What is the evidence that sound trav+fla0p0s3 fohwrwfx1 eol+55els as a wave?

What is the evidence that sound is 87 .kq o 1qopl0zxgt;awadl50a form of energy?

Children sometimes play with a homemade “teleom91ltcr dz : w;wb8 na t(nxqbl6:4o7phone” by attaching a string to the bottoms of two paper cups. When the string is nqaltlbbwodw(76o:9 x4 n mztrc1;:8 stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect t,dj :2ug)v,3)nazuhtyjg e1che frequency or wavelengtv3u:2,tncjhj a ), )dgezu1gyh to change?

What evidence can you give that the sps6/as kye1ues,vcz8vl0 a1)s eed of sound in air does not depend significantly on freqaz0 6s )e81s ssavv ,ul/1kyecuency?

The voice of a person who has inhaled helium sounds very high-pitched 4pzhcg --i0kf. Why?

How will the air temperature i7si2s g p3a;(j hehx(aw) jny6n a room affect the pitch of organ pipes?

Explain how a tube might be used as a fis/u quazpz* ,c j- 7ums(,imo+lter to reduce the amplitude of sounds in various frequ s-/zas (+ 7uuzmmcq*jip,,ouency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together a(zuj2:* yqlrm z .-tzks you move up the fingerboard tk2zj (z r-tu *:mzlyq.oward the bridge?

A noisy truck approaches you from behind a building. Initii pc,um+hgp haof 5xte,y. 3nm51a ;x8ally you hear it but cannot see it. When it emh8a aphn5u3 im1,x+;p5y x. etgofmc ,erges and 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 due *q2c:sve1n( ltm 6 8zficm0leto “interference in space,” whereas beats can be said to bece2se*f 0v1ln l(8z: cimt6qm due to “interference in time.” Explain.

In Fig. 12–16, if the fre 6g4u2-lbxjy 7rtomn 8quency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) u y 42n7r-tmj8bl6x ogmove farther apart or closer together?

Traditional methods of protecting the hearing of perufqo)(laq(k4hdgu2 - aue8u 6 5;p kzople 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 feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels dz a(kuqhpe4-)f8 65oag2r( uqlk; uu reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought o v(dy+iwz,lsl,cj ts2 7*xfy . ish-o(f as a superposti( hfxl, (i-ojy7ss. +, *vz2y sdwlcition 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.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same jnp oxx2/- o2jdirection, with /xnx o2-pojj2the same velocity? Explain.

If a wind is blowing, will this alter the frequency of t;: juh1 nely4wb;r2vh1hk- azhe sound heard by a person at knlj4 h-hzb ruy1awh1;ve2:; rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moni2os9jof:o(ie4oyy 1 ttor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequenooojt f4(sei92y:1o y cy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ecn)sef; /,h.lq 3 rcby 0zbnf(9ftzf 7mho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake.lc)srfeb7;hq 9/mn.f f (by z0,nz t3f $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belowuxd5 7 b/g3vj4fhj(ai7s d(kw the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s latvs j g(5w3jf 7hd4x 7/(iubakder. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavel ))nrp m30 1tpp k5e5ynr3us76xv n9x)sqcg jrengths 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 is drifting just abovwqisq*dkt w5j:xra 57d6 y,u0e a school of tuna on a foggy day. Without warning, an engine backfire occuq7s* d5qwy 5ka:xuw0trdj6 i,rs 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 x de*szcdum))rojc)d. 93n 8/dr* o bythe )d93 rj o*zcdnmsr8d)*ubyd)c.eo/x water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike thvw8sz3i * hn4iq2dc7ee concrete pavement. A moment l4*zqw2 cnvi d8h ei7s3ater two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over yg buwg*.-j,p/hgcn+ one mile of distance by the “5-second rule” for estimating the distance from a lightning strike ifp + gwnc.b*-hyj, u/gg the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at t i 3p) jvgyu,ne:a.lx9he pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whyl 6lwgfy) 5q5ose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired si; 9p7 wi0pcvawmultaneously at a cerpc7 ;p9vaww0 itain place, 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 widl1 , w i( f ,1rmn4km;uepem,43rfcjfth 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 1ifn f(wefmrlr4 cdjpku1;,m43 ,m e,intensities, not dB’s.]    dB

