What is the evidence thl4 f z3in*+ xslb8r.s. rmq-k 0b7pgalat sound travels as a wave?

What is the evidence that soundq+w9ws3 zet- y3u)5hdbtzx23 asz6s u is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a str wh4 4nfln;;hiing to the bottoms of two paper cups. When the strinf l;n4nhwh;i4g 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, d n,rl ,2w)znbho you expect the frequency or wavelengthb,nl2r), h zwn to change?

What evidence can you give that the speed of sound in aij b t9pm) r9.jg1sueo2(zb/9e uns re;r does not depend significantly ons/r1 bo)r uez (9sje 2tpm 9euj9n.b;g frequency?

The voice of a person who has inhaled helium sounds very hm51hvqmy7,q,cmzi s (u(1xwhigh-pitched. Why?

How will the air temku*jal0).4g5s.ne z6 xu/ b etan(wzwperature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to redu o,kkqqi:v0 m.ce the amplitude of sounds in various frequency ranges. (An exa,.q0 okmk :vqimple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as.-tu;aw8l ny(tcsza 5 you move up the fingerboard toward the bridgea.ns tycwu(-t lz5a;8?

A noisy truck approaches you from behind a building. Initially you hear0t rg2m.. y *dw-vbixi it but cannot see it. When it emerges i.my0 t.d2 gw *-ibrxvand you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be j*suh2: le.m hdue to “interference in space,” whereas beats can be said to be due to “in.emhj*h s l:u2terference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the2pfxk-o/z9 d ky1uaz ,*cfv: yb9eew / points D and C (where destructive and construc e-xko,*9yfzd9:vpyewukf1cb / z2/ ative interference occur) move farther apart or closer together?

Traditional methods of d) 3)qg;em lpoprotecting 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 ambient nois;)qmp ole)d3ge. 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. Each wave c 4i65a:l8;sn*xbx (evuu rkbr ige,g6an be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of ak,8rxulsr*6 ui5b eg6(e:v;xig4b n 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 the same directi d ,iy+ab /)wbvfb aaha8q5f0;on, with the same velocity? Explain; av+ ,a/bya 5d8 qwbaff0)ibh.

If a wind is blowing9sv- wf/ xz2we, will this alter the frequency of the sound heard by a person at rest with respect to the sourxs -f2 9ez/wwvce? Is the wavelength or velocity changed?

Figure 12–32 shows various 6;wpyuqt(* y5vru:4 bwdh*fupositions 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 the6uhdq*r fb uu(w 5wtyyp;4*:v whistle? Explain your reasoning.

  A hiker determines the length of 0q38ewoc( qxeaj :+oga lake by listening for the echo of her shout reflected by a cliw0(c+ jq ao ege38:qxoff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shi+6evg tx- *wp( 7cg +omd+bs 9ttmmzu9p 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+*g+ bmg6tc9to e7t(wsm umd- px+ v9z 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengvol8nt ; 0jub;*ucl p 1-culj-sg1 b8uths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat iwn ty64lp7j f1qb*6jcs drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on 7lqnwbt 14jfp*y 6cj6another 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 j;wv (j ks6ur;makes when striking the water below is heard 3.5 s later;k(vj 6;wruj s. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concreqxm hzupt nyw9okx)dvz16vv63; 3v0)te pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the c1 hqvv;ko339)0z)uwnvv6 tmxy 6dpzxoncrete, 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 overts89g4)7 yvubzu eap7g.rbl +p5 vr0f one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperzpra7p.b u87 vs 4t+ 9g5f)ergbu lvy0ature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le/na:og)ytclev l44*qwp j*i (vel 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 intens5 m upx5ss86vuvu3tlj2m on)k34/ jovity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 99wz9iah 5m+ re5 dB when fired simultaneously at a certain mw ih5za+r99eplace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fourk:b oos -wt1atc/gd,x9zts17 equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut ddsczbt1-ao,1ts/x 97 tko w g:own all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, a6 ibjqqee,++whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devica+qqi je e,b+6e? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal col9;p(0vqxzg.8 glatwnversation. Use Table 12–2. Assume the sound spreads roughly uniforml(zxv; t apw9 0qgl.g8ly 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 mj 7z,c zwv+e19m ;+anhqq xv.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 r4 0wua :ggnxvz 4,xuzs*ewd/5ated at 250 W, while the more modest amplifier B is razuwg, w gzuv/04xnd:*5xsae 4ted at 40 W. (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 re8kar4uq3 4n3 z exxdb6r ,qi/rgistered 130 dB when placed 2.8 m in front of a loud a33qr ux8b r,64/qzen i4xkrdspeaker 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 fa fl0jeh 6 r*48.kchoa difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hia8 6kf0 he ho4*.lcrjfnt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fajo5cfbz08bpp1yp;3to pky) ) ctor will the intensity)bj yopf;pk po)105y3 t8czp b increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dcus8/oug 6i8 oisplacement amplitudes, but one has twice the frequency of the other. What is the ratio of theicuo8gs86 o /uir intensities?   

