What is the evidence that sounw osi1n:)r847f2aggyye.b u ,gbtpc.d travels as a wave?

What is the evidence b3 i3ujaqa/6dthat sound is a form of energy?

Children sometimes play with a hom ( ak* 6cm-+znu2qgg2tna6jf7nz:ok uemade “telephone” by attaching a string to the bottoms of tt :(6n2k z7zn+nu-kjm2goaa* g qf6cuwo paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freque) 6d;;pwr nps bdcc:t7ncy or wavelength to chang wr;st;)ddbc p:6p cn7e?

What evidence can you give that vpqy.d/lj f4k6 um ,:m,k5y9 i;svulbthe speed of sound in air does not depend significantly q9bv:v.y fi, j md lklps/k;u4u5y6,mon frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Wh o,od:3m7ezg kje5gh .y?

How will the air temperature in a room affect the pitch of organ pipes?3k( lq v;md*)rqiyv:y fhz ..x

Explain how a tube might be used as a filterwzdbcb;b i6(-x cf:- y to reduce the amplitude of sounds in vari:; dxcb c-b( fb-ziwy6ous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig.2;-87wqyzysvf/oru1 u: m usv 12–30) spaced closer together as you move up th z v 2mur1q:sf;w-/uyyvs78ou e fingerboard toward the bridge?

A noisy truck approaches you from behin9 vfdid i(- .7fy0btqed a building. Initially you hear it but cannot see it. When it emerges and you do see it, its soun7if -9iftb(d.yedv0 q d is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space w5jwn7 *a3ge2pw* zbg,” whereas beats ca3 75g*wzwawjn * gp2ben be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pzw:zz ;in8wx ( (nmy+points D and C (where destructive and constructive interference occu;((wpmz:xnnw 8iy z+z r) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in ar xuctf6qr2f 2:eas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively nx:6ur fc22q tfew technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can 0jcw6 tzplr75* a*t snbe thought of as a superposition of two sound waves wj7zctl w0*n par *st65ith slightly different frequencies, as in 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 observexfj1 o5qhv3/gu,-a q nr move in the same direction, with the same hfoa5n3-,/q q vgxju1velocity? Explain.

If a wind is blowing, will this alter the frequency of the sog zbx:8u.6rjxund heard by a person at rest with respect to the source? Isgj:z8ux.xr b6 the wavelength or velocity changed?

Figure 12–32 shows various poscdoe5l imflo4 5u 3d.8spyxq r.k +s l:7y46vpitions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the ch4 d. 5 kplfm 3q6+p7u.8dcx:ivles4rol 5oyys ild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengq0.pwv zqab ;+p zj:p:th of a lake by listening for the echo of her shout reflected by a cliff at the far end of tp:zp: z;bva.qwq +0 pjhe lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the siy txs2 +wyr 32,db0gelde 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 vw02 yt+gx b,re23ys ldary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air58zpwda( gh5 5iywavquw:2 u / 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 ab(n 6lol7s(edkove a school of tuna on a foggy day. Wisel7o( nk 6(ldthout warning, an 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 c9*av i5 m2nk 8qfw- l4cjm8sauliff. The splash it makes when striking thevfq*8 im89 n5a4 wj2lauk- mcs water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the co -bk pphj: iszs 9ir0izt:k:7/ncrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Tablek jsip:r/i k9t-::pz bszi07h 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made dxp8w70 ind3k over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike ifk8 ipxnd0w37d the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitug 6ek89znn23sipp7 fy of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level gd q-le5*r2, 6gcp-bebvayzu 6r.b - mof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simud 9ck)zd2f c* g7 o847.f;wzdkrcpdqnltaneously at a certain place, what ;)cc.dzk7dn dzrf*q 8gf4 2 w 9okpc7dwill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain disxrnm ,so5/6-trfjzoneh3iv , 2 bzd(65y1t b dtance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wo,5 15ro-/x3 ni,t 6jbdtdrso vemfhzb 62n(zy uld 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-to-noise ratio of 58 dB, wherb3dya 3n;vn7tao04 q aeas for a CD player it is 95 7b 0a; qnd433otana vydB. What 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 speaking in nor x li4b.qdho::mal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. bohd:iq 4.l :x$\approx$    $ \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 whosqlauw(c//0 f,1l6 i ycnx,pu se 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 raqj7+lfw m.kp: b pe+f05:d cvdted at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibec:k7vqpdb5.: pef 0d+ jwl+f mls 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 dwq96tzca8r)h 4b;vi c B meter registered 130 dB when placed 2.8 m in front of a lo8w9c czv6;hbatqri)4 udspeaker 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 typicalwh: o ((bn)q57oqxnpdly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by thq 7 ((pwh:qno) 5ndoxbis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inte,+p,fa3ab k.-fp2bfo vbu )etnsity increase? Increas,f.bu kbto a pfp,v-a2+3eb) fe by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equ(r/4 awjvs*up-l3sd dal displacement amplitudes, but one has twice the frequencydups(4rd/sv lja3-w* of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a s..lk-bwd ns-p ound wave in air that corresponds to a displacement amplitude of vibrati-kn .l-sdwp.bng air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what so,* zr*xsdhouh,e4*,ssrn9l t und level to seem as loud as a 100-Hz tone that has a 50-dB sound levelxtue, h9 s,*rhz r*sdn4l os*,? (See Fig. 12–6.)    dB

