What is the evidence that sound travels as a6b; wulqcub33 wave?

What is the evidence that sound is a form o; os;2j+d zdkof energy?

Children sometimes play with a homemade “telephone” by attaching a stringl, a7glo;0 o *5,ibmdyxo lc7j 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 from one ,xjl;,0ymb c7a7ol* o 5g idolcup to the other.

When a sound wave passes from air into water, do you expect the frequency ormlscb: v) ;03ofxli0i wavelength to chal )mivoxb 0 ;i0f3lc:snge?

What evidence can you gidszjoat,h1.a*b esjjv6z2 l *l)4 h v;ve that the speed of sound in air does not depend significantly on frequea;s lh 2,so1 l4*t v he)ajjzbj*.dz6vncy?

The voice of a person who has inhaled helium soun9xkwh eq*a 51qds very high-pitched. Why?

How will the air temperature in a room affect the pitch of or dbm3bxzd38 8hgan pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soh 4d*3r pfw.wwunds in various frequency ranges. (Anw4rp fw3.* dhw example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tpn)hij w)6 0kvnxl25pogether as you move up the fingex j0i5p)2lkn) w nvh6prboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it m-fvk7o86a (h e.gy qobut cannot see it. When it emerges and you do see it, its7 mk8 (hfoy6v gq-e.ao 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 to “interference in space,” whereas bt5 q q z5j-,ovq+-ibmzeats can be said to be due to “interferib z5 v5omq+q-z ,j-qtence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the z :19z,0;zia +jyprcffubsr1points D and C (where destructive and constructive interference occur) move farther apart or closeri+ f0bj 9 zysr;zpar1,zu:1cf together?

Traditional methods of protecting the hearing of people who work in areas withk pl0t ,)myeq( very high noise levels have consisted mainly of efforts to block or rep let) y,0q(kmduce 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 reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wa4md6 t rvef*lty6ex :5ve can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apem6 5t6fld4 yre:vx* tart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directio* 9g xw+kqy3jk2s1fo6o,i w jun, with the same velocit 1iwxq ,uwkfs92 *ko+ joyj36gy? Explain.

If a wind is blowing, will this alter the frequency of the sound hearqovdbnn(/ o42;ay p1qd by a person at rest with respe2obqnd;n1a 4 p qvy(o/ct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mht k nh5dpmz*7b:qeo(a,)n/il p. f.uotion on a swing. A monitor is blowing a whistle in front of the child on .h h/ pmf : *) nun,btd(op7.qki5ezalthe ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length 1jcui,/-ly hi of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the elih c1uy,-ji /cho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sid5f taqcsa*/yge 7 51are of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table s cae*/taa1 yf5 rgq5712–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavewt;m+ cs lam*)lengths 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 above a schoo5;okj0 jqj7dx9;ez 40-ojf egseqt5d l of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heardjg0eejq9f;o j05x-ko4zq; 5d s7t dje (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top)+qo j:+bvmfw of a cliff. The splash it makes when striking the water below is heard 3.5 s late + qf:vw+mjo)br. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete r dj;knjm939dpavement. A moment later two sounds are heard from the impact: one travels in the air and thm93dj9d;rnj ke 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 cghz4e3 q x4ybjiwsv5*zfgj0 d)a)52mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) svxz b)q2*f0 j4g) jiyzd5ew5g4c3ah30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of as 2t ;.kv:xk0cdtn;en z9t+il sound at the 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 levqdi i/+s urgr ;qe9(j2el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dgk 1s:c6tsfbs+znty5 (67isf2 bkmt ;B when fired simultaneously at a certain pb1ktffkm; s52cnbts+s z6ysg 67i (t:lace, 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 wita86e ko4ngcq /k83t /)/ tok.djmm dsth four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person kmtq.d ke)coo /as8k 4 3/tm8nt/d6jgexperience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-q3 i+y1q7g2gx7 nbvltcju 6w9noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and thei1xc 6+bg 37uvn7qqwyl g2jt9 background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fro(o sih i(qg2ys f:ethi51u0(cm a person speaking in normal conversation. Use Table 12–2. Assume the soc0 uqigs1o i:th((h(iyes f25und spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an .9u7gon 4pdqg l lgm-+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 avdf xxs;s -cy+rgnxpox+d . /:1,bm.mt 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a mp1d .x;v ,sxgb :xr-+xdmynco f.+s/ 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 mhfp5xu1j u2 x cpj16 2rnl4v/seter registered 130 dB when placed 2.8 m in front of a loudspe 14njx5/rpxuf12s p l6 cujh2vaker 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 in sound level of 2.0 dB. What i*sol ta:ye6l6 s thsla y6e: ol6*te ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) bw.cno0 * ro/;ar scsu4y what factor will the intensity increase? Increase by a facas ;u0 owos/4crrc* n.tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitude+o+,.)f iypf gc jr1aes, but one has twice the frequency of t+1jaoi ,fcgeyr. p f)+he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) oyrxb,6b b+ c2 faw3/4yses ,pdwn,mn6f a sound wave in air that corresponds to a displacement amplitude of vibrating air molecuymrn wpn,f d,6s/e3ax,ycbs w+b642 bles of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1s +*purz b vet(yf)pni-f*95q00-Hz tone that has a 50-dB sound level? (See F by+trp9vzf npq e)( -fu*i*s5ig. 12–6.)    dB

