What is the evidence that sound travel 7uxt-cn w -eiytt3;4ls as a wave?

What is the evidence that sod,h ,)m zg,qzvund is a form of energy?

Children sometimes play with a homemade “telephone” jbry+5q5xj.4 l q:mxvz5 ir:nby attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cunj qrxb+5rz5j54yl:m i.xq:v p, 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 frezx 8:ph958equ-pw6ie0vn aay quency or wavelength to changev9 a zphq xue:6ai8w 0np-y8e5?

What evidence can you give that the speed of sound in air does not decnj e 954-dlwf t19h ft6f4qxdpend significantly onjhfx9d e6d19t -clnqw 45t4ff frequency?

The voice of a person who has inhaled helium sounds veryxp*:wia:crg qr 258jv high-pitched. Why?

How will the air temperature in a r dw)o7. lzk,jooom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amz,*n,xqk6d 1 dyg:s elo9ip/ zplitude of sounds in various frequency ranges. 1pdd,lzx* g 9skiz,6y/o n:eq(An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together asltw )-kvhgjp ,z3zy/ i:zq9j .wjx z*, you move up the fingerboard toward the bridjy h )/wkziwt-vgl.z, zz:x,j*qpj93ge?

A noisy truck approaches you from behind a building. Initially whal o9/3vff7 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. Explai v7lfhfaw /3o9n. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference ce.2 uhh/mpgtz( 5hq7in space,” whereas beats can be said to be due to “interference in time.” Explainuzmg(2e7 5h .hqhcp/t.

In Fig. 12–16, if the frequency of the speakers were lowered, woux0 ijsvaek1 ge **a*)jld the points D and C (where destructive and constructive interference occur) move farther apart or closer to1*ejesx gva*j)*i a 0kgether?

Traditional methods of protecting the hearing of people wsz9-y l 71v6;mllwlm nho 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,n-; lwl y l71mvlmzs69 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 can be th-ew + zx(x3,,3cw. sg69lvbxtr hxhmkought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain. zxb .g ,he+ , wtxmvrk sc9-x3(l6wh3x
(12-31)
(12-18)

Is there a Doppler shift if the source and obse5a pgd4v9yrn:rver move in the same direction, with the same velocity? Exp r5dp4y v:9naglain.

If a wind is blowing, wcxb vmm7;r d8pyw0(i ;kk;h) * 8vfsvf,iwk v6ill this alter the frequency of the sound heard by a person at rest with respect x;vimi*,bvf;wd06r k wch;k(8yk87v ) mpsvf to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various posjy,zf77+nw9q dxni3 u6i y;ku itions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on yw79i;ixfq7ndn3y z 6j , uuk+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 o5 ( 6u:z7prj .whs5f 8porswtrf 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 wf:hozs.(78rsujr p5tp5wr6 after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the 7xpt1,s v nnsy-iq3kc0 g.jo)waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How pyco0-qv,t1)sgxn7i s .j n3k 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 209eet0-*f bebce 2wt0t $^{\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 61.hi;rt ije ml iwtt5a2nb;psgo 7;*of tuna on a foggy day. Without warning,os.j;ir5 itttb*w2 ;1ag 6nhl7 i ;emp 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 striking+gh4.ksgx9+u65xnl lhdle* i the wat l6s+lxglk5d.x un 9*ihh+4ge er below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ea kab 0f-lh2s,pos6 ck(r 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 concrete, and they are 1.1 s apart. How far away did the impact occur? l- oc6kss2pa0bk(hf, See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-sej (j:0qx( gg rap3)fmdcond rule” for estimating the distance from a lightning strike if the temperatur3f pm )xrdja(gqj (:g0e is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 12)kfx:oii1 7o x0 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levet+5ch4 xunq0cm 1qov 3l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a 3m 8fc9z7qh azsound level of 95 dB when fired simultaneously at a certain place, what wf9z7c m8a3zqh ill 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 wi tk ii94:bj o1l-hb7wzth four 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 down all but one engine? [Hint: Add intensities, nkz7 ijb4b1:9 liwto-hot dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wher6 61hqz, v)kjifxmxy: ue)2ne m )qgr;eas for a CD player it is 95 dB. What is the ratio mkq 2ev6)gf:j)h)ir y ,6e; xunz1xqmof intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking inb f3z.cp49bxt normal conversation. Use Table 12–2. Assume the sound spreads roughly un.p4b9 cztf3 xbiformly 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 eardr+c3f(e - e32xn4ifto v,buicxp o0o( wum 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 amplifier B iso;sdp/ s cv38j rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in 8vps/ocjd;3s 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 :npm;yk 5odq(in front of a loudspeak(m5po;qy: d kner 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 fcjyx.b 4pue 55y r*47*nsfkw)jm a6ydetect a difference in sound level of 2.0 dB. What is the ra bya4yyxf*e* 7kjup n6.rjf)wcs5m 45tio of the 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 what factor w)gg(qs+ aqg0p: cnlk7c ,2- w9jhob)r1qd kmmill the intensity increase? Increase by a fac okk2grw1+p aqqc mngh ()s,0-) jl: mbq79gdctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal diszxnc5w f0iw 8a5) c0ebplacement amplitudes, but one has twice the frequency of the other. What is the ratiae0)wnw 8z0ibfc55xc o of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thomw )ul+k m5:q x.;ontat corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at ) kqxw: ;omluo+m .t5n300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lu lj8s17 +nardp2t(esli n 0k;oud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)idjluk0p; +a 1sn7r(n2sel t8    dB

