What is the evidence that sok7 7verl6wbrbrmph10+ s fy ,3und travels as a wave?

What is the evidence that sound is a form of eneo3sq) mr46 evorgy?

Children sometimes pla x6 lma/ . dj g(e5(lc.r+a*abogp5/gqcqx ur4y with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels fro5c6rggab+*..(5 cl / mxdq/(juaxaglqpr e4om one cup to the other.

When a sound wave passes from air into water, do you ex,rqgl-en acfz x8 p6/6oy(a e/pect the frequency or wavelength to change?6xag, (nz6qe /p-ra l/y8fc eo

What evidence can you give that the spe)5 lp kv. 2;d9gsute/ubtissh0jn,;eed of sound in air does not depend significantly on frequenc.j, u l2bt/d 9g ;ssh5ei0ntvpk;e)su y?

The voice of a person who has inhaled helium sounds vert7v)ql .e6 xe:pn1c bry high-pitched. Why?

How will the air tempera 42xsio6 -eqvp8y,hzmuc3 +bwture in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter tczwh 3zpu1q q6y1vw+2 lt:d)fo reduce the amplitude of sounds in various frfq+u)hl2 pv63 zww1 cq:ydt 1zequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1a1:qfsbpwb d *x.jm00n:y2h8/nlcdw sjyf7* 2–30) spaced closer together as you move upsjfw/aj .0 yn 7:c0*:nm8wp1 qdxl b 2b*hysfd the fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it bu h;kq gdo:n)( kpj6n dlr(g7k8t cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear k8( p(on6g)7kg; djhdkq :rnl more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spa yn;l3 dk+2ypmc+ a:6nv7yv a9moolg. ce,” whereas beats can be said to be due to “interference in time.” Exp6m+. ;coy72l+:a a 9o3gnld ym npkvyvlain.

In Fig. 12–16, if the freq uzehcb. 83k8+x a(fpguency of the speakers were lowered, would the points D and C (where destructive and constructive interference occuk3ufbap+zg e x.8(8ch r) move farther apart or closer together?

Traditional methods of protv87dduj. f4 mide0b h.ecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, i f b0ve.jd.muh8d7id4nverts 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. wqlksr7t nn 3 -uea./312–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. Irqntewa/s nluk7-3. 3n 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 ind2u gz 5.i3em)j0tec i the same direction, with the same velocity? Explz)gc0m 3ej.de 52uit iain.

If a wind is blowing, will this alternit3abbp6py4 4 2y8 yt the frequency of the sound heard by a person at rest with resp24 tai6t pp8nyby43by ect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions p:ug1k;0m ojmd:h(iqof a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A th mq:uhp(k0;mdo1: jgirough 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 eiymau8o2p axv .-qx 85. x.stucho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aftexaat - su8.ovx.qipu2xy85 . mr shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sided4. nzp)vg- x6+vkzsj of his ship just below the waterline. He hears the echo of the sound reflected fromkg4zz6v) jx snp.+vd - 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 not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 6foqbiz*qx)5u /j j(m20 $^{\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 of tuna on a foggy da)j4-bqu4gx qtq. a( ery. Without warning, 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 fishaq eg4jr )u.4b-qx(tq,    s (b) by the fishermen?    s

  A stone is dropped from thkdx(58rz 9jn ge top of a cliff. The splash it makes when striking the water belo(x8z n 9jrdgk5w is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the vw9.tulh8p3x9s visfy ,: z2 yground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travelslsv9styx,p. y8 fzh92iv:w3 u 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 one mile of distance by the “5-second rulgc z6ft/1rf1+r k .file” for estimating the distance from a lightning strike if the temperature is (a) 30 t1 fk61zcf/rigrl.+f $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain m. ebiu3s*)vybk7(uw level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose iv: e0t wqy)-jdntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce y:xcy )mupc;kpu - roh.2sd5/a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hintu 2ykrd c.5p-cpm:sxoy)uh/; : Add intensities, not dB’s.]    dB

