What is the evidence that sound tra)fjepxfnwt :rc 9*1 0bvels as a wave?

What is the evidence that sound is a form of energy?jtcsox p(t1 ,,pbh (m u+z1)mzi26smj

Children sometimes play with a homemade “telephone” by attachn2 u4 jt60u/jxbl vxa2ing a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, thu6a0 bxj4n/vl2u2tj xe 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 frequenc wegbziu5,6 3fy or wavelength3uizg ,5fwe6b to change?

What evidence can you give that the speed of sound in air d:74kp * p mk*q+v4ha;cugcrmc oes not depend significantly on freq m au*pk4pc7c+rqm*hk:gv4c; uency?

The voice of a person who has inhaygmv v3x6 ,tr;led helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of ob7s1pyo8-gpfye s;.x pj)sc*0:mmz drgan pipes?

Explain how a tube might be used as a filter to reduce the amplitude of07ttcwh()i rqj 8)it i sounds in various frequency ranges. (An example is a car wt 0hti )8qi(t) rcj7imuffler.)

Why are the frets on a guitar (Fig. ni*pz09 7fbvo12–30) spaced closer together as you move up bzop i7f v90*nthe fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially yy zdfxbjw d+3hepgx.3 n71.-w ou hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear morxed jy hwbxpgd3f+w.z3.n1 7- e of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can bttednb do9 egk5b+*+ b7 2lt*ae said to be due to “interference in space,” whereas beats can be said to be due to “interference in time.”d tl2d*bk+*7ntt beba5e o9g + Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouldh7zp qmxwo g*d.b +dxa( 19jer-84 utt the points D and C (where destructive and constructive interference occur) movodt4-+ 1whr7dj.9egq8pzxmxub (ta*e farther apart or closer together?

Traditional methods of protecting the hearing of7*(y3udhj8p sjasx3 r 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 noise. Instead, a device is used which detects the noise, inverts it electronically, then feedsh *a3dsu83srjjxy7p ( 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 can be thoutl,uu5mw.*lvf2yws 3a+(gh* cep4feght 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), 2+e(up lyfws,t4mf*a vgle5uwc3h .*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 direction,:xz+ y:vod yg. with the sxvyzydo:+ g.: ame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heao)g9*lpijluqc 57b no61ijt mr28xk *rd by a person at rest with resp76igln u2i1 ooq jxtrk)bp 9j*c8m5*lect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. Abv8e)r 8r ijbam4v1)9 .myrlc monitor is blowing a whistle in front ofi eb8ma 1vbjr) r9.r8l4vmc)y 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 shoujfy)g k 41u/mmt reflected by a cliff at the far end of the lake. She hears the echo 2.0y) j4/fkmg1um s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hegr nkj p:4:p2e 83cwoo jkw2r(ars 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 nn:pwe(r4 o8cok w2 :2j3jrpg kot vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in oh)+ba,jhx s5air 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 jtc6e5)6b; ir1gkc tsri s6at 9ust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heari )t6ssic5brrkce1t; 96a 6gtd (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frorx easj mh;t4vo;4 :-fm the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cl-tef: om sx4r4h;;jvaiff?    m

  A person, with his ear to the ground, sees a huge stone strike the conco1bjkr wsx(an9:xn ri5p9. 8hrete 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 1.1 :1jrw.as k89 h o9(bpinx5nrxs apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over p.ka1 ee l (+y*vlydu mpae ;)g)flrx6rv6v(.one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if t yl(;mv6lyv .d + (arpv*lx1re)a pe6k)f ueg.he temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain leveljb --p3v ad fdq5u,bk. 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 4 g1we8j86oxvwvht l/lyx m76of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level on whnd*.,*akhn .p ru9zwn12yf 95 dB when fired simultaneously at a certain place, wnh.,. uhrn92 kw*1ywa p* nzdnhat 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 four equally noc ;3irm11c t n4kq8jqzisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the cr mq;8 kc1zc1jnq43it aptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is (t9 -sn*jig gisaid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of inte9gj* ins-(tignsities 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 07i f kavuqg;6tj(j8 nperson speaking in normal conversa(a; vgf8 tku0jni q7j6tion. 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 eardrum whqrebbu+uu -sd 4(4 exy5c2am(+hgvn ,ose 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 atjlghou-,c,cphk)pr 64t m::k 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 point 3.5 m from a louds 6jcr,4mlk chp:op, gk):ht-upeaker 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 g62. d7lpc 7en2r 3wj+tdwylyloudspeaker on the sgle7wlw j6.dyc rdpnty+ 23 27tage.
(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,mj./ mb1 gtuw:)lz hy level of 2.0 dB. What is the ratio of thw:jm,.l1 h/zmbut y)ge amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wha07 iexeaolcr65 g; ,art factor will the intensity increase?60or5x g,recaa7;lie Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, butextmmhws u*2*2l t.:oimw38s ej :fkrs 7x4:h one has twice the frequency of: mxs e*j4h w7:2f o2sm3e8hi:k. usx*rtlmtw the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds to/5c(y :xuxy o6c uiu(x2t.kb o a displacement amplitude of vibratoy(562cuuktu xx(:boi./yx cing air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud tukfv3+j0j0(t: q+w0 pkyxa i as a 100-Hz tone that has a 50-dB soun0ja jwy(ku+qp+ftk:x3i 00 tv d level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencq tm3 d )jay+sg+ij-i.ies that an ear can detect when the sound level iyj-it .dj+ +mi3g saq)s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whatup. bz5+pnsm l. 7:xdk is the ratio of highest to lowest intensity at u mxlnzp:bd.p s+k.75
(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 fre(q) vojgy:y1nquency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the s1nyj(q g )v:yotring be placed?    N

