What is the evidence that sound travelsuke l rri-rcxt(9*0.k as a wave?

What is the evidence that sound is a form of energo.-e *lgvkt0 zy?

Children sometimes play with a homemade “telephoner v ul9cfa-tpjro e4:aee2x 42.7jrv 6” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearljr xaov r-rete.2 4ajc2497 lfp:e6uvy how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expec324ixud (wwpkx- .a lwt the frequency or wavelp2uxx- k (3w4i.wd lwaength to change?

What evidence can you give that the speed of sound in air does not depend rkcc,4i-( 3bx-.vxnov0 ccol significantly on frequencybvnlko3,c iv4-r (ccxo.-c x 0?

The voice of a person who has inhafvq:e.u8 hp/c* j8dc nled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pi *jxrs1bp w1x 5td5lc8pes?

Explain how a tube might be used as a filter to reduce the amplitul )zd7b .de srm2b6u+qde of sounds in various frlse.b)zb67dr m q+ ud2equency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fiabbv 2pmb*6vn.j 8 m5fg. 12–30) spaced closer together as you move up the fingerboamj.v6m bavnf*b8pb2 5rd toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it k r0d k)bxu/j5but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Se )k xj/5bdurk0ction 11–15 on diffraction.]

Standing waves can be said to be due kknz 8bz11 t ihtov,px/8+q t6to “interference in space,” whereas beats can be said to be due to /1ob8kz tx ,1t ktiqz p6vh+n8“interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointyw)z oj :u4 /q6* zryr0c7biurs D and C (where destructive and constructive uyr) *cz yri6/w4z 7jro:0uq binterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who ub.w m3z/(psp work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detectsp.w mu3zb (p/s 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 /4 i3 xe*z g+azyx6 vtiyegm6+xd 8(xvin Fig. 12–31. Each wave 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),4 ezzixyvggx/t+(3i a+ y*x6v m6 xd8e are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the samvouzq)..:5zt fe z.iae direction, with the same ..5tavq iozez fu:.z)velocity? Explain.

If a wind is blowing, will this alter t98 8-oz d56x+hossf8a xdym vihe frequency of the sound heard by a person at rest with respecx6af9dsivh xo-+d88sz5o8 y mt to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monbpk 9eycy v*a +n(:q6tlz4+zhitor is blowing a whistle in front of the child on the ground. At which posit t(e* kzyhzq n+yv:4c96pla+b ion, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the l/:l hq3wzmq5g rn5 l6rength of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hearsg5qmlr hwnrz ql536 :/ 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 below the waterline. He hears theq0y);z mjd2s skqwf10 -upig0 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 )w su2;yj k1pmz- gq0dfs q0i0in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at ie50q 3zmrt9k 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 school of tuna on1s 13z0j1 tpu1z *folblw5ljg a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig.*5j1wpol0zllzf1 u131 tj s gb 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking th/so 92y3 w 6njf uxivbedx0.-ne water below is heard nj fw9sdu2x3/e-x6o .v0by ni3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr:eo*+(hainj quwox0 ) ete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they arjun)+i (o wo aehxq:*0e 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile ofi +f cia,tm62g distance by the “5-second rule” for estimating the distance fri c+ta,2gf6imom 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 t:i(-rl5:2-pq f6j qskvzqtb f he pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity is 2 +y8xhwq9.yaeflws y p:vs1 +$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired s) ic:teagaxgnq;; g6nza0u:/imultaneously at a certain place, what wi/ )6i: xae;u t: z;angggca0nqll be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpl.3 n x.ssc gesvsw32p4.rqds*ane with four equally noisy jet engines is experiencing a sound levesse4s* ..s.3prwnq23g s cdxvl 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’s.]    dB

  A cassette player is said to have a signal-sji3q d0et*khb- jq/ 1to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. Wqk03tehqs ib /dj-1j* hat is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakinbcyuu9) q 6nar0zrh;x 1o6it *g in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over aut9 cno; )u1by6rh6 0z q*arix 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 eard 5r5k qy 2;wndf)dmap:rum 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 rate* ) do gm,(dxc71m3zvck fruz+d 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 m frud*mm(c c3g+z1,f d7)vor xkzom a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when place:f. ag7,q divmd 2.8 m in front of a loudspe, gm.7iaqf:dvaker 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 level0 c olf 1yt7gu1a6cpo2 of 2.0 dB. What is the ratio of the amplitudes of two sounds whoco7 l0gpayuc2o 6t11fse levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trij 9:g wo9hrdwb g8eq2bh gqimn362d:3pled, (a) by what factor will the intensity ejoh:b8 3d39:ngwdh2 gq 2b69rqmgiwincrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has st9i2zu f/cj9z .ps 4qs94aa btwice the frequency of the other. What is 9aq p t./4bs4szzsij2f 9acu9 the ratio of their intensities?   

  What would be the sound level (in dB) of a soundrj voo.8 0a; 2i:xmipo wave in air that corresponds to a displacom r8ov.2 ji0pxao;: iement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thatwuvn*t 6f9cd 6 has a 5dcv ftwu696n *0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can ddyvu2 a-esy,,hw-ds- etect when the sound level is 30 dB? (See Fig. 12–e -sahydy2-d-,u s,wv6.)

