What is the evidence / *rmvypen9. dthat sound travels as a wave?

What is the evidence tha5x/4i 3*rpowpcmh k. pt sound is a form of energy?

Children sometimes play with ofm9r6/ s5v*h)q x rwoa 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 atrs5/6) hwoqx*mro vf9 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 water2;7- tn zm hsqgazy3h2, do you expect the frequency or wavelength to n-zz3mq2 ;hgty2 a7sh change?

What evidence can you give that the speed of sound in air does not depend signift) ixk72eu+y hicantly on frequencxhie k) t+yu72y?

The voice of a person who has inhaled helium sounds ver 9o5lle irha(+aw5(yo y high-pitched. Why?

How will the air temperature in a room affect the pitch of orgaj8vd2nn hqc05fta;f ly:, y.wn pipes?

Explain how a tube might be used as a filter to reduce the am( i bf9 /jlowa sa49yfwyxa,:/lm;1llplitude of sounds in various frequenc a lbx l:wjla 9m,l4o/fsafw(1yy/i; 9y ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer to+uy)vfu r7e 5dgether as you move up the fingeue)v+y5fd u7rrboard toward the bridge?

A noisy truck approaches you fromn:t;5 g;f xmbp7eji f, behind a building. Initially 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 fe mfg, nip;:5t;7bjxnoise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due a90tkjx- -b amto “interference in space,” whereas beats can be said to be due to “9xb- 0-jakmat interference in time.” Explain.

In Fig. 12–16, if the fraexs13 1 i1xduequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move 31udsx1eai x1 farther apart or closer together?

Traditional methods of protecting the hearing of people who work i c rodsh8kf)(0n 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 headof0d8sh (r)ck phones 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. 12–3goc4c+k d.4 i3. g 28dvtrsn;)aqu kgr1. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as rqno; +va .ku4ig 4c ) dsg2t.g3rck8din 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 wdx . km a1 a0vrme.rkr;:n:(uif the source and observer move in the same direction, wit( reax:rudn1 vwmmark..:; k0h the same velocity? Explain.

If a wind is blowing, will this alter the frequency ol 0 5qrdxoxt/2-i z l/fqa)jl4b*1qxwf the sound heard by a person at rest with respect to the source? bl f 0qzqx alixj/r-/)xtl*w21d54qo Is the wavelength or velocity changed?

Figure 12–32 shows various posi,c a. /:is k s9golfna(mq6mf5p s88hytions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency9iqfhns c 5ps.ky8 m fmoa8(sa/l:g6, for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout rdc3-oh 0xy4zq foak+0 eflected by a cliff at the far00-qx coha3 f4zkdy o+ end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just oyqkn 0g kjzj2u.5b()fi3)id w 8x2 +1cl rdjhbelow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the oceanch kjfgjwon )2kb+2l)qij 0 53dzi1u.y(d rx8 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 wav*h5oav f*-6o +cgehzbitk9c6 elengths 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 ju;/g7:hgcni r* eor7pqn hj 430 jd8rdwst above a school of tuna on a foggy day. Without warning, an engine backfire occurs on a:/7n;cw rjg4 0hehopi*g n7rjqd8r d3nother 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. Thec njzs h4*bhjoxt q1 4s,m 7h1k:r4r3l splash it makes when striking the water below is heard 3.5 s later. How high is qth ,j44jrkxs:7h1 4ohznmr3l sb*c1the cliff?    m

