Hz) when the temperature is 6wc,o (ku1o cx1tv,ekqt2/ hk 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 h61 wxrx7qba9ou+x(e at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should zt /.ek-,)ky.ol5nnmt a9drmthe hole be that must be uncovered to ple5t.9z m, adlyr) /nko- nk.mtay 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 ca -+ nmotvm2u1/ *dcizhg 19axsn resonate 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 di9s+xnu1c 1 / zm-2vo* htgmaclosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is opeua5nx- 05kf965h p txtv (uonln at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. W5t(l x ukovx59-nth 6n 05pafuhat 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 bi6 0q 8al-sj6df lz(ynf )gd,$^{\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-lony-mm x,ra( suclc06.u i1vuu3g organ .36mus1lcmxrc v iu(-yau 0,upipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal rgc m(+1(o 2e)j*,qlhtrheiiis approximately 2.5 cm long. 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 wr12g, +mhjq( le)oii(*c ehr taves 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, 1n c)ler a8ogz.b(+rztx, o+u one of which is s1o+gxb(.,)e 8rto azu rc+znlounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C *,p6xoi.0f e*dmuz+ts 3ly q m(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 X) operath7l-pzvdov *jxd ;l* 4es at an unknown frequex* v7lpd-jh zv;l4 *doncy. 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, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork anp3ui 96)bcockd 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reas bu6c3c)9 iopkoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensionu, d3 7e5rzzjwc1x7.sn lcvc* m9hen6 in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? z3n*lz1,7v j.r hmdenc5 wc7sue6c9x [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identic8 6c*drcx bk,hal flutes each try to play middle C (262 Hz), but one is at 5.0°C and t6c r ,cbxh8k*dhe 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; whe28tk*z3ot nhmg+y7 f en 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 frequencies are possible when A and C +7ko entm2htzy*f38gare 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 one bj-98;basrp)0mcgn 5ju p em/speaker and 3.50 m from the other9 n;ga5b0jce-mp /u8jbp sr)m .
(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 t:k asgw89im m v-b-9- 0jbbtmfuner hears three beats every 2.mbvfm80 9jk t- bi-mb9gw:s-a0 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 many m59myppg 44lfbeats per second will be heaylppm 54 g4fm9rd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firo,yd16c*e9jyuc9wz x7b h 1fbe engine’s siren is 1550 Hz when at rest. What frequency do you xuzb1y6 dj97f1y wb,cco *h9e 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 frequencyizj8nfo:xu v, k3kg0) do you detect if a fire engine whose siren emits at 1550 Hz moves at,3:0nzxkfi o uvgk8) j a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift; 65cv u6ka(gtdmjbi vki v--9 in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward t ci5vk9k(6;vugji-a dmb-6vit 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 frequene qmpmg57, ; ,e7yrel3e9bowycy horn. When one is at rest and the other is moving toward the first atel 9y 3e5eq7,goybm ,7rep;m w 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 40kwxkgq3w r5 ihq5: sultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s wg4 q h53xr:q si5k0wkWhat is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speedru q ye+y2b8w yf:we u92y:9nwxe5hz; of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency down qyye52uw:;f89erxbe2w:+ 9yzu h yes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a7d.dp +x* ixpx qd1;zq moving flat train car at a frequency of 75 Hz, and a second identical tuq7d;z *x1 +.pd qxdpixba 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 waves . o 4crnnr7z. rb7bt0oto measure 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 4r ntbboz.n.o7 0c7rr 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 +ox,dt:lsh s8yi5fj 6 ultrasonic 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 sjfj6 h8;1bx day1f 4iuound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rf61i jy;4dfx juh1ba8 est,
(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 speed aqr jn w2(:/xxwt 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 where the speed of so vzz+2 )bzdo0r a4js-nund is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mot)0oz sa2zvbdjnr +-z4ion?    $^{\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 tua8 xy0ak2- lzhe thin atmosphere of a planet where the speed of sound is only aa x-l2k08zuyabout 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} $