What are the lowest and highes0fll*)z7rnyo t frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)nf loz*l07r )y

  Your auditory system can accommodate a huge range ogr7l;snei n ;5g /j1)wie1qu if sound levels. What is the ratio of high lg u jrsn);57 iq1ei;n1iegw/est 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 fundamelnh 3 :qqk-ln)qll/ ujjzsu23v,)ny( ntal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must nqq) nvkn -3l3(uh,sj ju/)lq:2llzythe string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible yi bg 0z bsefln ymi10chs;/.e ,2;wh4overtones iwlhgi1 b/.beh2 efisy;m0;cn4zs, 0yf 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 expki0l 74yqe b(09xkr;h4zcpee u4j+ yc ect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube?(q7 e cb4u yc9jz4+ilp k0e04y ;rxhke    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organjaf8s-4q2z)8htfwd g with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be theq4z8jf ) 2fth8 gswad- 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 a fxw9avy-2ljj13s4 , a(orxq as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its orig xfr3al2o(w-xv1y,aj js4 a 9qinal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above midd qg;v e5c1bb gsgyj72sd-.ot: le C (o2e j-5cs1gy q7 vtb.gd:sg;b330 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 p.4h ,q 95flds.//lv,g cgva:l pebmle ipe that emits middle C (262 Hz) when the ac.d:,.mvsp5b g4l ,fel 9 l/lhg/evq temperature 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 20 db0b6a ot.meu )3rgt ;-sl ck4$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the w 4;0s - qa3h9olmkqbi 7iwqs8flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 29sq 0l hbwi-4o kiqswq397ma8 ;4 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 urt*bcy8 a8uv7y*5mdat 264 Hz, 440 Hz, and 616 Hz, but not at a d *78v yyu*aucbmt85rny other frequencies 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 1.80 m long is open at both e+-cancabraik .2d v 3 2gvdgf+5rcy3*nds. It resonates at two successive harmonici3 fr vncd-ky5vgba*3d.gr22c++ aa cs 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 9i0:5elaafh ld8 kg1da3 dx3f(l-lad $^{\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 forq;j*;hdmqa+u k p.f 6s a 2.14-m-long organ pipe at 20 u; f;qmh6jp.dk +*sqa $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2ip 21dip -18danf2d gl.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 answer to the iln8i df-21d1p 2ai gpdnformation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one)b s4arba:; ym beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in freque ;) bby:4raamsncy is the other string? ±    Hz