  A person, with his ear to the ground, sees a huge stone str3,:loqk*d k 8op45fcifs0 x llike the concrete pavement. A moment later two sounds ,30ffps loco5kl4i x q8*kdl: 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 one mi *a.(kl*euhynnqsf9 *le of distance by the “5-second rule” for estimating the distance from a lightning stq nl*s9y.fuk eh*n (*arike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain l*pcyg)8j p-r devel 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 levelmr.wbar9ri .q o514 sl)l9uhsxg ;rj* of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lnkfrnu;b0xezfk7 ;1m 3i5em a2l1 h*zevel of 95 dB when fired simultaneously at a hnb*n ;k7 f0 mixkleez 23a;zfm5u r11certain 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 with fo(wic6o 7 y 0u i//ll;vbcyl1pkjq3f1cur equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the capibjc1l 7yvw;o/k3 p1/c0(yq fllc u 6itain shut down 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, whfj3os o08n/ r 4c:uwwaereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each8cuwaf o w:sr0n/3j4 o device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spe-av n 4q,ajq8uw0/su gje*j,neoh.bfu56x( eaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unifor4-jx*n , fe hej8aqvu 56 obqj,(wsguaeun .0/mly 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 whose area3lbum0h+/u a 1crc*4b9z lwdy 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 ratjv4l m(;7g0p4dna+;jo xto u n6 m5iywed at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 niy4d 4 v;joot(n wg;+u0mjx6pa75 lmm 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 dBs m2wl *zi+n6uol9 ed; meter registered 130 dB when placed 2.8 m in front of a louds+sl2emouw;i* 9 dznl6 peaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference. ddyow 8tm t.cto6 i*z*rkq+0 in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels di6+ kr*z0ci oqto.* 8ddy .wmttffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound ial,*z;qxg n3 ;a lz7o-n9ev twave is tripled, (a) by what factor will the intensit;z*nga9vol,3 x-tezn ;iaql 7y increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equa. gg-fn tjkjj,g35;o tl displacement amplitudes, but one has twice the frequency of the oth-gtjgnok g. jtj3 ;,5fer. What is the ratio of their intensities?   

  What would be the sound level (d)p* sy .gg5plin dB) of a sound wave in air that corresponds to a diss 5pgpl*g).y dplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level t7 rrvo xt7 +0m xp) p2p2q;+ef.my;ixnnoj9vzo seem as loud as a 100-Hz tone that has a 50-dB +qy ;vp0+ofpnix9r mzxx)n.e7 jp27m vo2;rtsound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies xr-bhr7 p.fm b26ry m*that an ear can detect when the sound level *7r -6prrmbhbm.2y fxis 30 dB? (See Fig. 12–6.)

  Your auditory system caf5kx3d6 zj:dt ndkz ktd:-6-bn accommodate a huge range of sound levels. What is the ratitx56:k d:6fdznz- k-j d3ktb do of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a funzu. hg39p;zls damental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensugzs.lp 9z;3h ion must the string be placed?    N

  An organ pipe is 112 cm l g og rm8o/x w-kh7))whrpb.q6ong. What are the fundamental and first three audible overtoneoo6h b wr gpq)8wr/7)xh.g-k ms 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 frocut5)k1.; rt3h0sjno vqj*2sy ams 1km blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tub.3 1t0 hsnk2m)vok raju ;scjty1qs*5e?    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-tgbz x+1 pw*b.sube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths ofswp* +bz. g1bx pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequencw6- ;huy4,4exmt 7ft x bbsn9xy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingeredb,b 49st7;6m fwt n4-huxeyxx at a length of only 60% of its original length?   Hz