  An organ pipe is 112 cm long. What are the fuw0 xr4;xqg9jcbw +p -0:ivbfn ndamental and first three audible overtones if i4 p;+09-cwx qjg fbxrvw:bn0 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 would8*d6o)shvje-y z h x-f you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if youjy)- xhh-ov zdes8f*6 assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the rang:02 vvlucrm7 vt 9zs/p+x h-pte of human hearing (20 Hz tvzl0 +vh/ x79t:ptvc p2s-m ruo 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 frequency of 540 Hz as its third hg pifn:a .cwb11t7q1iarmonic. What will be its fn11.1tpf7ci :gw a ibqundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lqw(2zb35sfc2x7 qd zjong and is tuned to play E above middle C (330 w(3jzbqfqcz dx5s 227Hz).
(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 ju6+oftm ;pz+cct00i pipe that emits middle C (262 Hz) when the temperature is 21 cmt+pfzi+6j oc0;ut 0 $^{\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 h:no .z.u ye-yj2m f+rat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ofz4v* mg r9 nytc3+ oa61lnx,il the flute in Example 12–10 should the hole be that must be uncovered to play D above middnal myi ztn1l9c63or g,*v+x4le 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 Hz, but nof qb txw3aq :5s*o*9 i+xb7leot at any other frequencies in between. (a) Show why this is an *fbobl+ wq5 xe st3x*97o:a iqopen 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 succrq* ihn5p oq56essive harmonics of frequencies 275 Hz and5i* q5r qn6poh 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 6)6zxexsa stfwwh9),d,(zpk9gup i s7 la/a. $^{\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 with 4izw6qqc( a9ol4e, njin the audible range for a 2.14-m-long organ ic, jq49nza 4l6qwoe (pipe 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 opevh-ks3ku 6xhzc q t24zo8.-dxn 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. oqx z2khh4z8 sk3v-.xtud6c- 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 wh5gub 9 gx ;;kdg/wrvw4l5 wz:hen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the od gh;l5zgwwwk xu45 9g:v;rb/ther string? ±    Hz

  What is the beat frequency if middle C (1zxq+-: w) qejsp 8+rqjtgv3f262 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 :ojl)l 5/7lxzhht5( ih iik47hjfx0mkHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard byh/h7ihixjt m7l4ilx:k hz()55o0fj l 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 whm 9guu7kx9e 9len sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your re7e9x99km ul ugasoning.    Hz

  Two violin strings are tuned to the same frequency,hqo,pt,g wsfz.0*v1,vw i g)i 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? zf q*,v1 ),0,vwtigg hpi.wso[Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes: elg)6 :6r fxtp(lprk each try to play middle C (262 Hz), but one is at 5.0°C and thet(6)le:x: rfkrpg6 p l other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and 9;uhag0mh*x0hhz7 xfC. Fork B has a frequency of 441 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.xaz ghhxmf0u9;h 7*0h 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.x f26y9mtb- 5k x,xq8 ybyc;ax(u 2lkb80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other. x 96qb ( yf akk2;b-b2mx5c,tu8xxlyy
(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 u v /)73ky3mjwrs w9:fj )roghpiano tuner hears three beats every 2.0 s when they are played together. (a) If o/s9ogm)ur whry7 j j: 3vfw3k)ne 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 waveleng rkdd2(p q-y7uths 2.64 m and 2.76 m in air. How many beats per second will be heard? -d dqup7(2yrk(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1oyt2r 2lprzxk e+12wt inx1 (vv +89, em+vyye550 Hz when at rest. What frequen et2k x+z+evynpw9,+ 1 vy22xmyv (1ilrr oet8cy do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whosak3 h:b;/r dfie siren emits at 1550 Hz d/3h a f:ibrk;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 20y .npkl;evqdg( o-qc. y g;:)a00-Hz source is moving toward you at 15 m;ecdg ynp(go yvaq q;:. .-l)k/s versus you moving toward 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 1djprr.u7h n*a.v-ew equipped 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? Assume T = 2h7-1 adr .*nr .pjuvwe0 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and r5l ). :emv.)k/i/rbbc ebv yxqeceives them returned from an object moving /q .ev:lxr.c) i/) b vk5mbyebdirectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a kl6m2( pv r6tzo*-qlew+8wb nspeed 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 thezl686ob(qr+plwm * 2e ntk-v w reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exoyn +s* ei yn8,np2j5fperiments, 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 rest in the railway station. What beat frequency was heard if the train car approached the statio pi * ny+y825nfs,jneon at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves3 3l8o6e5* n:4v he 5d5 yfkjcp qdt8uagzf5sb to measure blood-flow speeds. Suppose the device e8bfdk3guh * nl855s e56tde3 y5opv 4: fzcjqamits 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 from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency 1d,h0a y yr8d:j(tiaf $2.25 \times10^{ 6}$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 ofoio rvh,+hefpnzp96pg 8p w5h5 ,1:ff frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who ,w,58+:ppnfhf9g6iepo5v pfh ho 1r zare 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 qnj*x f/) hap2its 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) Wha onit 94+0vdieo gd)d*t is the angle the shock wave makes d 9+oi ) vdi0egd4tn*owith the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed omqw(66dfa*xa ck za*xc12p- ef sound is only abou-f pwq*2aex mk*c6z 6 ax1(acdt 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 k4u gwbz6 vyn;f.(wq0wave angle it produw6nu (.zfgwy;40vb qkces
(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 /h0qiz1+qpun $/theta$ 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 exac+b jcps xz/679pmk v-t6yv1pxtly 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 distavv czx+ 1-j/x6kmb6 79ypp pstnce 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 sou1;7+0lf20e1vg kzw cmjcbwdwnd pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in freshcl gwvw k fwzeb;7d11+m0c0j 2 water)?    s