  What is the beat frequency if middle C (262)7o+l3fpo ff bhoow..l , js3b 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 kHnsm:(7 ju.b eyz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill wh bm .(uyse7jn:ine 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 soun.dlq6) chjgkmf f2cl 2zf1 16pded 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 ql6cjl1.cghfff6 z2 pk )2dm1your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in ofls*hn.9 saw(ne string is then decreased by 2.0%. wh9 sns*lf.a (What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middleqit(9m7u vvqas1g9- b/yv2aj C (262 Hz), but one is aybsq 7vg1v9(29 aujt/ivm-qa t 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fo uw7t2 duhv*as/9*0v.bwih ew;c fvx0rks, A, B, and C. 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 e*tcw./7ahu d huv fsv9v*2w0 0xb ;iwand C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart , ulm:0a6bq;3r5l 8cfmngu ji. A person stands 3.00 m from one speaker and 3.50 m fra5i bq:u rclu,n3;6jlmf0mg8 om 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 suppmiiq: q:mo :2aosed to 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 frequency of the oqqm:ami:i : 2other ?   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 mb.x 3oye-sv)l 4+2cmyjcv .qz fg0af, and 2.76 m in air. How many beats per second will be heard? (Assume T =,. q)j.-4bv lsoga3ze+ f0 cym2cvxfy 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1cz ,he1s6*p dj550 Hz when at rest. What frequencd*hps6 j ez1,cy 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 detes 5nx)(:uu s .x4 lgl frqc,rk :d3pd/zpa(y2tct if a fire engine whose siren emits at 1550 Hz moves at2ryas t /: szllkd3pudg pqx.c)ruxf5,n:(( 4 a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in b938kyx sb4wms:c9p8 9 z,3n fsgvslmfrequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freqyp:3,3 9snb xcmgs949lkw8 f8mssz bvuencies 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 equip,swtdh; dzf,;,7 co nnped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m;z;, ,dc nod,nwfts7 h/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 r *g( 9ookns5yha29ggkHz and receives them returned from an object moving directly away from it at 25 m/2yo 99ogh(arkg g*ns 5s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flier58k+np ooj -cgx 5aj9s, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectx n gjr5ca-9p8 o+jok5ed wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played 25b fg rajfo7-m3 9yoc;kisgg1b 7e5 e e,rul.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 7b2j 5f7r o5-gkeagey,s u;rfol3 bmgce1.9i the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-f)sx.,ejk o4fhu qy5 2:jdko8llow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in 4:)k yf,luxs5 djeh8oo. kj2q large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ldjt):menq nq),:bh2 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 s3mdo.tbu94lmd j)cd * ound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers ctmo9ld djud b 3).*m4hear 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 mo)z wxw/j me30etw,tga7d+:y gving on land 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) What isisb domyex) l8w.r93; the angle the shock oirlsy d;. xm 3b98e)wwave 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 oy9zitud;5vihb3 k u0:f a planet where the speed of sound is huiid:yb0 ; ztu59vk3 only 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. Determin awzn:+6m*pmc87 ifnle the shock wave angle it producesmc7li* +:n8an6zpwm f
(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 z m1g hc/9y4ne ysylec49 42vg$/theta$ 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 exactjipzc w25 ;0(tomuw2 bly 1.5 km above the ground flying faster than the speecom;2 u(bt2w0zwj5 ipd of sound. By the 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 sonar device that sends 20,000-Hz v76 o)bv-z)mbo c 4o+kzato.g 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 .ogvzt o7 o 4zm 6c-)vb)oakb+is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves arv7)wqfcrxw n fm;7cj.f49puqb3,(jxe there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphp;vi:y(2.l*2armi (w hg yzg oony. It consists of many pyim (. w(gg*a or2hzip;2yl :vlastic pipes of various lengths, which 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 thres(ie23( rb 4it w+ik0*s: 0w goonzblgfhold of human hearing (0 dB). What will be the sound level of0ie oww(*gngs rbb2 i4z 0ik:fo 3+(tl 1000 such mosquitoes?    dB

