What is the evidence that sound travel8s0nb;xe * gg.jj -bbts as a wave?

What is the evidence that sound is a fo ph 4a8hqnuhvrxuf ,up7 2+4r;rm of energy?

Children sometimes plabpims,u /hq3;2 m+on cy with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the o2cnb q/; m ,h3+uspmisound 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 frb6 /)t q2/s+a alkybpyi*oqb-1j.op dequency or wavelength /2 l-qdib1.o/aob6ypayp)tj k+sq *bto change?

What evidence can you give that the speed of sound 9tu/im*zv d ysf+k+o:in air does not depend significantly on frequenc z muiy fd:ktsvo9+*+/y?

The voice of a person who has inhaled helium soundsd4;t:jj ebe1m2tdmv * very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgokf2v t5l(l;vn. j h)zan pipes?

Explain how a tube might be used as a y -nrytvuu 7 ;c7)3a2a-odkpxfilter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.)ont adkcy ay3 )u2--7 rxupv7;

Why are the frets on a guitar (Fig. 12–30) spaced closer tux;g9whbp)j 9f ghx*- xz)d -uogether as you move up t9h wxfg)-- j 9bgdhu;upzx *x)he fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you heare.e7p+g,pw-. tgqa wv it but cannot see it. When it emerges and you do seg7a epv.-.g ,+ qetpwwe it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in raf:u3 wpi,) vrq.k3x space,” whereas beats can be said to be due to “inq) r xf kp.wau:rv33,iterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would th7yefz o +wry4n71vv m3e points D and C (where desyy 7wfz evo+n7 34m1vrtructive and constructive interference occur) move farther apart or closer together?

Traditional methods opakd t qt8(ha5;b g3y 1 or0du7ogvi/,f protecting the hearing of people who 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 detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise7o18h0 gyuapqvd/gkt 3 ba;5(,iro dt. 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 thoughtl* zb*sazbgdv 2i,4:x of as a superposition of two sound waves with slightlbbd:g s,4 zz*v2xl*i ay 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 souz3 etvzh6 br;n:e:av- rce and observer move in the same direction, wi:v: rv;ez6nh-a t 3bzeth the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hear*w+ w9 zeq9fl h6b6kerd by a person at rest with respect to the source? Is t96+6kr fel eb9h*wzwqhe wavelength or velocity changed?

Figure 12–32 shows vario xwinl r7eh48(us positions 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 48liewx7rh n (the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by liy1/3bad m8r 6w;nyi(kx(j sz9uqjo /u stening 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 shout y/daxs6;rz/u9jou(1ym(b3 q n ji8wk ing. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He aw g7g(:a3swh hears the echo of the sound reflected from the ocean floor directly below 2.5 s gawg( :hwsa 73later. 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 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths i8rkdf km8owi2;m 6vb1 n air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a schonn)bx- e4f w;wol of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1w-w4fnn ;xe) b.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash-bo; cyul0cf+ it makes when striking the water beo 0lbycf+; c-ulow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sqbcfv3.jkw evs8 87h9ees a huge stone strike the concrete 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 a 388wcv9fse.7q kbjvh way did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over on2wq:nyldo,2 a8k -fxue mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature idf,- q8k 2nlou2axyw:s (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 po+jja(/ ahw. 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 whosj:*sbi/dez2 o 8q3-o j9xix uqe intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a souiza b0xv dek7r- 9d/8wnd level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? b/x-wd8ied kar097zv [Hint: Add intensities, not dB’s.]    dB

  A person standing a certad0duc*/n pd7v3 zaj/ gin distance from an airplane with four equally noisy jet engines is expej /p 7n0*ddu3gcd /avzriencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hawjs0:fqjs /fd s)2 2laxt; g3eve a signal-to-noise ratio of 58 dB, whereas for a Cd faqtj f3;):202ses/wx jl sgD player it is 95 dB. 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 normal convdtc 2*+*zo ibe3)gj hyersation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered o )2h+o*3 jiygtc bdz*en 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 strth3 2prgox(- 72 uvmyiikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is r6 gf)4q2x okvgated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker cokqg62 g4ovfx )nnected 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 dBid 6)u3- cw2oh9-;ov/ wzusxw z y* sqmpie6z: meter registered 130 dB when placed 2.8 m in front of a loudspeakerzso)- / 2eoq 6mwh*:iu6d-yw;zwvs93ixz c up 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 7q7xl ax8t+ g:pf 290gbynxlg2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sect:nxxlx0y2b gf8g9+ap7 t7glqion 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensbj 0*nbqcnw0. ity increasn .00cjnq* wbbe? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplipw ve g+)iun7)fyv5n *e7il3 aff)6 bhtudes, but one has twice the frequency of the other. What is the ratio of their intensities vlvwf eu)hnp7fyeg)65in3bi*a7f)+ ?   

