What is the evidence that sound travels as a wufe x*;gxu8g7oga/ -zave?

What is the evidence t,z +r8 xbvg y,sceqw(wk+:.df hat sound is a form of energy?

Children sometimes pt(edzmnvu-;)gh,3lsq, l j ;zlay 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 dn,g3,; )ez t(hum; llzjqs-vcan be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into c7 :vysrq-m 85hfi7k wwater, do you expect the frequency or wavelengthc8ik q 57r-h w7vfmy:s to change?

What evidence can you give that the speed of sound in airrg t)e0/+nxdl does not depend significantly on fre/+n)exgd 0 tlrquency?

The voice of a person who has inhaled helium sounds verycs6qzzz89 ;pk l87jlt high-pitched. Why?

How will the air temperature in a room affect tbm8 e s(cd(a(phe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude sklo wp8-5+r/p u,k0turwq.mof sounds in various freq/+p .krum58kqspul0 -w,rtwouency ranges. (An example is a car muffler.)

Why are the frets on a guitar tj*2 xmwj xqy(cd 7doqk,. z hl,d)5s1(Fig. 12–30) spaced closer together as you move up the fingerboard toward the brid,ckd ydh,zwq* )osq15t( jdl2.jxx 7mge?

A noisy truck approaches you from behind a building. Initiallyrvr0i+ 4xdi p* you hear it but cannot see it. When it emerges and you do see it, its soud+p 4irrv 0xi*nd 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; m,g-wi(m fqm space,” whereas beats can be said to be due to “interferenc(ig m; mw-m,fqe in time.” Explain.

In Fig. 12–16, if the frequency of the y:bsd *) qjlqp,d7b7k speakers were lowered, would the points D and C (where destructive and constructive interference bd7 kb*7j:,ylq ) qdpsoccur) move farther apart or closer together?

Traditional methods of protecting the hearing of peop(. cv3+ gf/g1xvxn+ knlqm5ntu89kh jle who work in areas with very high noise levels have consisted mainly ofhxu nv 9qn1+cv53tglg+k8n(jfk x .m/ efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eaqmky) 4iij4 dfnk4n8/ brb7: rch wave can be thought of as a superposition of two sound waves with slightly different frequencies, as i y n:drmib8ij4/7n4rq ) kkb4fn Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move iyy/+/ 9psgrxe (9rhzn; otkg/nup)s6n the same direction, with the same v/+ nex;h/rgyzs/)ur ( ys9tpnok9g6pelocity? Explain.

If a wind is blowing,/snx rd q,,76es xx/xy will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelen,/d xnx,76xxeq/ srsygth or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mshea 2 d48j-apux ,:auonitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explai4 s-a:a 8e duhpujax2,n your reasoning.

  A hiker determines the length of a lake by listening for the echo of nr h8mm+/ hy41ftii6 cher shout reflected by a c8 yhf4hn +mr 1m/6ictiliff at the far 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+-)fx d jtvh4g mcq7s ulf)::a 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:4j7sfcq+vxt :l-fmu))dhga is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2nyudk7a7 6k 3x9 tr qre j-,nyawg3)/f0 $^{\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 as)l*aagd;j d/; bkp*bl sbg 0pq5 +3aof tuna on a foggy day. Without warning, ana3 qa );k db*pbb*;0 sla/g+5lds japg engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whe:g,ra f4shouw s6w46wdm1p),n9 tssq n striking the wat 9spw6tuw6dgfsas4)nm:w hoq r,s 4,1er below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the gi egf(lu53r :wround, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one trwig( ue5: rfl3avels 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 rst ljmrpmqdq ebgj)l-a7;17( )g8 4a made over one mile of distance by the “5-second rule” for estimating thtb))l amq71 -eg4dq7gm p8 sj(rarjl;e distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? t 6vc)o6o ocwju*p5 aq1g.z+z   W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level ofpff, 8ciw1s50 f+ tdsq a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when zom). cx0.cds fired simultaneously at a certain place, what will be the sound level if only one is ).dom0 xczs .cexploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wiuyt077fk)v;ut 3y8a voc 1yecth four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’c) 3t 1cy auy7v kft7uyo80;ves.]    dB