  What is the resultant sound level when d:de-z 9rqui .2imaa *5soi,ui-kzz,an 82-dB sound and an 87-dB sound are heard simultanedziq d* ie-i.rz m:9 az,52siku- ,aouously?    dB

  The sound level 12.0 m from )36i7d a)t wv uyh +1+jsgspfha loudspeaker, placed in the open, is 105 dB. What is the acoytui1+jpg7 3f6s)ash +wvdh )ustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pcvat,s k 2ryk 7*otkm)q.g34power output drops by 10 dB at 15 kHz. What is the power out).marc,kp y4vs2ot 3* g7kktq put in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protec h o3n/nz v84ascv6wt)bs6;w etive devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, anwheo6ss)z/ 3b;v v6 a48wntc nd that the average 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 communic qsin;x) t:5 ram1mhd5xfk v+,ations 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 violin is tuned to a frenxuwf-;.keux (klo(*v :lyy8quency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points withwh/y1bwnsf-zqsh :ww5j nb9 , f919kw a fundamental frequency of 440 Hz and a mass/9fs n 19ywz,kqb hwsnwh 1:f9w-bw5j 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 veq dkdntuoi *p7e55eog-jvpj0n b51 ) ;rtical 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. W vdq7 o) ; 1*tgo5j e-kudpin5j5epb0nhat is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g c1f1rk; 9tsqnpw9 5jdis 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 resq 19tcr 1psf9djk5wn; onance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate afc ey(lshduz;4 6, 6tq.x as7ys 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 thmb4pw, e3:bw9:cv pjtj 3f:o-0yymcr5eos 1ue 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the f , e :r-u9fys1mt 4pb3cbjc wyomeojv ::0w35prequency 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 whistlesmj;d2vm.cf71rgs j t ;. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other tra .fm2 d;js71mt;rgjcvin approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yoar kjdn41(a+ tu is 538 Hz. After it passes you, its freque4a(1 kjatn +rdncy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can pihie cr+;( ;ql.ma,o estimate 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 clhp.r;ciiea m ;(,oq+ertain 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, soun)r.cj(*-n d.a gxlz ccding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thec c - .lzng.xr)*dcj(a other?    m

Two loudspeakers are at opposite(ppvm *lf /bwq/er3w* 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 listens from the position A, in front of th*pb*/r lf3qe p(/vmww e 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 normall zd bxy:)*6r)erp7ia z- 4bex22a99j v pvohmqy about 0.32 m/s what beat frequency w9-*q2j epv7e 2hbzbxa: xd)rraz4 9p)ymi vo6ould 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 $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth atoec *y-c iv 4bju)bwi p9(-3rx 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.*(i ire9-pux)3c ywj v4 -bobc35 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 approaches a moth. Thfb*dhwm h zu 7ut(x*m5zo;0 *me pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the neth*(;* xumz0uwm ofm7 bz*5dhxt chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send skrw.*b kk tu,6ignals 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 music rk6*uk ,.ktbwal 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 li83h vyg8 +h jbwy 8,i6olg3yvlstening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the loc3b68h vlly +h 8i gv,ogjwyy83ations 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, . jl9iua)g-hvs6hz * hcalled “singing rods,” 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 li.-*h)asijhz 6h lv ug9ttle 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;bw6xy aa/t;s o(ss2u ;*alp g;ra/ wy threshold of hearing for the human ear at a frequency of about 1000 Hz is s *twyalara/; sb ywx;;opg 2(uas6;/ $I_0$ = $1 \times10^{12 } W / m^2$ 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 kbn)x-6a7t2ouj b er:qu2 o;ba 1uqh-erver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude?:n2-q-r;ouqu6)bu ah7otxej 12 babk    $ \times10^{4 }$ m

  The wake of a speedboat is 18.gj 2ruf r)ho5 $^{\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