  A cassette player is said to have a signa8q5z5+2mfci d* 7igrynfdu q .l-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eay d5z qn.7fu8f5dgci qm r+*i2ch device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakinzkj6vjq8 ::ri wkob5 m-n4w4 dodd7x.g in normal conversation. Use Table 12–2. Assume the sound spreads. wkdz 4:k8r5d 4d wq6x: imv7n-ojbjo 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 whosx. cuy, ni)mq c 6ql)ha4:1aese 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 yrdu a4l8j7d.fr ib(7B is 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 turn to8 rd4jflbyu.i 7r( a7d 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 inn;y7r bh96nyv3 (to4ip,mpbu front of a loudspeaker on the staimyu npb67; onvhb(43 yp,r9tge.
(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 differg/ (v- 9sgt q9bicsad1ence in sound level of 2.0 dB. What is the ratio ofg 9qd9 istgbs(/1v a-c 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 tripledm e2 oo;:6pfqp, (a) by what factor will the intensity inc6e p;2mpo: qforease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fdoqcr;x7:l:ro/x 281r jpf q.qxv i+9 cqvc:grequency of the other. What is the ratio of their intens2q;8qj/:x:rv.fqc d qgoxv+r1 lc7cirxpo:9 ities?   

  What would be the sound level (in dB) of a sound wave in aox1 +xnu* 8n+rexv/zb ir that corresponds to a displacemezrb*n+18+ unx x /xovent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have o(mfqv ,l fa5-ol8b3uwhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See ,m-f v(qlo5b 8al3fou Fig. 12–6.)    dB

What are the lowest and hig2:u;1 jm0egegn5u juwblp 6(m hest frequencies that an ear can detect when the sound 2g5 pe0nmu6:u 1(uj jlm;bgwelevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soun9xw8: t9vvnh pd levels. What is the ratio of highes t 9:pn98vxvwht to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of u f l4xkm d8fdq2:ik9j 8lfnk2pa :r13440 Hz. The length of the vibrdkdf:r l4 anfu kl1x8 i89mjp3f22qk: ating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three /i ;nhj4koxuq*e d.p 0audible overtx*4j 0.uki p/h;eqnd oones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you eojs94/ eq qbu1w;dj; oz)n8 waxpect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assum)d;qw4a/zu1;o en9s 8 ob jqjwed 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-tubec,hlbmi2v +*y (1nbjt pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ra b +vcylb 2(hij1m*,ntnge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string fc y 40gw;p9kf)f qx+96 iujephas a frequency of 540 Hz as its third harmonic. What will be 9 j0wy k+fe)pc9q x4ugpiff6;its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.a vnw65*tuv3yr866sx5x l s ua73 m long and is tuned to play E above middle C (u tawy 8l5n63*5sx uvv6 xars6330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middl4n am5p9a q*pie C (262 Hz) when the temp*q9 i man5a4pperature 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 20avpog-ne ,elap iua701d-7u6 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiect:swjzp/.c +j e of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle jjz/ ptwc +:s.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 264ai dk v l hj;yx(sn+t0((4jz4c Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is0tzc ;4 j is(xhnj v+k(4yadl( 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 52yac2-nzf l wends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What i-f2ycl5az2 wn s
(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 w x3bo,l( lwk5$^{\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 wi 49lv47fb x+/i doyjvrthin the audible range for a 2.14-m-long organ pibl+y7 4 xfvj49o/divr pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm loqsm hf3+p lvhlf7*+uo3 (z(c xng. It is open to the outside and is closed at the other end o7 h3 uspl+lzx m(3cf+(q v*hfby 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 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 trying8y4 mv axti1yuc snm276pi93 q to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ± s u67y8 ivc3npq2 ymmx4a1i9 t   Hz