  A cassette player is said to have a sig tt+flg)rk sr mb*yi 58l1gb d-a3zi//nal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signb l)idfsz r/agt tb5i-lyk18rg+/m 3*al and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fro bm*vn,d7 5vmom a person speaking in normal conversation. Use Table 12–2. Assume the v7o,vn* bmm 5dsound 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 eardrum taek(l p:5dilm2s z ,1whose 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 ra27ysiexk 61+;u t)ym/oy7 s ,msgzd eited at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decek)y usso7t,y iy+d7i x26gsze;1 m/mibels you would expect at a point 3.5 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 medx)bpdb:-zm 3ter registered 130 dB when placed 2.8 m in front of a ddzm : b-b)px3loudspeaker 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 differejk 880. yhqb 6ttf+z:hrbn7mgnce in sound level of 2.0 dB. What is the ratio of t:z8+tbhyq6 r tk0mnj. 7h8 bfghe amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensi rb:zztl xuu 7)59o4 dbl+nqd+ty increa:b q4 7du+ blr)9uzozx dtln+5se? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have 3r+wij mtx wx2pe-(-q,if* rjequal displacement amplitudes, but one has twice the frequency of the other. What- x3(wq*xtrw j+j 2e,riimfp- is the ratio of their intensities?   

  What would be the sound leve6lx2navhg ,zrg3 w1; nl (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules onx,a lh1g z3rvw ;6gn2f 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to 0a f tj:vuk*i7seem as loud as a 100-Hz tone that has a 50*uia k:t7v0fj-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detecth1: 3wid88xoqx*ual br*w)zh when the sound level is 30:*h rqax18d whl*uwb) 3i ozx8 dB? (See Fig. 12–6.)

  Your auditory system can accommodate*8ah-gdqa ,y( hbslq( a huge range of sound levels. What is the ratio of highest to lowest intensitlqyh( ga,-*8s( hbdqay 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 fu9fens i:it 5ed07 skg8ndamental frequency of 440 Hz. The length of the vibrat:i 57se f0i tsgkdn9e8ing portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lonu /.g5z i+mmt. e3ti)a*kkskz g. What are the fundamental and first three audible overto*ikmt3k /.kmiez.)z +sg t5a unes 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 fromq5-jw+ if:7cjvx u)u n blowing across the top of an empty soda bottle that is 18 cm dejqiv-x)5nuf :cw+7 j uep, if you 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 dxs 0vznac,b 3sc0*6uopen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be th* , 0c0zb3csasxn6dvue 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 harmwt pzv+i:iv0 m(yj50 j,g ba(fonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original l5f00api ( vv+m(w:i btjjg,yz ength?   Hz

  An unfingered guitar str+v eb;t)fyirk(e. /g sing is 0.73 m long and is tuned to play E above middle C ( ;ty(f s. eb+v)ikg/er330 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 thatxdyd md5 o:(x/tstx8a70u/e s emits middle C (262 Hz) when dt57t ou/x:e 8d xm(ssxy ad0/the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at,3,c(putj ufez:0y6z9efdb,oljq c * 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fs;ft)1 xx:idrnn (no ,lute in Example 12–10 should the hole be that must be uncovered to play D a1r)f;nnx nsd:x(t o i,bove 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, 447 5b6tikt :8tgcyq cq/0 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a 5t/tqtc:q8bkcg yi76 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.u(5gxrb7 /fb z It resonates at two successive5 /rbz7ufb(gx harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 *olwpc w1mh;9$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.;q(dwwo ,bqhjd5 3l l614-m-long organ pipd5bl(hl qq wdj3o,w;6e 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 op*hc a:ccgzbn9dh -.)(f+wsk )8nxr bben to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the sta d c+a9g:)n)x*szbrnkb.wf8-hhc(c bnding 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 p- .o6hlsdls;2i.y fcto adjust two strings, one of which is sounding 440 Hzhylsdpsc.2.l i; o 6-f. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if midd yklav+k-d1e3iq +(h rle 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) operatesjlzd6frq( *vj t hu)20 at an unknown frequencfl2(rq6*zv t d)jjuh 0y. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4t3k5kfph14 o )e6q;u;hzp6h;jzii li beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasonpl)kzh6z ;uo q3 ;;h6k1 th ii4epjfi5ing.    Hz