What are the lowest and highest f,g *fq)4y9i8x/f0mikhi wfd g requencies that an ear can detect when the sound level is 30 dB? (See,9fgi/g xy )idmk*hfi4 8q0wf Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wh 6 x4nhne3(toe4is 6z: ha,uklat is the ratio of highest to lowe4z lu6,s6ai :(xekt43onhhenst 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 fundamens:s,t7 ;rgfen t ay7x*fy8ey3 tal 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 mx e; yyssgtt*n,77f8y : 3fareust the string be placed?    N

  An organ pipe is 112 cm h:e ), tmwljf*long. What are the fundamental and first three audible overtones if the pipe is h)f mlt we*:j,
(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 from blowing across the topgja+;;fvt 2xv of an empty soda bottle that is 18 cm deep, if y v;j2xg;a+tfv ou assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the * qqcwph5k5rjl:6/h76 kk xyds2 lbh1 range of human hearing (: 2b*h1xqhyl/k w lkk65q6rhp c75dsj20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third h (rsiai)q:e: 8zy9dzxxn et2(armonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originalt n8edzia zy9x(sx i:(:2er) q length?   Hz

  An unfingered guitar string is 0.73 m long and is t /bzi *6x xifjo: ak5. cw30zrf 9j,qk/f.pucvuned to play E above middle C (330 H*3ck/rcxo/ pf qbkjvx6j. z.ffw,:auzi5i 90z).
(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 open0tv(uyc. y ;qn organ pipe that emits middle C (262 Hz) when the tem0q(.;u vytc ynperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 -0x3zs4os tl h$^{\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 hol 3xmzgfer,z /fx-ye g(w 711epe be that must be uw zz1fy/7ee gf(e-rx1 gx mp,3ncovered to play D above 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,gz+ ;-sa mt;+4davcoc 440 Hz, and 616 Hz, but not at any othe;t ;-cam+go4 c dzvs+ar frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two sntyopiuh*1aj;dt4nb;p p2ulfn4 7 t7 d* 0e5yuccessive harmonics of frequencies 275 Hz and 330 Hz. What isy;5afe*d0n7p bt2jh 7pu4 4*lt ontpny1 i; du
(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 yjwh ,lw/ 5;jdrw*g hqa)bd3 6$^{\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 n*mv f9dkx- 5kaudible range for a 2.14-m-long organ v5 -*dxknkf m9pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is glob u8fqb 578fjz(a, 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 ibb,oqzf5l j u(8a78fgs 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 adj;zk6vpgrd/ dddzi4e ai (:3d. ust two strings, one of which is sounding 440 Hz. How far off in frequenk 4pzddr d36;i/ a:e. v(izdgdcy is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) an -nzhcg83h;n; p vhm5ed $C^＃$ (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 ( x ,cye4dz24 f6g(f: ;bduugzabrand 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 ,(42 bg e:uacx dzzug4 yfd;f6operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whe)*4s,wk:gobskv r 5(e67e k dse(weyj n sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is thk kd s egv5(r6s4os*7kw(we : jy,b)eee vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fre23vg 2qjkl0 .vb+oki yquency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are plav0j 232.l k+oikbq gvyyed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middleqmwp55 /qmic g5r4m:a C (262 Hz), but one is at 5.0°C an:mmm wiqp5/gq4a rc5 5d the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4410 0z/a.w ta jr3bhzpd1 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 frequen za01jb0rt/ 3wadh.zpcies 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 tuq d