  What would be the sound level (in dB) of a sound wave in air that cor6: ugpq op f4xm24iti2responds to a displacement amplitude of vibrating air molecules of 0.13 fi 2g6xpu4oim :qt4 p2mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to se9w-j26a/qlh zvx.g08ipoxw(c(oa o lt / ozp5em as loud as a 100-Hz tone that has a 50-dB sound leo/o2t j h(z /cpv8wa9l axzpi60 x5g-.w(oolqvel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soujv7:2(auaxy (y i5oxeb+d6 eqnd level is 30 dB? (Seei2exb a6dy :y (oj 5xeau7v(+q Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What isy kl3e0y3e n ,zdxxa4biq4p,4 the ratio of highest to lowes3pk4,d4a zb0 eily q,43xxye nt 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 length of 4j58oc:*q mmjhqh c -rthcc4 j h5moj-8* :hrqqme vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible ox3z; (u jc 5rnc tz+63yf nxk)lv67dnmvertones if thlc nyx)z53x3trd6 c jzn+v n fu7k(6m;e 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 blowing ac lw 07aey *w+veb2 up*nqs2l r64v0ffzross the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closefe* 60v02b 2n f4*zl7+veul swwapqryd 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 pipj iyef ke-l52vh:4sh 0es spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the len-iyhje5k h0v 4e fl:2sgths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 c1vgi h-rt/3 j7dgso x99b yjjx37zb7yd+ni6 Hz as its third harmonic. What will be its fc- /9 nyhsdj itgj77zbbd1xv3rx +o97j3i 6 ygundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar sd xhcf 1qar/8:tring is 0.73 m long and is tuned to play E above middle C (qrf:/8h1 cdax 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 open organ pipe that emits middlv x4d3/bsuke3 e C (262 Hz) when the temperature is 4bx3ksedv3 /u21 $^{\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 a48w(jtu lt *ozt 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 12–10 should thp y5 2qkgq8, n*l2dukwe hole be that must be uncovered to play Dkydg5l2n qp, u8*2q kw above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, bu2fmj9mxj rdhxzv:.cf;o,e9 6 4p9p mk t not at any other frequencies in between. (a)p4 fmo2; zxxcderk pv.m:,j96mh9j9 f 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 mz ,2c1 qu*vanj long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hc 1qnjz2av*,uz. 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 bxvuuh :gzjvh .e1(:c* 2 d;ks$^{\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 fof + ,ekyim*zy/r a 2.14-m-long organ pipe at iym,key* z+/f20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is oplm *d-be6xrngec i (9q:dn(1b en to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. Weiln6cx(gbq( r*1dm9d- e b:nhat 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 t,7l; qixhg2) wl dla7lo adjust two strings, one of which is sounding 440 Hz. How far off in ,ix7lal; w2ll )qdh7gfrequency is the other string? ±    Hz

  What is the beat frequency if mid z5t wha ni:dax6p77oezl40m8dle 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, whia9df9tik-kn i 36 tw)ole another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whinf 9k)tina69t d-koi w3e 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 350-Hzovw.q a;;fcfc6 dz(,vzqnx44 tuning fork and 9 beats/s when sounded with a 35z,; 6zo a4.vvwqf cx 4(dn;fcq5-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tud2,75,oma bt tkt bl7gned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings ar7b db5t,,lmtakg ot2 7e played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to plahqp,2;pu g2oky middle C (262 Hz), but onegh,pqko2;u p2 is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bu1 zm rtpx*.-sgvkfn vy*2 7m, has a frequency of 441 Hz; when A .17fz kmrny pu,v s2xv -*g*mtand 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 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 3vh36bw*p qnq45 nr u p(y3vs,n4v agc7.00 m from one speaker and 3.50 m from the othe *sv 7vq q4w5 yn4npa(nh6upr3vbg3c,r.
(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 vn;994 u5djzmn0nzq4oiz muj. mf:h/g ibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating mmi zj4ognnmznqf9zuh/4:;ju 5. 09 d 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 q j53f38j+sttptz y8c m and 2.76 m in air. How many beats per second will be heard? (Asj8y3t+q s8ztpj5 c f3tsume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eng:l. djd5qk v )e*n/x9hrxs dk6ine’s siren is 1550 Hz when at rest. What frequency do yoqjl x6e):x . h9v5kddn/ *skdru 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 frequency do you detect if a fire engi/mspy 0 nnu15wljk7 3xne whose siren emits at 1550 Hz moves at a sljw sk mpn1 503n/7uxypeed 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 moving toward2 rovyaijfromz/:6k p 6a4*.w you at 15 m/s versus you moving toward it wo4v6a mr ai.pf6y *k/z: roj2at 15 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 f-n1vub:5w kbvrequency horn. When one is at rest and the other is moving towardbv ukv-:5 bnw1 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 ultrasonic sound waves at 50.0 kHz and receives t/o/xpa9zxd)r;n*nr) gs0l1(s of efthem returned from an object moving directl )znr9so1lxxfe0/;g o p(rtdsnf/*)ay away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a if.kez h+do- 8qdus75 speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave wh.7-uddf5+se k oi8z qith frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopples4+)z4ada lx tr experiments, a tuba was played on a moving flat tra) zx44 d+saatlin 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 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supp64xxq(rh rorch/ mv:q)8 g+ iaose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is rx(c6qx/ 4+oarh i)v gr:8mhq 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 ultr07wdvc -x*i atasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind 7zua8ft iy(nja8 im(lcj;3w, velocity is 12 m/s from the north, what frequency w w((act7388;u alz m f,jinjiyill 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 modm fu 7h 2ytbw8,7eo-fving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound isqk)4vfel /3fj1v qkk , 310 m/s (a) What is the a) jke1vl,fqv3qfkk /4ngle the shock 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 atmoses/ p h+grwz6p)-8cr tphere of a planet where the speed of sound is only abour/s6phect)+w 8 - rpzgt 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 of 2/kpyw:td5ecean. Determine the shock wave angle:f/deyk2 pt5 w it produces
(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 pgcuug j)p n4)lu9e c4-i 4tw*$/theta$ 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 99rpc6.bvkaceg lf3 6lj* +an above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizvc pg*b9la 3.ae+ckj r9f6n6 lontal 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 tha 7;qc0tas pnj51g kj5h(qutx1t 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 tq1xk 5jh5;j tt qsa7n pcu0(1gime between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human31f,v qlfq5y(vjt2 c wmfg38x audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disi2bm cvtv e0n4z8 m:h.p sbpt68mfi3,play called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on b43 8fi6mm:8 vppbmttnsz0chev , b.i 2oth ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold ofy*hd6 1ubx1w2f b ayb.dsw//f human hearing (0 dB)su ayd6wby2 b1b.w1*/f d/fhx. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when ckjrn6/ jgt3-an 82-dB sound and an 87-dB sound are heard simung/crj 6 3k-jtltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is g, jcu3tw 4nm1105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally,ugm3jnwc t 14 in all directions?    W