  Two violin strings are tuned to the same frequenczh5zp+e )n/ m -jfzj-by, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency z/)-nhpjz mb5 e-z+j fheard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two id1 .d7mqg i(/h iuftvf)entical flutes each try to play middle C (262 Hz), but one is at 5.0°C 1u)/7fi(mqfi hvtd . gand the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B u cqhse,h05o/has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible whenhq5c/, u 0oehs 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 mvs 7zy9 t0cq/l i0f0th apart. A person stands 3.00 m from one speaker and 3.50 m from the 0ts 0/iv9 7 zcyqlth0fother.
(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 suppzu,k5w m611laqp - e.5re /x6rwbakajosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they abw zlreuaq5awer 5x1,.-am/kpk 1j6 6re 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 manawiu:2t lxe0byzzlnj/ h- 2r6(u ,(fdy beats per second will be heard? (As2rtle nhyj(0duw:l2/-zi(u xazf6b ,sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eng+;4cg beily za1z3 0s,icpmbwhs o1*)ine’s siren is 1550 Hz when at rest. What frequency do you detect if) l 4cb;*c bg ,1wosi0zepyz 13smha+i you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yok9a ju8g a 9xd)*r;erau detect if a fire engine whose siren emits at9*;ar8aur 9eg) dxkja 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freq iie.e0zm-o e4uency 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 frequencies exactly the mei ezo0.e-i4same? 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 sing+g*xxf- vc4ajle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest v4f+-*gxajcx 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 ultrag0yi.jp spw ,:( j .l*kau(vbasonic sound waves at 50.0 kHz and receives them returned from ay ul(awb0j(a . ,pvpjsk*ig :.n object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 ;yogdm z(*1 fq)j xz:km/s As it flies, the bat emits an ultrasonic sound wave with frequencyzk f;z :(jq mg)y*oxd1 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 iu;voxa a1:5*d f:f kzon a moving flat train car at a frequed1:f5 va; u:f kzao*xincy of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flowja/t;jwvr qo/tpazb57 6pcoe )s+ 87u 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 78povwap 7q / zetr5j)acjuo t+s6 /;bWhat 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 /xmswsko0fru f w 7;nym 1m)6+ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When thecwv2k 3t6 34o-ro76jq 3ht6*wug qkd2jm pgsh wind velocity is 12 m/s from the north, what frequency will observdjcmjqo62s3phwh q6v-rgt3 u7 wt4o26 g *3k kers 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 movingmpj.us) +f 7lxnmmupc+k+00 g 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 iszoh-3md2bo: d 310 m/s (a) What is the angle the shock wave makes with the direction of the h3odo:2d -zmbairplane’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 th*z(2pzzuxrst98 1 wwme speed of sound is only about 35 m/s 2 smp w(zr9x1t8 zu*zw
(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 strikec3ucaji683,d6 axg bss the ocean. Determine the shock wave angle it uc ad3ci3bg as,j 686xproduces
(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 * i/g2t y,g5xg0wswyo,s+njqlxks4 ($/theta$ 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 k tc,q 5zt9zs:lbtfd 7 -epee9ya+06amm above the ground 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. 12–34. Deter 5 cba lptaedytm7e,9:9 -tf0es+qz6z mine
(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 ro7s k9 mn6gr)h26; kun+clxq sonar device that sends 20,000-Hz sound pulses downward from the bottom of the bo27kghq+69)lmr n6x; kosnruc at, and then detects echoes. 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 therlar(t7 0wtofy7b7;qg e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer prs,e/o6anbk fpx e65)ipe symphony. It consists of many plastic pipes of various lengths, which arefpon)s 66,b/x5ekre a open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makesw;e l9.s ua/cdp 06kdb a sound close to the threshold of human hddec9k;0lp/ a u6sb .wearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and kh+0h;zth7.szqh a9f fsyt 6:an 87-dB sound are heard simultaneously? z :s.+s hhhy7t; 6 ahffzk0q9t   dB