  What is the beat frequency if middle C d:*qe 9e+.lx x,ys zmns0dz nug9*9 ph(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 opeo hvo nhf,omx.55jnamo)d jbz9u -* 27rates at 23.5 kHz, while another (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 played simultaneously, estimate the operating frequency of brandb5o-7x5ho,hvjmd)a 2*f o nnjz9m o .u X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuningzcc(*g2kl/6 vx-txksu h7(nf fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the str 6 n(-f*g uv(t xc/7lxshkck2zing? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The :6b;e -wkgupptension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eqkpe ;p :g6ubw-. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play m)w *6; ()kedmudb jy.qrr frgtcl37 *niddle C (262 yw tr*cdl(bg*k;f rqmurd.7je) )n3 6 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forkbj jp50r0+ts uy r,2rgs, 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 and C are sounded 0+rbr gjyujpr 2, t5s0together, 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. A person stands 3.00 x/ojp 9kwgrnq8rjiaisg37fq/bmr(2 9a):9 t m from one speaker and 3.f /9 n2g 8pgaabr:qjj) 7r r3ixki/9qm (t9sow50 m 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 s4a/qrv mtc0g5 upposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a a v054r/tmcqg) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air.d:o;4ew)gwl .s/d ep 0d9zi gzmuk76t wcr3s . How many beats per second will be heard? s g)u: /9z s7p;gd d0w.34weem6 .twkol dricz(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ce7-/iwvo cu g3ertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a spe- guci w/o37veed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detecv x nu4.fzwm.n5,bgy 1 xgp(g2t if a fire engine whose siren emits at 1550 Hz moves at a speed 2g gv(yp n.5g,4fbu. xnxmw1z of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz so wadj7x1s4- giqu zck,bf9d(el;z6 )gurce is moving toward you at 15 m/s versus you mov ; db79azk z-l(qfg)e,w6dcxsj1gu 4 iing 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 equipped with the same sin stet;i;a9ru,2k xt 4rgle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest he;42e;, sia 9krrt uttxars 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 somp,ioq;/m)a*+ aripqn v 6z;w und waves at 50.0 kHz and receives them returned from an object moving directly awayqqirn *wpm6,av;; zoa)m/i+ p from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emit*u7 :/s .8r4vwnd- jb wkujbfeyorh+:s an ultrasonic sound wave with frequency 30.0 kHz. What f8j+s/4wue nbr7.*bhy k: w- fo: jvdrurequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expe6rm /bl1tqn7 triments, 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 t61ml nb ttq/r7rain car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ucc)dsxd7 ddbj ze(8rd 29q)w7xs8 u2xltrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1duxrs d x)z7w7q82j(dcde9bs2 8 cd)x540 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 us-7uw6 ywax:fn1ee x2ay1 yx1bing 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 sound of frequency 5 g e/dwc7a6 t:b/pw5ab70 Hz. When the wind velocity is 12 m/s from the north, what frb7/cbeta wdag6p 5: w/equency 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 mov0s na;3vtppf boi; o,;ing 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 spee+.;x-sa2cb3m-l 4p fwpaf ah 73 )1icnmkakopd of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’occl 3m k -h3afik1pspna+aaw )m b.2-;p4x7fs 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 spx3w99w*yp0yrte ug i8a( uhk. eed of sound is ewuuy xrah(3tgpwy90 8 9ki.*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:oxqd w+a ak *+o9qb9y. Determine the shock wave angle it pro:a9y obk9+wd aqx+*q oduces
(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 ,r( t/jt5 y f2vj n s/qb4dsbt/ d*6vfdo8-lhb$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km asw cs:4in:t2t t zl4zam7wu1 1bove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the planwtnmaz1 47c i:usw12t:sl tz4e 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 sound ni,d1mw )zpjw2 /pyen7 s(*ow pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desp()dy /1inow*njs mz72 w,ewpigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there inb-h ,me+6gp b9+ipo to the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manyu x6 8m+w-q++w+cn3toe rvige plastic pipes of various lengths, which are open on both ends.+mworc +i+et ux3n gw8-6+v qe
(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 e--gs ko u;:4* 5dmmtsu+8ddhbt1vurhold of human hearing (0 dB). What will bhb*5-;tr k4vdsdd+8-g m uoem1 : usute the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 85t w 7lmpes;ia;v yb)(7-dB sound are heard simultaneouslyli ptmebya5) ;vs( w;7?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.;w r/4:gg kfhk What is the acoustic power output (W) og;4h/k: wg frkf the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is ) 8 rx9xmiurww3iq2wu2 cv :8/zh3jgqrated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. x:w8 839c/gmq2uw 3iizux2wvj )qhrr What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft 5n)sf2 ll2wkiiu(t* c typically 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 intercepted by an unprotectedcs5ikf u2t n)2*(will ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communica.sl;c -vdh*dg m2 smp5tions 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 5mrr0xfyn9u huse0i0d)c ;:b 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 h6i4d1h *mfcr64 ym/*c yhte,xoly 1fcm long between fixed points with a fundamental frequency of 440 Hz and a mass pr6 ytcd ilm4 6h41yhcof** /mey1h xf,er 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 abovrpyiqb 9 9pda(hz+0w:e a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slo :09+drpbpq wyh(9zai wly. 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 neardspo h*jq5h5) 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 )oj hqh5 sd5p*fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as o2e4:fz*ljpn j9ls qht:uzg7e0 dq*2une 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 r3h4lx) 86.ewc- qetyox6pl qm ange coming 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 source than the other. What is the l-)xeco em 3 668xqqyh l4ptw.frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationarfje. i8h mas r9f:b7shfvp9,7 y. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is a7i 8,fs rvs fef:h.p9j7bm9hthe speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afterqvrb+c9iu/qg o m 1fe1wy-f44 it passes youq4/emc91ryf qw u iv4of+ gb1-, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the4 a :1d,;bq f+ywolc6bwhl ; qt6.5xkb mr)czw speed of cars just by listening to the difference adyb xmr 1fhlc4.wl6tk5+)b;wc:z, q;6qowbin pitch of the engine noise between approaching and receding 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 of 11 Hz. The ui br2xx:)yp 1-vj og.shorter one is 2.40 m long. How long is th).iuv-xjpor x y1bg2 :e other?    m