  Approximately how many gqzs7j4m4-w gj8 mjn1octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display call3ck/xiinxn+ p 5) ,wzoed a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on icpx+o kzxwnn5) i,/3 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 soun;a/ lhts sqk(*d close to the threshold of human hearing ssh(t a;lq*/k (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sou7(/ldva0)3j auvrtog xox:;qnd and an 87-dB sound are heard simultaneouslyu(qg:vax)vj307/ atxrol o ;d?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105nt(inna75ro6/adly(s cp *5m;bp e/d dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in apoytsn7(6( pea a *5;l5rcnndm/ idb/ ll directions?    W

  A stereo amplifier is rated atkj.weg q3t/4- c btx-s 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is thj x3t .-bqgw/stkec-4 e power output in watts at 15 kHz?    dB

  Workers around jet aircraft typic7*izv9 d yh6wnally 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 e7nhvd* yw6 z9iar 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 )pg,t6rd0e mz systems, 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 viol8lz zi-vsl d,henzph,58f:jr7 s 0 /mdin 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;bz ,gcw(miw( 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass iw (c zg,m(b;wper 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 open tube filled qor8cp/ ec11qwith water (Fig. 12–35). Theo c11 cqq/8pre 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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a:d )*a6v *fu*u9xzgt0b)4v ra wfnqc n tube that is open at one end and also 75 cm lofvc)tv 4f*6)wn 9a u:zbn *q0dr*uaxgng. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed toj)pe42 * eriym resonate 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 pure tone in the 500–1000-Hz range coming fr0j7h0d7 3mth kd hv2ytom two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves abou70k7hh jhtvt2d y3d0mt 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. O9wrfxfo73h y3 dav (y1yse 8y.ne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the sp 8w9 fo.y7 e31ra3(yysyh fxdveed of the moving train?   m/s

  The frequency of a steam train whistle as it approahkcvnzk:8vej- k61wn gn7 a0:ches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assu-k:kac: jknhvg07nz6 ne1 v w8me constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by myw*onp0yx s8t( 3sw3 listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose xy 3wn0op3m 8wss*yt (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 fre xwr;-7lbqylwd n.. r8dk2l5dquency of 11 Hz. The shorter one is 2.40 m long.dnyb .ll-dw;l . rxd5krw7 8q2 How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s ms/h-5w+2mc wcl* ioutationary 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 the car, (b) he is between the speakers, at B, +w uow/ccl i-h*mms 52and (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 p;)w0lnfhs 1em/s what beat frequency would you expect if w)psh;0 e1fnl 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 $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/qyv *ha6lzv :)s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat afa)z*hq lvy: v6ter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moith d mq;)+zb* d2x7liq;ce :ith. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away caq ldic;7tx2: bmi*h +ie);z qdn 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 Alpine2gfi1cb rl;c- l2 5.tahlaky),h2j bq 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.hy2cga- h lb2 l)atbi51 kj,c2qlrf; 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 stereomaj3 oeabg3sr1l 0. 4v listening can be compromised by the presence of standing waves, which can cause aco.3j4v3gmeo a 1bsalr 0ustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called-(h mpl1 k:euogmmaq4u m03 agaf.g)* “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with t pa: oke1(0 3qal m)mgu4*u. maghg-mfhe 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 the3. gar +qojt6rhwbgv8tc :2e, threshold of hearing for the human ear at a frequency of about 100:ob c,t .qvh+36a8et 2 wgrjgr0 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 observer on the ground hears the sonicryizhp 73ec1 * boom 1.5 min after the plane passe3zh1i*ec7 pry s directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15zbg.snb5 f5brfmc6 lxn (- +7t $^{\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