What are the lowest ejx,fcewznn4/4r d;o5k;i2 7 cdmeh )and highest frequencies that an ear can detect when the sound hf,zx)7weje2 dn i4c/5 c rde4o;mn;k level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range ox5kuo6 t8py )gtte7b) f sound levels. What is the ratio of highest to lowest intensity at ty b6tkogu58t) )pex7
(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 frequzz)r h u6(xpz9ency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0)(ph 9z xz6rzu.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What4f4b-bzz-qx c are the fundamental and first three audible overtones if the pipe qc- 4bxfz zb4-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 frequenazpj:,cwz(0+px rce0cy would you expect from blowing across the top of an empty soda bottle that is 18 cm dec ,0+zxzpc0e :wj apr(ep, 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 v w :bzp:4z4yli;j+j.wkr3rs with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requiredb.::k4 zjwv 3y4ij+;s lrrwpz? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thiwd87j7h3d3dt5wptp b 9 a0,fg avsq2zrd harmonic. What will be its fundamental frequency if it is f8p 9s a7adt3g3 d,75hpw2bd0j ftv qzwingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tpobq)s)gs f s1/ho+y2vp y50zuned to play E above middle C (3pyqp/ 1+yz g)h50ssbf2svo) o30 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 that emitcjt*:tff/o wc ,s )xp*s middle C (262 Hz) when thefcow px/t)j:s**tcf, 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 wt/)y 7/tzq6wu(jwer at 20 $^{\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 12–1hwynh5,w w8b3 0 should the hole be that must be uncovered 3bnh58,ww wy hto play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe-*l+. t 4d/hbm sdsjke can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any otherlb*d h4+m/esj- sdk .t frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at twj ddj30cslq) 1o successive harmonics of frequencies 275 ld30 jqjc1)sdHz 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 .r7*dm 1edqpr$^{\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 2.14-m-long org:l l (h 1aq+a+6b kyknhn;zrn9an pipe ata1hqnly+ ka l+(:knnh6z;r9b 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximat; .6rpj-yv ;rvv9p5nvw fft+r ely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the freqr5 + j9f-fv vp rtwpv.;y;v6rnuencies (in the audible range) of the standing 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 6(z (6k3lg3hppafv 9.mmg;sq tm jyp7 when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency (mmpm.as;l(j fkv 9qzyp g6g3 pt 6h73is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)).4908qcc y q f e2(flwfiikxx 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 l58i7 qdyxlym:v k7v4qfyx dq,,4ey 7.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separatyx, f qiy47v8dd7ql7 e4mqx,v5 :ykylely, 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 a 3.b+f;i/sr6wtm d cfk250-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is thc;ikwm2 b6.sr fd/ft+ e vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensio 0uxn ulz,w bszt.o4-8n in one string is then decreased by 2.0%. Whatl8-zsou 0 z,w4unxtb. will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mimkz:z*yd(p o(ddle C (262 Hz), but one is at 5.0°Cd(yom(zpk :z* and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequl shk nvm23tf-t*u4 a,co(u)j ency 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 and C an-t,jk*u43uc)sh ( av m t2flore 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 from one sp8 kow4dwoaohxyp82)4 eaker and 3.50 m 8a)kh84 2od4 opxwo ywfrom 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 vibrating at 132 Hz, bbb-*s1)rugo5 sa 9v olut a piano tuner hears three beats every 2.0 s when they are played together. (a) Ifo9l*s ru5 abgs)-v1b o 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 g 1qltkmfc 1**2.64 m and 2.76 m in air. How many beats per second wilgf *lt*mc qk11l be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz6i9c)yyt 8 byc when at rest. What frequencyc6y8yyb) 9i tc do you detect if 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 fi /7 udinat1gtk qlmuj8 )79 ej/p-z;drequency do you detect if a fire engine whose siren emits at 1550 Hz moves dn)1ta/-k 9;iudljj78m u /z7 tgpqieat a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequvm(zk*g 3/s quency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Am s/vqg*zk(3 ure 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 fqzi:*w 0n7i n- :qyj mjso+t,at rest and the ot, in o:+:nyq-*tjjwf 7zm0 iqsher 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? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ul9z4eqjwj89 (iil m7 zx* wey4etrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fi zw(4j il qj89e*wz9e4xy m7erequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the34 u3p*z+-eaztg xt0ui-xtb x bat emits an ultrasonic sound wave with frequency 30.0 kHz. Wtzt3 ix4gz-+xu* pbu-t30xe ahat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origincea5(t(3bfzo+.vn 4wq rbh-b al Doppler experiments, a tuba was played on a moving flat train carw 4chqv 3b5oet.+a-nbb zr((f 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 10 m/s ?   Hz