  A person standing a certaini ur zs6+1ojn13dyzav o95*fj distance from an airplane with 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 y+rsa9n*zo5i6 fduv1j 1j3o zdown all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas fono-3+fddwx + f/b 0oihr a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devic-+ bfn /x03iwh fod+ode? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of so c:r8 .pm5bhdu h- mewidh5/1hkt;f.m und from a person speaking in normal conversation. Use Table 12–2. Assume t1mmb5hkhm8dtecd.up i5 /; h:w-.hrfhe 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 strikr+pu7lpu o+,d es an eardrum 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 modestybqd131 ne .p(t bsbp- tq1yi* amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.qybt.s1 31id1*e - q nt(pbpby5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of a 3wd s)fbg vql.062ikjloudspeaker on the stage.jd6kw )i f0bq 3.2gvsl
(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 diffe(f -k1(xy7o 0wezzxzrrence in sound level of 2.0 dB. What is the ratio of the ampli(0r1-zw(fyxz7xek oztudes 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 will the intensiha4wl30 isz: cmmoqm6t(r2c ( jg k09stm (0ilajrs 3(zst4 0ckc2ogqhm 9m6w: y increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal disp; u4gvji p kyeo-bi8s82 z0zw;lacement amplitudes, but one has twice the frequency of the other. g0uz eb;vj42w-zy ko;i8 is8pWhat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air t fa( 8fb(e+p6qe.ydl qg pu8c*hat corresponds to a displacement amplitude of vibrating air+(y.(pa68*qe8 lgce udffp q b molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone te);rhvls l 1ajhgj 39;8s,ly ghat has a 50-dB sound level? (Sl8yjl1 )jv;rsg;hl9, esa hg3ee Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when .(rwtt4pg(wl 1uejgrt )c50 v the sound level is 30 dB? (See (g .5 pj)0c4grrtwl1tevw (tuFig. 12–6.)

  Your auditory system can acsk3(5qwkv 6w h ;5swvxzq1h7hcommodate a huge range of sound levels. What is the ratio of highes(w; vqzhhvs35 kwq6 5xs1w7 kht 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 fu) c aju9 ,-a h-yyz9 p9itwt6nth3:geyndamental 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 the string be placwhpn9aut9yt 3y ey -:igc-t)h,69ajzed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threg - uie7a6tfi -9zenk1e audible overtonge i-z9fe1a k7tn iu-6es 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 expect fr0 ljyde2,tzvba d qjek**+(.mom blowing across the top of an empty soda bottle that is 18 cm deep, if yovyz+ (** j, m0blq.2ekdet jadu 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 s yrqwq qp8lq1*y*fr51panning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requirp rf 8qq5r1w1yy*qql* ed? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Ho.ipk5o4 gna, z as its third harmonic. What will be its fundamenta5gp, o4 ikno.al frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovey dg)8u9gvs1 iymf) m* middle C (3)y m8m*sgg1 f)yi u9vd30 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 emiffdusl92.;8p;v e /ao j qtru)ts middle C (262 Hz) when .8ud2uv ;r9qsef jt/a ; )pflothe 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 a. lsy:uqotzd;bk 1. *nt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampi)n.yl y,qv ,fle 12–10 should the hole be that must be uncovered to play D abl)fq nyvi. ,,yove middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 nf ;ww0ltl f+2ehwb *4Hz, but not at any other frequencihn+f*w20 wl4lwfb; e tes 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 1hemhc): i6i tends. It resonates at two successive harmonics of frequenciestc:ihmhe i 61) 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 v/l 8eq ).ii0wwazpm($^{\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 rangq2hkg5x71qg dd *j:d ybpr)z2e for a 2.14-m-long organ pipe at :r d7djpq2 h zg2)yg5bkxq* 1d20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is av*lu nsc ;t wrr-h13:ppproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in 3wc1sth uv; rr*n :pl-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 trying to adjust twekdwui 4e +, ng-0j e7ds1cmo*o strings, one of which is sounding 440 Hz. How far off in frequenen*we0+m1-d, 7dsok4 g j ecuicy is the other string? ±    Hz