  A stereo amplifier is rated at 150 W opj eovv*e 4il8 d7jt25utput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the4e7p8lt2jd*5 vv ji eo power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protecti-/ (fm4fv jauu2s:2;em yaccvq*rfm; ve devices over their ears. Assume that the sound level of a jet airplane engine, at *4 v; q2uy afce-csuf2m(mram/:fvj;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 from a jet airplane engine?    W

  In audio and communications systems;qa5pu2mrz6rh-- nep, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frywxc 1x*ls*4qx 7 r2z1jv7d kpequency 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 lonlwy- 3.f j/ugkg between fixed points with a fundamental frequency of 440 Hzkf-3ygw/ u.j l 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 abqq/a;,wzyh h b) n6n1 4tto7ogove a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fo;ohqo wn) ztt741,nq6abh/ygrk?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one cs:hdh rn/3 / hjbh i1(39qsmuend and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in hh9 cqs3nhr 1b(hu j3/s:dm/i the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop )2dyr6+bd /obr c,o ax($\frac{1}{2}\lambda$) 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 t. 5ru,xot ll1q:o(cxd he 500–1000-Hz range coming from two sources. The sound is loudest at ,cl.uoqdx(x:t 1l5ro points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz wl 2k cagf(yh .2m;fh)qhistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beatc2aqfh;2)lg y.fh(k m frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Anf rh9m d)v-f7fter it passes you, its frequency is measured as 486 Hz. How fast nh mf v7)-9frdwas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed loxo)t( kd.d( 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 fu. x( dto(old)kll octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frtk- (t7lccnb4 p)m(ir equency of 11 Hz. The shorter one is 2.40 i-trnm t4c p7k)((cbl m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves;cqat a*7ylf xt5-j8y past a stationary observer at 10 m/s as shown in Fig. 12–37. If the stt*a;cl y7f5a jxq 8-ypeakers 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.dgb:qg q7lvl7 sh v,*:svb75l32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected fh b:5:q b*lvdlgql 7s,sv7v7grom 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 shvh 0v/ l3/ca d6x(vfrpeed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is// (vhhx0 6f3avlvrc d 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-w 2dka/pxgy zv.a 7 mr4qd)w+s *l-d4 y(dwvz sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and eacd.2-4z*l xv-mw+ zv4sk7w/ydqdy(g war a)dp h 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 chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once use8dld4aii*:zm6 w6j nkdjqj47d to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long kmja4jidzjd8i:7*d nwl q 646horns 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 presence of stand5ly yy hn(nqo;r 4o6v9ing waves, which can cause ac oh yq(nvl5y94n6r;y ooustic “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,” involves a long, slender t8pviuf4tk:nxw188orym t7* aluminum rod held in the handr m kn718u8tt8i4*wto:yf pvx 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-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 human ear jpyd ;tgf7l :cbw(lt/k8*jq5at a frequency of about 1:w*t y /5g qp c;tdkllj7(bj8f000 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 gr. qv,5k*wlvs +-ol b (e1iifnround hears the sonic boom 1.5 min after the plane passes d vfllwn is -qk5o1r* +,v(i.beirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1d6w2l9hv s8xt 9i2bye5 $^{\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