o9;8a(erer9(lggt k u/1m from one speaker and 3.50 m q /(u;da9toel kr91 ( r8tegugfrom 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 py6 wlzbbl7.pyl0ik0/+pat 1supposed to be vibrating at 132 Hz, but a piano tuner hears three /yp61bill0wtb.0apz l7ypk+ beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the 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 w+ c*/xwu ij0i zx/mpw/avelengths 2.64 m and 2.76 m in air. How many beats per second will be heard?u+xic j/m/i/0*z xwpw (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency obote-x7f s2iaac 24yh.* q .usf a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you-hf ioa4xb*tcu.2 sqa27.ye s move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire en*kc h45le7)k /e) vfoi yxrx/agine whose siren emits at 1550 Hz moves at a speed kyf /c4)7*rv5khax)e eixo/lof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in f2lf n0 /jvjvv4requency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two/ vf0v 4jvlnj2 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 single frequency horn. Whe *wg)zxzw76vj n one is at rest and the other is moving toward the firs*gwwj7 6 )zzvxt at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them r3sm(g m9sr 4kx/5 vcpleturned from an object moving directly away from it at 25 m/s (9gsv3 rm/l54 pmxsck 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 emsz3g,x50hdj zv/jgq.3 r)j ejtj,+x vits an ultrazrv0xz/.j)dh+ j jqs g ,jx5j3,g t3evsonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a e7d5vs)cg6a q moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone whil 7a65g)qscdeve at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood- c,prq-0yg 4o545 0ke fxel +iamyvz1lflow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to401 y l f+m4qp5g0e,o cz-evk5rl axiy be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freq:i y4vgz*4:0pi+brvhq :v w p l7a3wjtuency $2.25 \times10^{ 6}$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 veloci4 -l2yd( crs.p)vvo fw08w fow.tsp x,ty is 12 m/s from the north, what frequency will observers hear who are located, at re(.- p )r.2x4dpto ysv0l8cfv,wofwwsst,
(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 i-ju pz qx9 .1nkbar/6e0 ur7enf 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 Ma)aw,stvr- gn0w ;ru04c 55thdexb;y fch 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of th v fher5w; st r-xb40)g ;tw05caydun,e 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 atmos ypt quyk7a223 mxc(8cpnt.-goq9lg)phere of a planet where the speed of sound is only about 35)3puc.8-l92y(k c2nm tygtqq pxa g o7 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 8pf g1iiq9hq1 the ocean. Determine the shock wave angle it produc9 qi1pqih8f1ges
(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 3o p8fp.hxun;v lvzq .*w7x y,$/theta$ 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 above the gredgxkw)kh xk: rp6vph:v(, , /ound flying faster 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. k/ kh: 6hw)xpkd,,erxgvpv: (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 thay5x3d4c t5fblt sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects ec bdxyl4 c53tf5hoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in thew/zpag ap)3 sm- q8:uk human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has 51ni,gna xs )lo2za y5d-pok,a display called a sewer pipe symphony. It consists of many plastic pipes)os d, 5nlkyp-g,a x1 i25oanz of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m frof pj.j;kpb3u7m a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? p3fju .j p;k7b   dB

