What is the evidence that sound travd ,- h*pgfyu:+ .u7aaqz2dt euels as a wave?

What is the evidence that sound is a form of energ6v6-dn+.d noa6h qzu/n;m awgy?

Children sometimes play with a homemade “tg5gtg:v9v/ ok/9htw delephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the:vwd /gg 9h5 9ttvgko/ sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency o m ;,r;kj2h l)rtaxpb:r wavelengr2 p:;al,xb mrt j)hk;th to change?

What evidence can you give that the speed of sound in air does not 1w-q11gr7pe0 fx g raddepend significantlyf reg01gwpa- d1rxq1 7 on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whu0-fdz+k mgii. pb))7p 0nzzsy?

How will the air temp-838k)h -jaf zvu/ wglqaa4je erature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sou -b+ps x )y)qxp)a)fflnds in various frequency ranges. (An exa)f+ p)yp b- qfa)xxls)mple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) fhxfh3qji8u u47 g3s1)9hayl spaced closer together as you move up the fingerboard toward the bridge?hx1iqy3fs8uh 74jlh 9ag3fu)

A noisy truck approadv9flg u pg jx46nwg471vm3 q1ches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter”p64gq4 31du 1jxg w gvmnlf97v — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sav3dc aqp xcf t*74x3n)id to be due to “interference in space,” whereas beats can be said to be due to “interferen d 33c*qcpfxta7nx4v) ce in time.” Explain.

In Fig. 12–16, if the fqqxgy6a80e 3j :fppq1requency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move fartherfqp06jg:38y x1eqqpa apart or closer together?

Traditional methods of protecting the hearing of people who work in areas ott +7a)b0rpgkd8*f i 1w7 jccwith very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in additijt0b 18 awot)rf*pkd 7c+ic7g on 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 wave can be thought or5h ekb6bczeuve j9t3i 412)qf as a superposition of two sound waves with slightly different frequencies, as cqbee5 34 21rhjv6u kz)9btiein 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 in the sala y:df6v wl ,(0g y8e4e/fsvsme direction, wigaslve4 8f w(sy 6vyl/f:ed,0th the same velocity? Explain.

If a wind is blowing, will o(;ix/ h(fski1 l.sws this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity cs hk osi.w(fs1(ix/;lhanged?

Figure 12–32 shows various positionszqq* m.x6 j8 iv2/t*w3qgx wqn of a child in motion on a swing. A monitor is blowing a whistle in **8q zw/t3.jmnqi xq2x6 qgvwfront 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? Explain your reasoning.

  A hiker determines the length of af4r 4n r ug94y3z*dmvg +xyhf, lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengthguf4r zdy4yhx, fmv9n3*g r4+ of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side(wflr. h4ag9s 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 12–1) and does not 4al w9s ghrf(.vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in qb-u sp 3 /br,7g xkawoe9p/;wair 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 school of tuna on.wxli 7p27wgo)6kq yg a foggy day. Without warning, an engine backfire occursgk7). 6wqiox pw2yl g7 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.,p3pyl c fl38 wewhe8. The splash it makes when striking the water below is hch pp .3wlflw,ey838eeard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strrc mgpf9q8 ,el5w u47pp+fu6h :dc8xnike the concrete pavement. A moment later two sounds 89u,d cr5p76 l8gu pwn:fhpq+efcx4 mare heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-eie/k1c ;frw9w1k*r b/i -uiy second rule” for estimating the distance from a lightning strike if;r1w/wkk 9cyf iri e i-ub1e/* the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain len24d yrb aen):vel 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 0ofy1vh9veav 1*ix+l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firepvy-dto-yc)b7kp6 n8r f- 6zfd simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not d- ) - fny-6pb8kc ozf67trdyvpB’s.]    dB

  A person standing a certain distance from an airplane with four equally no,e+ k7zbsh 8,4ds/riu /s akg-md.ci xb*3x ndisy 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: Ag dnaemhzk,cx3 /8s- u.,idk* r/i bsx4+7 bdsdd intensities, not dB’s.]    dB

  A cassette player is said to have ru i(y/d 2iel6 wxg;z4a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the dei/6ly4zuw(xr g2; ibackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normatn9b 2si0qza q50syx6y-u 0m kf3kj)hl conversation.k)35bmxn-iq0 uazqs2t h k 09j0syyf6 Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is l1lh .y 2u k9y +q4xbmrkm ;j*y riyp6xa(b;x+$5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while ugeh0o3htba0u-4fq3;5r:fin,du fz the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels e 0u,ruffu3 0 abh5iq4ngt zh-;:df3o 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 meter registered 130 dB when5p1*speins oqrl2 iw j fn(:.bu8s9 4u placed 2.8 m in front of a loudspearf lnbw.ie*:8 u12 s9 qojnpsup(4 s5iker 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. Wha * kd x)e9b47by5sj8mtxx ubrj9o7s *et is the ratio of the amplitudes of two sounds whose levels differ by thisbdr9*xbe57 bjky4j) ex 8s o97t xu*ms amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soungc k7a:segk+ 5kn35kvd wave is tripled, (a) by what factor will the intensity increasekk7ensk5g+5 : kagc3v? 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 twice the freque o90f-hdnd0/.kadyk incy of the other. What is the ra/n i. f0 oad0-9hkdkydtio of their intensities?   