  Your auditory system can accommoda(-atbq dne*2ote a huge range of sound levels. What is the ratio of highbaqt2(e-*don est to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lely:.4z jfp8ewngth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mf 8pjy.4l:e wzust the string be placed?    N

  An organ pipe is 112 cm long. What are the fx* sufxdj56:5svmlk0ff s0 0nundamental and first three audible overtones if the pipe 5ukfs0f:svn0 6xl x *sj 5mfd0is
(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 fro;:gt9bgm+rmtc6: 6 x,tvdd b jm blowing across the top of an empty sg6, 6+tbjvd;g 9mr:ttc :m xbdoda bottle that is 18 cm deep, 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 open-tube pipes spanning theiu*-r70q lumf cl66e *d7oz pj range of human hearing (20 Hz to 20 kHz), what would be the70uqpe *ld im6z-l6jo7*r cfu 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 jqk.com448z )thyd-j third harmonic. What will be io8)c44md.qt kzjj h-yts fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7o xog*a - v,t ;cmmng1d(3mhy9er64oz3 m long and is tuned to play E above middle C6n,* egcgt14m r3zo-(vo;oamdy xhm9 (330 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 opvffz7a6bzlr4a:v:q-1d( h ysen organ pipe that emits middle C (262 Hz) when the temperatu 6baa flsq z:r1yz7f4vd-:h(v re 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 andwb g+s(l/9irv00si t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute x69oks5gsh5;d xnho4in Example 12–10 should the hole be that must be uncovered to pla5g;9ndxkx5soh ohs46y 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 r p 02v9yyzb3akk up /zmlg408xesonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a c u0y2gkym z/ z8lxbvp4309a pklosed 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 resonwwb62 l. x2 chbnho90*c97 idkzd1)r pvze3hy ates at two successi76ndr wxypl102h 3h9zcw.bcb9vdhiz *)2ke o ve 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 (dwip,kp1gb4q 4m t)no+zpa,$^{\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 ma41/:ifb vcwpresent within the audible range for a 2.14-m-long organ pipe bfcw: am1v/4i 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 open to the 6e*m,xzclw mp 3-8 uh-3y xtvcoutside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in t8 xv-mcz mely3 xup-3 hw6,t*che ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust twlfl4tkhg: 8 4jo strings, one of which is sounding 440 Hz. How far off in frequency is the other strin8:4 hglj 4lfktg? ±    Hz

  What is the beat frequencd 44*e3g7ueui3g sarw y 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 anden3 5f p3p mexjf;z;2other (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 fp;j3en2zfdx3 5em ;pHz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/,( e18:xpmczdt a7lit - /qvybs when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vp ,lybi a:(1xcd7/vq-tz 8em tibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the samhzue yrr774,nkml ge,m-9vx+cv / q;ee frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two s;4mye/ g7 q h mc7lr ke,uzx+n-,v9vretrings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mid)/jhh44q, covr jlzi0dle C (262 Hz), but one is at 5.0°C and the other at 25.0jj)i,q0 4/4lzhc vr ho $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. For.7xo jt2tn+w9 ir ck0l2pte9t k B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A an29ji+ctt k90nt l2.o ewtrxp 7d C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.8z r,ogyeg-0q52pt q pd7,ipk swe7+(c0 m apart. A person stands 3.00 m from one speaker and 3.50 m from re7t( q,d gsp 7ckgzqy02,iep-+ pw5 othe other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner he fs0rbcmj26qg*.h h 1qars three beats every 2.qs1* g b6rfh2c.hj0qm0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in ai i f3xo6 ;+uhjib 1t4ppaeip.6r. How many beats per second will be heard? ji 13;pte bfi .4up p6iah6+ox(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ce d)*n tp9a1j)yfhk 6soekze+ (rtain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with ah an +j9de) e)kof1k(y szt6*p speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wh cdedtde 7n2z(:.dmse. 5spc4at frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3n(5d2:.se7deecd ptmds 4cz. 2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yp)pvz/,nrx7d84 ,cy 3ne8 e(h ly njxeou at 15 m/s versus you moving toward it at 15 m/s Are t,zy(j4r , /lhdn7e vpx8xe e3c8)nnyphe two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the sa dlyo x3uk.-(z71hpizcj0/zw me 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 horns emit? lpdzkw z0.7(cz/j i1o y-3xhuAssume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 5e kus/m 78 fvazca/ck zcw6mb ;8(1gz/0.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fw1g8/f(k mb8 /suaame7c zvczzk6;c/ requency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the l7 bkb/;3tug p8u aq6lbat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the b7 l;qbp uat ub8k/g63lat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origincac ov1n)og a:t,3,fh krr9)bal Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of)31vk9aro:at rochfgn ,,c) b 10 m/s ?   Hz