  What is the resultant sound level when an 82-dB sound and an 871 2c.4bwill zh-dB sound are heard simultaw 2lhc41zb.il neously?    dB

  The sound level 12.0 m from a loudspeaker,ymc 5ej40siwm9kzopku 5o1 72 placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dirjpcke5z91wmymo507oius k 24ections?    W

  A stereo amplifier is rated at 150 W o+tlliwl12 en: i*-)9gxsx t ooutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kH g2is+-eotnxti) 9l ox:wll1*z?    dB

  Workers around jet aircraft tc(r3vlyky6; b 9as7 owypically 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, aky 9w7b( sva3; y6clornd 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 sysbqyavh0on 0 f 0vd;p15tems, 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 tun ei- ppo:f kjm2zm1f-.ed 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 cm long3mk:aa v 3lp3a between fixed points with a fundamental frequency of 440:a3 m pvkaa33l 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 above a v*fmm8l2k-7ure thg6+raf mi-ertical 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 with2 rf-7ulm 6k*m igrm f+h8aet- 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 mimke lv+)y;v1h y26 ocass 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 stri ;) 1c+2lhvmeviky6oy ng if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obserb ax/lyq9 h;,wved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in th6on f;c(cttl -e 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To detern c ft-ltc6;(omine 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 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The c yk2ix 5zsg+ rrv-l.+igm5jr7onductor on the stationary k5+v sgm r7.xili5-yrzg+rj2 train hears a 3.0-Hz beat frequency when 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 Hz. Afteuyn2. bu l(d+xu 0brv +csx7,jr it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? b+cx7vuud+x,.s brl2 u(0jy n    m/s

  At a race track, you can estimate the speed of cars j *::e3uvaqlz3ga8 s,zzo tg7oust by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certa tqag3 g:e7l, o*uzz8v3:z osain 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, lwxx6tz7 c2q u5wo)nt9rqb n047m mm,sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lonx n,w q6zmx2umtq)09 5nrwc4mob7lt7 g is the other?    m

Two loudspeakers are at opposite ends of a railroad car as itat(w qu /r:m,e 4;2dgvb cez4j 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 frequencyb (dw/;erqtc2u ae :jv44,gm z 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 (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in th o/qh2 i im6 bc1;bc+khv5y+vhe 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 2vh i+5bi cchbvm1o6;kq/ +yhfrom 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 whileeaqtr)ld ycoi 21 92x8yafg(c.iq 7 b/ the moth is flying toward the bat at ( qabyy ) ei2q7tl2cr.c d1ifo/ga x98speed 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 pulses as it ap4le1+qq )pttpuz*,/ g9wcn h cproaches a 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 from one chw*q,+t uznlchp9qgc/ )1e4tpirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38/r:va3+dna 9y ffss1f n0p oq3) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a 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 3.4fqvd1psn3f/r f+0o 3nay: 9s a 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 can be compromised by the presencx(h* nbuiy/;u e 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. Calculat/*n uyux;bh i(e the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender aluwu4y o.ai u(rw1 1dnrs8p.5 pzminum rod held in the hand near 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 ao8i rs1z4nwupa d5(pur1.wy . 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 d7yk 2mgv4 )zufor the human ear at a frequency of aboukzvy 42 )dmg7ut 1000 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.ia rd8w; d+jx1.ph;gsxrl hk(8ic 0e .0. An observer on the ground hears the sonic boom 1.5 min after th+as1c; 0irgl. 8ixrk jhp whde.dx;8( e plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 ky 7 komx da,+fl)*wj*$^{\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