  What would be the sound l fb4cyo kr7f uu0;7m*jevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm yb*7cf0u jr7kmu 4of; at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lou1aym +2p trc2md as a 100-Hz tone that has a 50-dBr 2mytcap +m21 sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when theu)z+wi +80 kdeoefc)d sound level is 30 dB?) k)d+e+odeci08fu zw (See Fig. 12–6.)

  Your auditory system can accommodate a huge range oelmfm(*(6r.xo 61svy znb y/y 80supif sound levels. What is the ratio of highest to lowest inlbr(8uv z y*oy61sm/0nm x(s efip.6ytensity 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 j:-3vrr6fi feej/t 8a:u*usfHz. The length of the vibrating portion is 32 cm, and it has a mass o:f seujt:jr*-6 8r av3f ief/uf 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 c nt2 -nty *;jdbxwdx1.m long. What are the fundamental and first three audible overtones if 2;dd-nny * tx1w.btxj 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 from blomt nf*b zb*evsx9)-l y /*q)tywing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed t*sn* v)ey)*fbt9q x/tl-my zbube?    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 thee *5g 5vv ;mzzl7yr/ya (j;pus range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes gler;up 5m;7v (asy *j/vy z5zrequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fkt(hdg(a f83yrequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is f ht8g(3day( kfingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abwyz,d/iv58 9/s- jzf +6f d2gp p3xeekr5mqe bove middle C (33w+ z deqj32e58fvyx dfk6mbg ,p / pe9irz-5s/0 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 acn(jvb06 axa46 ao1 v dy23tlon open organ pipe that emits middle C (262 Hz) when the temperaturecdv6y vobnoa0 13 ax6 4a(l2tj 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 bxxv .w 3di, :qm*fsa0$^{\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 f*a*9x xyc; -gp.ogs tthe hole be that must be uncovered to playxaytgxcs -p.* f;o9* g 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 H8: m4mpgqxmxqql. y10z, 440 Hz, and 616 Hz, but not at any other freqm8:qy0m xpq g1lmx.4quencies 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 isrz ,)n 0*c+we ksywsi/ open at both ends. It resonates at two successivekssn/wirye*w+c z ),0 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 ;-0ovyk6j rqj/28nx bni 0apm$^{\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 thep-n.4./v .k5ixd y) wukfkd9vy 8yly m audible range for a 2.14-m-long organ pipe at 9- n ).ylykukp8yvmd4..5w f/ vxdk yi20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longjsd qxv7j)g8 3 n;vgh7. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves ivgqsnx g;78h 73djvj) n 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 whi5zu;79 1u yp5ty u9/:djcz wijy kzm,en trying to adjust two strings, one of which is sounding 57u yutz9:yijz19u yk id mc,5jwz/;p440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if p1xdv0 z5l5:ou/bweemiddle 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 *tkq2*cf5 8pzx+ni pu23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by human+ f c*pk2z *pi8t5xuqns 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 4 beats/s when sounded with ah +o*a s/hy w2(w04ovt u0yftm 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning omt+stufa h(* o2hw/v0w y0 4yfork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequencyf1.d-v( dfdd , 39ngy)pqiqur, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strinr1. yfqdpv9- q3d)dg,nf( duigs are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C2d pt9uua4)cq (262 Hz), but one qutu92c )ap d4is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,vmg: 4oyj t9g--tm: vj A, B, and C. Fork 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 g4mjvg-tyt:j-:vm 9 o together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m fr0z9tjqyu6:wh om one speaker and 3.50 m t 0u9qy 6:wzjhfrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrawxq8g5plgt*rtu7.yo38s 5y( fg7e j t ting at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, wh8yxj 7u5te.t5 pgs fq*(tl 8ggo3ryw7at 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 fiat nady3q;39za0; pw(jy1c m in air. How many beats peraq3ay;9t pnwf10zc( d aj yi;3 second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain f6)ow*djf 0oznb7s 7ioire engine’s siren is 1550 Hz when at rest. What frequency do you detect if yo0 jizo7b7f*) wdsno6 ou 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 dgsk 89y3p i xpja-/3dv+a;sjfire engine whose siren emits at 1550 Hz moves at a speeg9jsv xi;3 s8dpj/y3k+da -pa d of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movingmoz0q x)8gf )eunl.p- toward you at 15 m/s versus you moving toward it at 15 ognf )0mqxpu ) elz8-.m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is -rg l,f b9gsm/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? Am/sgg,- r9bf lssume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soujy( 9p,so rr)vnd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequenp)( ,y9 rorvjscy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits to(1:h hj;uoi an ultrasonic sound wave with frequency 30.0 kHz. What frequenc(hit: ohujo; 1y does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopc p6q6pa3am6q7ydb*n rsknd93knf . (f:p+empler 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 app 6cfdrbkq7p*m:(3k f +np6 a6.asdp39q myennroached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds 81ncfvxrdg odt 7s2/-. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flotrf2g dn8 d/o 71xcsv-wing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraso )i6nd5zwx*:kjds: er nic 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 o4 bjd3)ugx8y+ l kcdc/f frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who d + c/)y3gjuxb l4kc8dare 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 speen,6edmbt4q4 od 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 sounjiv 8n vgqpyk/3+:bc b6hiha* ozc720d is 310 m/s (a) What is the angle the shock wave makes with the directiq*b/o2jv3+kv8 hha 7 c pngiyiz c6b:0on of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosp)+panj/c) j sthere of a planet where the speed of sound isa sjnpc j+)t)/ 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 strike48jlk8 ey 6esx,zl c/ws the ocean. Determine the shock wave angle it prow 8l,8k6jzc4/ ysxee lduces
(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 c4y*e+l-c j +,-7e/)*p rkoe 8kzsepagczr hu$/theta$ 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 lz5f+ 4b s/yse1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal ye4sl/zs5fb+ distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz soun zy:fg88wsua yk0ph nui5vor9,bm6k7j 6gx 7:d 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 thwk5:,fxjky7 08 8pohmaib9 ynzug s6g7:6r u ve minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible r1;umclg 6c5y -zu8 k9znf 1icfange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a d 56gxgfj-t*p7)xa8r k asv 2wj5k)oepisplay called a sewer pipe symphony. It consists of many plastic pipes of v -) 86r5jvaewtgkpk2ag 75fsjp*o)xx arious 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 f7gtjbg+3il z6mh (s )f s2+hbirom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoe+lzj)s6hi32t hg+b( sfbgm7i s?    dB