  The sound level 12.0 m from a loudspeak )8 obmhfava-.hpi3x2er, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equhmiaf- b)32o8v.phxa ally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ou- wu2 kz.ipyd /p-ugb/tput drops by 10 dB at 15 k- uz upw2ib/y.-p/dg kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft twn eicr96 bp;:-u0lll ypically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by a-ln: 0;u9ip6cerll wb n unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatioqe d- ,zm.3easns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 1sg m)srz)c6m .$\frac{1}{2}$ 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 lone,sp a:gqc -9szqrs 17g between fixed points with a fundamental frequency of 4401q ssr:qs9e,g7za c-p 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 vibratiul8:vv(v2 cfdbz8u,pl8p : gg on above 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 openpz8:df:b2v,8c8guvv lpg l (uing 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 n6qk2-+xdab3 lu/q v ag is near a tube that is open at one end and also 75 cm long. How much tensionvnda uqk/ 3b 2alqx6+- 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 resonate a1:e ee eyh/y/4,cge rrs 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 the 500–1000-Hz ra*i;9 y8lmad ftnge 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 *i yf l8a9dtm;farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-H )sm/oz t+zhv:i36oqq-oi u)tu;c+noz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?m+zo6+)t u o/u );vt hco3nqqz o:ii-s   m/s

  The frequency of a steam train whistle as it approaches you is 538 +nwco9;j k bnecbvh15a*+cn 8Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?ab c 1n+k nj*;ccobh+v9 new58    m/s

  At a race track, you can estimate the speed of cars just byy7cztfp(mb 2 w*9-wgc0jhky - listening to the difference in pitch of the engine noise between approachingjt2c7fy90 w- zgm pckb(-*h wy and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, proc .:f.jbc1 t-na olleqd;09n t;7szgkduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is; bsft7lj l d1gc..n nea;0:9ctoqz -k the other?    m

Two loudspeakers are at opposite ends of a railroad car as cf(lp m2vy,9bit moves past a stationary obsel(y vb,2m pc9frver 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 (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally abgi7an6nhc:+id 77e3y2 xjs u eout 0.32 m/s what beat frequency would you expect if 5.50-+:usx2n7y3i acn 6g7id e7ejhMHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6yt4t wxey/,h7 t cfy+1m7er8g.5 m/s while the moth is flying toward the bat aty 7 fhyym8r 1tw/ext,t4+7cge speed 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 puls 1eji,c /ljv ds/6,djhes as it approaches 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 det ,dd s1 ivjlj/hcje/6,ected 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 wtk;mm**lp rd(m 7hm 09js.jn used to send signals from one Alpine village to tmrdl9s m 7jm n*(p0m.wkh; j*another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromisedses -802 mfelkf,3b7q bmn qe/ 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 28,msb3lm20n-/ skf efbqq7e e.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 “singing rods,” involves 4dkc 4(em 8fkha long, slender aluminum 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 emkmkhe8dc4 f(4 it 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 threser2m1 ;r5gduztq/b /whold of hearing for the human ear at a frequency of about 1000 Hz iuz 1e ; 5/rdgtqmwrb2/s $I_0$ = $1 \times10^{12 } W / m^2$ 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 ground hears the sonic k82hs,/wow v7sq:hi gboom 1.s:2 hog8,w7k isqw/vh5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat)vky -fa: z)k9p. fbtk 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