  What would be the sound level (in dB) of a sound f3c r ew,u,8whwave in air that corresponds to a displacemen wcf8,wur3he ,t amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tong 0;tnhbn (f9ay p5y*v8mp74 isyxh4 .dwrqn-e that has a 50-dB sound level?dp4;5 gpyv-.ny hqr9 yw80n7 sinb4t(mfx ha* (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can x ;pqu ds39r al85ycn66y8wkkdetect when the sound level is 30 dB? (See Fig. 69xyawnq;uk6 ps 8dck 8y 5lr312–6.)

  Your auditory system can accommodate a huge range of sound levelsn hdr0r0 pg(l7. What is the ratio o0gdlh(p07n rr f highest 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 fundamenr7hcv ptd 6,os;7; uvxtal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of;r; 6vu tsx pdoh,c7v7 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamenta rwkhb+sew:.n * igy80l and first three audible overtones if +:*ysneiwh0br 8gkw. 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 p8,*ve+zsvk+ :)mw we(va3dj0w mqxnwould you expect from blowing across the top of an empty soda bottle e epx +*s wdmjmwq+w8v3vv) (zan,k0: 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 or; xnltq9 k4ldfy8sc *1gan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHztxqd9ll4*1;n 8 ks ycf), 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 frequ,)z/i -k+it+ mfsvahbency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lehavs-t f++izb)/,k i mngth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E: (xy1tzi/1hs4djzr(0vvo yo above middle C (33:vx /ivrd 01t 1 (hs(yojzzo4y0 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 ppbt9vgkz6: r 2ipe that emits middle C (262 Hz) when the temperatzp :kt26rv g9bure 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 2c *g ocx vpngw(j fw0*yt,8t720 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flut.y/jnd7ibk7 5p1ce ca e in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 dpcb57yejakcn /17i. 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 Hz,)1c0zi6lk nvtul3xd h0 o a+6c7-vtd v but not at any other freque i0kt+ lvxv3 uvlthac6od-c67nz0 1)dncies 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 )x a;t. +ux-fn bnaoq.1.80 m long is open at both ends. It resonates at two succeo-+;.qanx unatxb.) f ssive harmonics of frequencies 275 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 h6ff y7cbj n,sid;;3s$^{\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-long o r-wsh6 ,qn.dxrgan pipe at 2sxw.6,nd rh- q0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.m ssy9k,t e-v*+loyx/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 waves in the ear canal. What is the relationship of your an y -9+*motksxeylsv/,swer 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 stri(zodp*+ o2nrw8zcb j1ngs, one of which is sounding 440 Hz. How far off in frequency is the othercz *+1(onjdowzr 82pb string? ±    Hz