Two loudspeakers are at opposite en btb(c-oy)m; hg4kzrg47m 2r fds 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 t 4 -hrg2 g4(bm )f7botyrckmz;he observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blor8olub ayc- .8od 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 speed8c.ral-u ob 8y of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 ol(j012l,zp gqu -hh bm/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 dl-u2hz 1jl(0 hpg bqo,etected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high 0;hev w8 eksjh+ .w-fyfrequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms ap+;0w.e k8vhshy - efjwart, 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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from oneq ta30ng1ydgbb:)z c7 Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is 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.) cyb1z 3:bd g)ant7 0gqModel as an open tube.

  Room acoustics for stereo listening can be compromised by the pry.-wa: p3m/*ldc0f dys bte* mesence of standing waves, which can cause acoustic “dead spotsfedpys c am 3 /ylb*.*:0mwdt-” 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 “sing ie jcv:iy:+n7ing rods,” involves a long, slender aluminum rod held in the hand near :yjv :iicn7e +the rod’s midpoint. The rod is 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 jj6i kwri8:.z the human ear at a frequency of about 100j:r kj8.6iwz i0 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 2dj.6eu : ,s3y)mhsjqj .0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitudeujyq3d:.e h6s jsj,m)?    $ \times10^{4 }$ m

  The wake of a speedboat ik;6 gw q2brfuu7b,+zgs 15 $^{\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