  What is the beat frequency if middle lmt)e wuw- -px0(pp8uC (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 opj 2)fqx lowq/ iz:)s,jerates 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 frequ:j)xq/jil, o)2 szqwfency of brand X.    kHz

  A guitar string produces 4 beats/s whr 05ylh8 ga0wn fc.pe*en sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequenr0* .gw0naf5ehpl 8cy cy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The ten-vyugn7 fm- u--lg8kqz t5n+)-jr osb sion in one stringnyl- qk)g8- nf5zu-rj7tsg u vo +--mb is then decreased by 2.0%. 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 .(x-0bjt;bsd ,mkia d two identical flutes each try to play middle C (26sx,j(mk0. tba-d db;i2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frev.,e 7ef,fcj.j/ t qvdquency 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. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded toge fq,..d/, 7fjj evvctether?$f_A$ =    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 mmdh4 vwo4 27lj from one speaker and 3.50 m fhwj 4m427ldovrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibratinky xc+fu)muvu11t55 -aes1yo z5) tyng at 132 Hz, but a piano tuner hears three beats ev +vou11)exzycku1 ufs5yt-n5 )tmya5ery 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats per csiy42str o8g640z z;f(cxlc second will be heard?z2 xzcs 8l 4;6cf04igotys(rc (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sidd-yep0p- f*;d2 vbpiren is 1550 Hz when at rest. What frequency do you detect if you move withp*di- -p;pf d20veyd b a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do vp0 7haxciw9/38 9cjxgu jwk* you detect if a fire engine whose siren emits at 1550 Hz moves a9ak9jux *3wc/0w8cjgvx pi 7ht a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towf3nqh;qy,pi06wj y bm ;a8yj/ard you at 15 m/s ;6;nj3q8m i,y w/yjyfba h0pq 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 equipphb60jfa79 )q,+degj e-vxy ;g ft5iz yed 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 freq)0e6 -7i bqyf yfh te,9+;av5zxjdjg guency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them re4awm cxm1(1kq,nry:n (h rp )jturned from an object moving directly away from it at 25 m/s What is themcxknj m( np4 ,1y(aw:1rhr )q received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies,yt5tdi9hw; w2 the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear i2tdtwwy ;h59in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origini: 8juv:tprm a -;cg jk7lapi4ef.+f,al Doppler experiments, 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 bej4-pva8 cmri; f.f :k,la7ti+gp:j euat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ul8 smh6wbpkb2-nsocd6)7 og+l trasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissuenlo+ho)wm-bbcd s2sk78 p6 g6 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 wa7w2 3 al4*c welbuqjp9ves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When tkf2a d ik n jpk efg+4i)3c:;b,;op,hly4u,tvhe wind velocity is 12 m/s from the north, what freqjk: ku2ok,3nd;yiclehvabg,,4t; iff+pp4) uency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its sp9 k9lr2; llhsneed 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 th9y x58b* rexzve speed of sound is 310 m/s (a) What is the angle the shock wave makes8ez ybx* 5r9vx 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 of a planet where the speel8den;;y5w wvh5g zzdj)cv*9d of sound is only about 5jwvvcdwn led9);*zh zy85g ;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 sh8h. z/own p,s 4os9ilhock wave angle it piop n.ho, 8/4whszls9roduces
(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 / 8tq3sz df.2iwo o9gp$/theta$ 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.;7vy +mk;gxzd 5 km above the ground flying fdy xk+mz;7;g vaster than the speed 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 sonart+jbhc8zrw q r142g:x,o :alf device that sends 20,000-Hz 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 is the minimum time betweenaz2ft q:rgj18+: rlx4o,b chw pulses (in fresh water)?    s