  What is the beat frequency if middle C+p*lt n pa5:s. uuy:rx (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 anoampi kena; 1k(vmm; 4.ther (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 pl n4m;.kkip1m a m(ve;aayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350ef21m.z : tzg jk,jwk--Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational ,1z gzmk-j.kwf e2 :tjfrequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension ogq 7dor4e)m1 in one string is then decreased by 2.0%. What wiqeg1r4o d7 )omll 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 identical flutes each try toe- ly j8z l5+a*qnxlh6d4a; ukoa7:ha play middle C (262 Hz), but one is at 5.0n876a -kadel *xz:jqoa;lhul5ha4+y °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; wh tk8y*,fh6zf4d03 :ts4e s mzd/byg ccen A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the besg30 hd ykcfmbty ce:z4/46,zsdt8 f *at 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 x*k*hcgtez wv- 6jq7dg 2,r-*lnta.y 3.00 m from one speaker and 3.50 m ,he-d*2 kzyt7j6.lvqrxwctag n*- g*from 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 tlj v+.+2jzal ay,,lnd o be vibrating 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 frez2.+lv+ly la, ja jd,nquency 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. How39qt o oqdok5po;ab/ , many beats per second will b,a39oq b o;oko /q5ptde heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certajz+yx 6 .oivl;in fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move wixy6;iv . zojl+th a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequey2mwq04y - i01 *0c bypedmnsqncy do you detect if a fire engine whose siren emits at 1 qsw1 e20y pmq-mc0i *4ybdn0y550 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 toward you p7d+cdp pw1*pp ja.7n at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sp7pw+c.*nd7 p dpj a1pame? 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 equippeu.b p02b/os(5kwjw o ed with 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 the frequency the horns emit? A5( ou.0jbk2we sp/ow bssume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out/(1 9pskndyts(lq v k/ ultrasonic sound waves at 50.0 kHz and receives them returne tn/s9 ydkvkp 1lq/((sd from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a v 85.ozhcb j-gwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the ref5jg vocz.b-8hlected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving f7 +i,okpiy u8hai 4t7nygf1.jlat train car at a frequency of 75 Hz, and a s 8 1i.naptgk4y+i,hiu o77 yfjecond identical 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 unmq ( kr 9*-l2tcuojxyf+9 te3ses ultrasound waves to measure blood-flow speeds. Suppose the device emits sornt+e 3xf( j-qyul k2to9*m 9cund 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 from the sound source?   Hz

  The Doppler effect using ultrasonic 5ny wyccu*8 myyy,,p3bqvf:1 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 tz6pgj)/ bs r*mhe wind velocity is 12 m/s from the north, what freq*pg/ br)s z6mjuency 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 z 3tk(ntj d d35zl84vsland 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 where the speed of sound is 310 m/s (a) Whatbslt7fegc+( s)- g* ca is the angle the shock wave makes with the direction of the airplanesf)te l gg7c *bsac-(+’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,y g s/ctvr8g; a planet where the speed of sound is only abvrtgy ;,/8sg cout 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 shocp *8 5h0mcsuu6(bmg n8efp7pb k wave angle it produces s8 5 up07fgmcpp68eh un*m(bb
(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 q/(rxdo7l x ueb)5byz*j:h 5c$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhe26hhxk:dfs1i+ 2bab i+ e ivv*ad and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By xb sihdv f2 ab1v2+:k+i*h6iethe 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 sdx6hs4 e9)of7j d0 ilrku3;rh onar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum de30 r) ;6j4 kdh7ixfsh orl9edupth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves a6od ins4wean 9;x/c n9tp- v6wre 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 consists ;sb5xgk;p( mk; 7qbpzof many plastic pipes of various lengths, which arks7(zb;kp;p;gm q 5xb e 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 mak f*r8y gdc*.ikes a sound close to the threshold of human hearing (0 dB). *r 8* fgc.ikydWhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dBi2w x,ga ;wo2z sound and an 87-dB sound are heard simultaneoxwa ;goz2w, 2iusly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. fw46vcq nkp 1k5om3-g What is the acoustic power output (W) of the speaker, assumi65pw fg-nqo4 c3k1mvk ng it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpu1, cl ss+: 9wjalrq,zot(mog+t at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wattw1+lom ,tgoa9 lzjcs( qs+:r ,s at 15 kHz?    dB