  What is the resultanf.,dfu v;,xj8h s)bx/m5z ud lt sound level when an 82-dB sound and an 87-dB sound are hearduxd 8lzfus/fvxjm;b, ) .5h, d simultaneously?    dB

  The sound level 12.0 m from a loudsp tafj5cc:aog6/ l8w: eeaker, placed in the open, is 105 dB. What is the acouw /8g aelcfo: :jact56stic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power o+kx1krgee8 v7 s qq33futput drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHef 7+eg3x qvkr8s3q1kz?    dB

  Workers around jet aircraft typicarq0d4b (n0pv/z cefo0lly 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 an unprotected ear at a distance of 30 m fro40e(fqndb vrpz0 o0/ cm a jet airplane engine?    W

  In audio and communications systems, theqfj)c/iucn nf8( 6kv. 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 frequenpz 7i3/i (jpd.kq1i wrcy 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 betwbhh095cs )lm5eckk : heen fixed points with a fundamental frequenc5:0kb h5hes)mclh9 kcy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with lt (8i)* *xy8j+ofra xd p8lutwater (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 hear d lxt+y(x*i8 r8lu8*)jfpaotd 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 nea i(1y4rmvv))1 yts fifr a tube that is open at one end and also 75 cm long. How much tension should be in the i4 t1 (yrvimfsy1)fv)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 ortmo:+ mi8rs6 +-n8 apq.p fdebserved 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 the 500–1000-Hz ri/l xh/h4h s-d5+actqange 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 l 5sai/+ /hdhl-htqx 4cevel 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 a 98 kamj* wue(mzt8 rhho,.4atrain is stationary. The conductor on the stationary train hears a 3.0-Hz beta(k mhuw.j oh8ea,*z 498ramat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistler,0 vo ;8bwlu/r0v khn as it approaches you is 538 Hz. After it passes you, its frequency is measured av /8kbnr ; w0,uo0rvhls 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can est2k( /zz f:jfstimate 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 the straightaway. How fast f:zjt2skz (f/is it going?    m/s

  Two open organ pipes, soundinzfw96+d./g q( rbl 5d qotuoq5,vr*kpg together, produce a beat frequency of 11 Hz. The shortd 9qkl56qq+z w5v.f/gdtp*,rub (o orer one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statia;3vtmxat 4 g,onary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (caamxt ,g4 t;3v) he hears the speakers after they have passed him, at C?

  If the velocity of blood flovy3; cs9bxi/6vz/ salw 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 ands; zlx3i s/a/9vc ybv6 reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward 1i )j23n ldh gtasn:6cthe bat at speed 5 m/)hjan snt gi1:3c dl26s 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 approaches a+fy .*c( mmnrqvd+hl 5 moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms *qvnf5+chlrm+m .( yd long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) q3udz+ dr8. 2 .*gt- yfdcubzmwas 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, and it is callf. r8db2zu*tm3 dg+y- duqz c.ed 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 cpn6i96qgxz *n1l:*hmshdp -4 l jxl e(an be compromised by the presence of standing waves, which can caulxle* hl p 6si61qpn-g*4znj:(mdh x9se acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invo(s kywga-jq 9;lves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroke-ysw g;(jka 9qd with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the huma 041nv crpths0n ear at a frequency of about 10rt4cn h 1v0ps000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonigko/. 7q l,edgc boom 1.5 min after the plane passes directly overhead. What is the plane’s altitue.7l gg,/d koqde?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 i.nu aj7i3g/ g$^{\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