  A Doppler flow meter uses ultras1p2y5oeup 6 lfound 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 frequofupl 2y ep165ency 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 fr nj mp-g/i:6loo5wwt)equency $2.25 \times10^{ 6}$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()q0 zc wxv0dj: 11pedj 3ndxj sound of frequency 570 Hz. When the wind velocity is 12 m/s fro j: ev11zjx30q cnjwd0 )xddp(m the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at szu4yo wg++ie,uo t9620 $^{\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 gbj .a:oh3e x,yl.38r9cgej dspeed of sound is 310 m/s (a) What is the angle the shock ejac9brd,x3 jy:goh 3ge.8.lwave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters th1m8 7aig:tbum;-t z:psrezx 0j5(ijx e thin atmosphere of a planet where the speed of sound isjmxi ug5xbtj z s01;m7:(8rpe:az t-i only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine t 5oaa ix/,-cbunr556 gtdubf5 he shock wave angle it pu56fa n/urig 55b, c o5tbdax-roduces
(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 pk8+yhhz+ 4f/ olb;ha$/theta$ 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 abovwuc 5m2 .epo5-pib r5ee the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontrbp5 ow.5cue-e2i mp5 al 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 sn(ng.,l+5erm jk sr; fg: 6bvgonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh watervl(m,6+ f .b:egn skgj rrg;5n)?    s

  Approximately how many octaves are there in the human audiwl+2 4pan fe kme z7yyeal- eyr/073;rble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has es rwgu26z54qa display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are 6uze5sg2 wq 4ropen 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 pm*6 j ;12alfdtdhtz 5m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the soum5*2 d1jhtpd az6;ftlnd level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an vgt .lk*ol9a33fjo 3zyh(e 5q87-dB sound are heard simultan 3y *zjkl5(o 9vqla .3otfegh3eously?    dB

  The sound level 12.0 m from a loudspeaker, placed i/h n)ikgq8;x29, c6uqowkrxlz: f*x a n the open, is 105 dB. What is the acoqxxqkux),c;k 2i6*8 ag f:nlhr9zw /o ustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at cjw+hc;v6/t n1000 Hz. The power output drops by 10 dB at 15 kHz. What n/cj;6+hwt cv is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typical47o.hg qur mhe+, +h0q -jcuuxr 9a wx4xgq;3mly 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 woulweom ,ax934guhqhx4+g+0r7qumh;-.q jx cr ud 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,kb7qbo n:6;m0 mgk3/0 qlphep 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 ac +uu; lbg1u3v-g cl,p 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 long between fixed points with a fundamental qd4.3 :gw rwwbfrequency of 440 d4q ww.wb3 rg: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 vi.u qrkv4gz1t- v 6ka,z+ksge8bration 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 u.g8-kq41 es,ktv6grvz+ zakthe tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube thf7dh/0 t z85s3 :os*llbzmsi aat is open at one end and also 75 cm long. Ho l5soh:f*mt/7l0sdb8z3sai z w 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 resonate as one foj0 8sce xr*au-,f*m mull 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 ran0bi0t; z k)gt;a0,*cdoaxy3xj dto5 age 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 thatt dxk 3; t0)dcoy00a5o;i*g axjtb,za 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 :pdogtw1om4pxq 60 n,stationary. The conductor on the stationary traiwtmgn4pd o6, oq:0px1 n 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 appros( m3m-jc7a3q o.f;odynb ry: u;a ad1aches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant ve:ya-.muc;qy d;d 1m7(3roasa fnj3bolocity)?    m/s

  At a race track, you can e+:,cg /hxovt7afr/ xrstimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on tho/7v /,xh :rat gcf+xre straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce g 9 16apdn6yn99ut aqma beat frequency of 11 Hz. The sho9 966na1ntdpu9a y mgqrter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends ofvtat2cw-n12 + jkw/r xk:d k+v a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is betwe+2-ajktk2v1 c wnr /w+d:kxt ven the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of bloodu bn u*jn;k44h flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the wavesnk4nb; j 4*uhu travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward vev ceg+ao*fe6,ic8 57ru 6rvthe bat at speed 5 m/s The ave,658+ue*cc6 rfg7v e r iovbat 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 am g0lb;pxg 1 9u(+ohag9i tz6/chx o,gs 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 detected by the bat so that the echo from one chirp returns before the next cg6hmah,gl1x9 9(x;g+i0/uz gpboot chirp is emitted?    m

The “alpenhorn” (Fig5f.zp sc9y46 cr)q*rg:rm.em xp0 j zw. 12–38) 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 3.4 m long,.r m4g:9jz*w 6c fr05xz pyer)mqspc . 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 presxqmj ( g-tw*z6a0-idsence 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 widzmx6g- t jwia-qds*0( e, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, ckhnk0 on v7h*w. q,kh,alled “singing rods,” involves a 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 k hwn07hn,*vkh, .qko be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the humanv x9;5gsc o-dy v5.nmjro1u :c+lpkc/ ear at a frequency of about 1000rjnox59vsocv 1p - 5.m yug/cld;:ck+ 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.rdinzrze r) (k 8f,vm63:j.c:+nn g:e.miexn An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s d::.n 36jv,fxc)neim8zee m+:zrkngrr.i (n altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i2)az 4hj ,6wjpr e;lwps 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