  An unfingered guitar string iej+010ycw oh ts 0.73 m long and is tuned to play E above middle C (330 Hz). 10yjwethc0+ o
(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 openzvfpo hgiafm8;30yz7lk8-1 3 dvx8r x organ pipe that emits middle C (262 Hz) when the temperazm8vd-fhixx 3710 g lykrf pv;za83o8 ture 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 20x e5ycuvbvr 05 9tsi5; $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be teig l 2 t(nmvf39n/ k1c;;ugkrw(b- idhat must be uncovered to play D above min/t9gi-m;f rnk b(gc ;wd1(u 23livek ddle 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, a,jle u:hz 9tc22c2pt lnd 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closp ejlc2t:l2u9 t2c ,zhed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It r e.)uhot/5se,yjl s *oesonates at two successive harmonics of frequenchls y.5 *t),esoo uej/ies 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 ;.(kdan2x -gt 1b kns;dvn3or 0 rd0xe$^{\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 4ohf53d tt(ug7x t f62duu4beaudible range for a 2.14-m-long organ pipe at2g 456t 47dhou eftubf3dtx(u 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately lc)tg57k8s( lyn oy8b2.5 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 oo)b (58g cnk7 y8sltylf 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 +42e l9nbqsyw(5(cy,zfg ikqs when trying to adjust two strings, one of which is sounding 44klb (,f zngy4 9qicqw(e5 2+ys0 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequencuj shv6ic+wwh ewlgpsyckh,3/*.p ;0i 6ha 66y if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) y yhynd/ 4gd9: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 simu4 y9dyd:n gyh/ltaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuvn8j2++x- baq8 u zyipie9e8uning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What isu82n+ uyi8e v+j- aqz8pei9b x the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tenk q.y e4cudja6 y33rm q11dyj9sion in one sq 3. m yq3 jyr96j11dkeuda4yctring 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 two identical flutes each t0 wao6l(/ uujgry to play middle C (262 Hz), but one is at 5.0°C and a(gowju 0l/u6 the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fp ls(cotic+b3n5/;bjork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is hetols n cb(bi+p/j53c;ard. 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 together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1a9b*(jouh u /z.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the o*u/(hbj9za ou ther.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hearp-1jl f-+dzv.;nv4wk/xu w uls three beats every 2.0 s when they are played together. (a) If one is vibrating at j.xwk pfu/vwlul14-;d-n+v z132 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 map xtb(ucgq 319vgy j(izp:n wj.d 5l46ny beats per second will gt1q 3 yc.(b ij6un dpw(9x:vl4 p5gjzbe heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz znc+t-6j 2 finwhen at rest. What frequency do you detect if you move wi 2izj-tncfn6+ th a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enf e fkf g ya/)td)q cr8e4p;* s(x/j;.zbd9cdjgine whose sirend cpb*fd/scd .x;fe9 e8ytaq; kzrgj(f/)j)4 emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hzu8t kab/ kbf5*z6yb 3f tir5c(lfr2z: source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactllt:t8f y (ifzczrb5*/6bau 3fk k52rby 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 tha d)xs:uc7hl.e0r+-na s03 qbgd j gw8e same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horn:a+q jwsne 7d0xsg3l0dab r8) u-.chgs emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonfl6g ))+yoklz ic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivflz+ gk)6l )oyed sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at 5e(7zvuq i/*mg8de c oa speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hea mgzoc(e i7q *8d/evu5r in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat ngll (v6.x+oq/tfsg ;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.;ll xov/s(fgn6qg t + train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound ncv3 +5llpqk+pq4y;d 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 1540 m/s What is the expected beat frequency if blol +4kqp5 cqyd;+ nlvp3od is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency *3 hx/f3fo ftu $2.25 \times10^{ 6}$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 the wind veloc n5:h7sk:-nhuyy l j.ufb9 8k+evorg9 ity is 12 m/s from the north, what frequency will observers 5y9h:. ul7jykf- ub8 onhevrsg9 k+n: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 mo yyo0pwdvz 05:ving 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 31+ 9hn( wwcyp:p0 m/s (a) What is the angle the shock wave makes with the direction of thc w(h y:p+n9pwe 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 theyg*fe74v5 uo p thin atmosphere of a planet where the speed of sound is only about ypv*fg ueo54735 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave s m.pwqg 7wya r,mju/7*m-ge.angle it produ-wmq7.g/emrsgy, p. 7jw u* amces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle q je w6qkjv-qy;:s d+6$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ovb+ (thga 3+.z bxzb;ncerhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has trave xn.hgc3;b+a(b +bz ztled 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 209kgrprlaz 18 9,000-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 mini1 9gzrp8a9kr lmum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human a0ki 9,uum6dr ru q0t1bimqsyz+/ na75udible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pip cl5))n3e zd27btetije symphony. It consists of many plastic pipes of various lengths, which are opendl5 3) enjzte7) 2bitc 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 makfl,kq3 z l5-7rs xnyh,es a sound close to the threshold of human hearing (0 dB). What wif zlk37ynlxr5h,,sq- ll be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB smik9xfcqj7h4 i 5 :2c8a4meiso /)wvhound and an 87-dB sound are heard simulsx7 e:hv4im mai ikh/2 cq9c4jf w)58otaneously?    dB