  Approximately how many octaves are thei5g c t2v61fzosz)jc7re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a civ) esv) m:n2,q8t qh8rjku5 8ixhj6sewer pipe symphony. It consists of many plastic pipes of various lengths, which2irkxmh )nqqvsc8e5ju6 8 t)8 v,:jih 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.)9l, ) ywjn5dox //r7h d mdd:iuso atbg(,zc*0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoe(9 ,7nocd/ j5,yr g l)whbi/*t :omusdxda)zd s?    dB

  What is the resultant sound level when an 82 5 +l2yvjyew)t-dB sound and an 87-dB sound are heard simultaneouelt52yvy + j)wsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in th4nit8nvg hlt3 d.a ;1me open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radia.l 4nat;v8i1dh n3tgmtes equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power oi rw91drs:2j *udke; butput drops by 10 dB at 15 kHz. What is the d1db i9w *:jke;rr su2power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear k,jnstd7x tw8lgp; +c/gp58 a i/vp)wprotective devices over their ears. Assume that the sound level of a jet airplane enginejdw7gv;+lg), t 5 8tckan8s// ppxpi w, 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 unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gaiqlgp( k2*rfk .s 6u/zci3wzu2n, $\beta$ 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 frequena 9w:tqs,yeb.-4 rm )aerv.ofcy 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 with a fundamental jx*qpsujvp gr :v15.h0 /0oskfrequqvjuvp rho 51jk*s0/g :0. xpsency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration abow-/ v*cqb)t a8 q8 0,sqep:ji3uy wzygve a vertical 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 openiq /wp8y 3 zv,yt j:-wqbaue g8)cq0s*ing 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 strin1-qx tqz. mp/dg of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) .q-pm /xt qdz1with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loophi hzvw gu r*/)v58b9dpwgu(, ($\frac{1}{2}\lambda$) 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-lil/wrpcrihr8)7e 7 )ztb5 .rfmul9/ Hz range 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 or/h)r7 ptzru c89eibl)r 5iwlm fl./7ne source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One trai+zil5)m((i i 3ph+il b:acyva n is stationary. The conductor on the stationary train hears a 3.0-Hz beat fmpaizhl5a :lb(3 cv+)yi(i +i requency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle br l/k i90m fp7r6h:ubas it approaches you is 538 Hz. After it passes you, its frequency is meai 90br lf:mk6p7 b/rhusured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spf 7 *5rklffbi.s: ap/aeed of cars just by listening to the difference in 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 iiarf*a kp.75s:lff/ bt goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, proa oe+xwd x1l9j6v/5hunt2u0 vduce a beat frequency of 11 Hz. The shorter one is 2 lo26t1au0djn w5 u/xvvhe +9x.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s3 8oh -gv(j* szsftc.qtationary 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 A8zs qjg-fh3sc(*.ovt, 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 blood flow in * t btnt87lov*9w; s rj:ti(azthe 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 th; ro9**l 8 tt(nswttvzibja7:e 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/s while the moth is flying towanzrzfdc9,w 5 t1t.s6e),r ldwrd the bat at spe letdc. z,zwfdntw9)rs,16r5ed 5 m/s The bat emits a sound wave of 51.35 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 puzbt u.8*qhz+ hlses as it approaches a moth. The pulses are approximatelyt.+u qz8* zbhh 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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signal ipkye ,9.jsi4s from one Alpine village to another. Sincyie, k94j p.sie 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.) Model as an open tube.

  Room acoustics for stereo listening ca*i7xefb: + swen be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m loix*s ef7+w b:eng, 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)o.stc8 c 5gi1xqg/nh “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is gt h)qg 5ccoi1n/x.s8stroked 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 thresholdgub:g2kmq-c6wwl/) t of hearing for the human ear at a frequency of about 1000gct 2mlg)k uwb :-wq6/ 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 obsg10i2 wny pld2rr l(;perver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitudeipr;2(dw ll ny gr12p0?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 ni01oa*. 0tajc18ziiy2wi gg$^{\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