  Workers around jet aircraft tqdb43s.w7 jl cypically 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 average human ear has an effective radius of 2.0 cm. What would be the power intelq 3wd.bc4sj7rcepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, w oam1r ; au8gannuw. wlx8s3 9)p0z8r$\beta$ 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 ku6z yn. u (7ldcph)(m0pqy,fis 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 c8z i 0k 6 jt1xi+y,dz93wtlpdkm long between fixed points with a fundamental frequency t0 dkltpdiy9 z8j61xi wkz +,3of 440 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 above a vertical ope,;4lh * sa bldviz/ (mggcnv07oi*m0e oncw8/n tube filled with water (Fig. 12–35). The water level is allowed to drs4i0,/zdi*b o0/na(;lv 8o mwen*gl chgcv7 mop 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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of m vm-e xh67de1g9 je+bhass 2.10 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 fundamenebmhhex g16 j+ -e9d7vtal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full looa a7(a zq svg4h26k(bbp ($\frac{1}{2}\lambda$) 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 coming9xt*u1bxg.uvczj -zv2 9d 9hc from two sources. The sound is loudest at points equidistant 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 sourcj1 vv x9 2zg*d9.uzhtbcu c9-xe than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-H4 b voe./c4.dj i h9fkpj7qmz*z whistles. One train is stationary. The conductor on the stationary train hears a 3.0-m7pe4*hjfb . .j/kz 94qicv doHz 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 538 Hz.ohmt x5y ao.z1tdka ;qh t609qwy: 9r. After it passes you, its frequencyw mt t qh.o9dt9k:016yyoar ;hqz5.x a 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 listening to the ok7q,z*mu 1uv4giypf swe xc723m7 y6 difference in pitch of the engine noise between approaching and fyx73e,uo4y2 pwu7 z7msqi gvkm6 *1creceding 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 a beat frequency ofbk ecv.c+;c.ir gbcx sr/.(n 67-.p9iptj ait 11 Hz. The shorter one is 2.40 m long.r igpcai..ixj st. k6btbcc9rv.;ne+pc (- /7 How long is the other?    m

Two loudspeakers are at opposip5o +aga fx qc+ae. jw6.,/i 7e8nvicite ends of 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 iec8xgcqo,aai.v5+/p jni +.waf6e 7 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 bl- .jzs88 r0i(dwlj pywood flow 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 the flow and reflected from the red blood cells? Assume that the waves travel with a speed of i(lywjd pws08z-.8rj$1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mgm9(c xtvc,05h z/lvw oth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Whamcz5 xc0,hw/vtvlg( 9t 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 ahi+yy.swc8tow8ct9 now;y f i :(s:w3 s it approaches a moth. The pulses are approximately 70.0 ms apart, and e:iy 8f9 y i.+snwwyt ;3twc8o :(hcwsoach 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 sg5bao2 g hw0 l6lg(mb5end signals from one Alpine village to another. Since lower frequency sounds are less susceptibw(2mb65 gahglb 0 5glole 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 open tube.

  Room acoustics for stereo listening can be compromised by the presjum ye4 u++w(sence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long,(m4ue wjs+yu+ 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,” involves a long, sle/7u g(1wekn(bg 9uovbnder aluminum rod held in the hand near the rod’s midpoint. The rod i 9(71ugunbk/og(w b evs 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 g*-/ v:clfkop ear at a frequency of about- kcg*/fo:lpv 1000 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 Mach 2.0. An obs)m s ;- nhmh+w;pt7vcberver on the ground hears the sonic boom 1.5 min after the plane passes directwpsn c v+ mh7);mb;-htly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1*q 7n cho;f8klrg 4pt85 $^{\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