  The sound level 12.0 m froma:; j5u2bdk1 o* eofiv a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) okva 5die2bu*o1o j;:f f the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outputy ov 9azm.nc,xfq m(0) drops by 10 . ,v9yfm ac xmn(o)z0qdB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically u84llu ng8ih;oxs/) zwear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of lolui4hn ;)zxs g8 u8/30 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, thcodfp/t/7-)t l9gqil if7mr3-(mutd e 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 frequm x. +zezuz3c;ency 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 lold60x)4 e/jza z-tbnzv1 t7uxng between fixed points with a fundamental frequency of 440 /av70z 4d6z bt elz)j xn-u1xtHz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube kcpu+ck tt n(*v9lbe5,1ie v3 filled with water (Fig. 12–3c c nbve1k9pk(i35ltvu *et ,+5). 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. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g )pw;j+2f 13meya somwr,k cp,g0rco/ is near a tube that is open at one end and also 7+mfm2/g)e1, w kc; pw,0p3 oyojs rrca5 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatz5 k fkyfbgheotf451 :-1dy8d 9f4pdbe as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a purmn,kj 0f(ncxjg 25, ,-ojjklqe tone in the 500–1000-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 one so( 0l5 kxo- qj,, fgmjnj,k2jcnurce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The cxltb 5b+6vrw 5onductor on the stationary train hears a 3.0-Hz beat frequency when+t lxvrb6b55 w the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 j1sb ko adbd69k(m/4q; 8molr Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the trainr8s dkm1b/964db o m;oakj ql( moving (assume constant velocity)?    m/s

  At a race track, you can estimate tqduqk) 62+odml8n k5wpb:ng/a+ hz ,lhe speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppos5nh dq8na6u2l p gmok +,:qb)+dkz w/le 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 H9d9 ys pi+8h.ts qpvl9z. The shorter one is 2.s ylpsd+ 9t9.ip9q8 vh40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it/f::twlfyj,+a n/j un 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 the car, (b) he is between the speakers, at B, and (cwaju jfl+: :y/t/,fnn) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s w9tkdqi3h w(o,0a j8*2k3zh6) xnmpc wp bz*qihat beat frequency would you expect if 5.50-MHz ultrasound waves wq8otz,)*n3p6b0h wi icqhx zj( a9 3d2w mkp*kere directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth hb:vv3aua: f6 is flying toward the bat at speed 5 m/s The bat avbf6uh:a3 v: 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 pulses as it approaches akkw(45g/3z* , wfseta -rgjrb moth. The 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 fro we/aj5 tf*gr-b4ks3zrw,k ( gm one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine2 tzw8ibw04l j 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 fl 2zwib8tw4j 0undamental 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 can2fbavv264 ba3yy njxo7 1) ner 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 long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing wavej3)1 6n2 ayfx v4rn2b7avo ybes in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long )anm 1fhiy06sdg -4gg, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice,gi0y1m 6)d -fsahg4ng 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 thresz.wza2b2 2zlpl0m q ,cbj-qjr94;vl khold of hearing for the human ear at a frequency of about 1m.q z- 29jj b;2,zv4pbw 0z2aqllckrl000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the gr9y*yq3v a/fl yound hears the sonic boom 1.5 min after the plane passes directly overhead. What is the planyflv9yq y*3 /ae’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo f h4.2*uk5iyj 02hpzibmptttghi(95 at is 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