  A Doppler flow meter uses /bk.du(n /1veudlm )qbh nx9 .cx 1;kqultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in1qdldnu.;mu)vb9(x.xbk/c/ q n kh1e human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencl:4av 9 i /a1pak8k;1bvbwmu hy $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind veloci83 -oxgne e:uuty is 12 m/s from the north, what frequency will observ8 n3-exu:ge ouers 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 objecea u:n6ikkl(y,.; (ocmwie2ut moving 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 speap fp a25982gj5l oug19vbvbned of sound is 310 m/s (a) What is the angle the sh vpl51jao npgu2agf 52b 899bvock wave 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 the thin atmosphere of a planet where the spk- rzl, fk++zbfku+ k-eed of sound is only ab-k ,l fkf+ uz++kzkbr-out 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. Deterp: k;40 aopqz58 r(bvcruz4glmine the shock wave angle it produces;a8uq zglb4 opz(0p cv4rr5k:
(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 b6t tz. lhsyl;-f;l(3 +mcmno $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhvd f9n ,fobys ,4g -9ijspnyenihqg7c..(a+ 6ead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0i4-g c (d.n9pqvysab ,fyohg+ 6s jien,fn. 79 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 de 9;o/8thj yzrvvice 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 wrtj/8 zy 9h;ovork is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human auddo0q7oi b- x a1vz3fx0ible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It idob1/4 3gm.;nkq 7snewwg1oconsists of many plastic pipes of various lengths, whi;/1s1m 4wkbg 7g wn3i oodq.nech 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 w6ojpry j7d,1m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound levj o,617rwp ydjel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB kq,szz j2n) v0 s qi**+ng cy5dqyrj+(sound and an 87-dB sound are heard simultaneouslyqq*0vys5n, qzsy+g ckid z*j2r)jn+(?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opmkggmqto jx8q3;,x4 v5b/r+v en, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dvkgm gbt8jvr,5m+xqq34;o / xirections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. h+rvr nia2h- 31 lauc)The power output drops by 10 dB at 15 kHz. What is the power output in wa-ahi)nu31avclr 2rh +tts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivesv ,ndf )(+ykr 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 pr(y ,nvsk )d+fower intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications syste,usd4t d(f fpnd23)9/ pvdkvhms, 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 tunedahw6re 1t (c2s8j m wma3v,iyb)m37 in to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 3glggpp(lym y:,/jb)+ m ;3ctotj wv+)2 cm long between fixed points with a fundamental frelg);wl +m,gb pvgtpj:jm/y ()+t y3co quency 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 vibidvxt5gj2;4c;cpiz 4 ration 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 fogx 5 ; d42itjc4v;piczrk 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 strint ddf.5eusi yqzpa6: ,k.m6*a g of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with tha .,.yud5f:mpka6sedtiz *q6 e third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as o phn2le3x:2cbne 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 in2fz/5pge g9 nja 0 g81kp.pfpxb*x+g m the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly whm0bpjx95 1fekpazp.g/ng2g*x 8p g+fat the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The cozzv8/tc h97 5 g0gdrlznductor on the stationary train hears a 3.0-Hz beat freq9/z8dvzg5lztg0 h7rc uency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trw1li au899w:2*y ks2gp rmgwmain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movingyl w29:amsruig*m928 kw1pg w (assume constant velocity)?    m/s

  At a race track, you can estimate ths * nghmug3.xmfr(d;(e 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 straight(g h3gx;r*.mndfm us (away. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a bo-y(ctu5o3my0sty;ark r,w p*v )7efeat frequency of 11 Hz. The short3mwuyf ok)v- psco,*yyr(e7;a 0t 5rter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves6o0 5d,oks6y bzd1qahb f(( qr-:wdvw past a stationary observer at 10 m/s as shown in Fig. 12–37y b,d(k-w q6qdfh51(0as:brzw dov o6. 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 about 0.32 m/s what beat e-qh/j+s3g mw 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 wave3we +gqh -jms/s 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 the .6mtfvll t9b0 f7(mttbat at 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 the0t.7v 9( tbl tfftml6m moth?    kHz

  A bat emits a series of high frequency sound pulses as it approa +)oc-)xetifyches 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 -i e+oyx)c)tf before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine v30kva/5 1eidoum*z wiillage to another. Since lower frequency sounds are less susceptible to intensity loswz/ u voei30akd* m1i5s, 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 compromised by the presenceeihg o0wnt,0s q/ dq)ib-.ar4 of standing waves, which can cause acousti gs/-,.40wd oqrqt b)aenih0ic “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 “s ys3-mc19j-ugimaw,k;lzzgh k8w7,linging 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 be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-lon3 7kh, u9-kg -zywlz ,lwi1mmscjga ;8g 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 thegxcnh7f8u5/ w threshold of hearing for the human ear at a frequency of aboutf w/n8ux hcg75 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at/ q*6b 0b4esdj)tj)yv xuvxckp/ 6g5j Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s 46bykbjtqe/ xdc506pv* j )/ vj)gusx altitude?    $ \times10^{4 }$ m

  The wake of a speedboahqe 4)cbp* i+dt 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