What is the evidence tzlyyt + qi*p0 5 8dpc*49uzbhahat sound travels as a wave?

What is the evidence that sound ic d*m; (p*4v h;spvut a:q(r9ewpddl4s a form of energy?

Children sometimes play with a homemade “telephone” by attaching a stringt8 r ww nrrbn:oi6 2tc7f8(r(z to the bottoms of two paper cups. When thebi tn62(w7f :rzrr(r c 8ow8nt 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 air9m,vgr -sk cpu(7l/zs into water, do you expect the frequency or wavelengts-k vgs u9(rpcmz/ ,l7h to change?

What evidence can you give that the speed of sound in air does not s j,d ce ymw.axld)mj u9h79-ag.s8i+depend significantly on fre,g).daai d+hym78lux9 esw-jm9 . csj quency?

The voice of a person who qub4z:xxy,is -5.9cx /3 saefui -u qyhas inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect thevt( ,pc9w y,;ht d9odv pitch of organ pipes?

Explain how a tube might be used as a filter to redf u.o cfry;a-/uce the amplitude of sounds in various f-f oy/ufc ar;.requency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together azi;j vhj5zrm93r ol )v0 2bdh*s you move up thjzhh;z92*i vodr53l) v j b0mre fingerboard toward the bridge?

A noisy truck approa.mp(9bn g1wh jches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its soum( .19 hbnwjpgnd is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said t2cwy(9 3agb ino be due to “interference in space,” whereas beats can be said to be due to “igynbc a2w 39i(nterference in time.” Explain.

In Fig. 12–16, if the frequency iv ;xkue6og0 wdh( 3udp9q4q6of the speakers were lowered, would the points D and C (where destructive and constru g0kdq4d6;we 3xup9v( 6oqiu hctive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas 3a wqn/ima7qp6 f8sbg,et 4d ;pog7o7with 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 noise. How could adding more noise redpatiq 7,of3ps;nqeb4 o7/wdgm6 87g auce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thou+d ; 2,xnn5oixodi08n rg)da zght of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies oz;d2dgnnxna dro+)x,i i50 8farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift 5c*f5;g v y(t w+a,fgd yt20pjiz8eah zeh2l ,if the source and observer move in the same direction, with the same velocity? Explai*z yhge (5lcgaa p+t0,it ;5 j 2e8yv,dfz2fhwn.

If a wind is blowing, w,+ k/pjl0in m 6yg)ol 84kytkj+eg- liill this alter the frequency of the sound heard by a person at restkly+-/ +mk6n)kl4,gtlj8 io pgeij0 y with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor o-c/6ss cofor 18 wx5qis blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain youo ox615ws8qcfos -rc /r reasoning.

  A hiker determines the length of a lake by listening for the yij5ortd*r 54 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 length of the lakerry*4i5j tdo5 . $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. sbdl c(;t yk)7 5w(lptHe hears the echo of the sound reflected )b;lcytsd7tp(w k l (5from 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 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air47 ;xwk1n auyval0vvh5f) 7dx 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 juo ejf6 tw 24d*ekdx87l+f5bktst above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfirelkoxd76*45 ebkd ttj+ 82fwfe is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splasxk,ym2*tnx /ean0w:ki zhfv,l4f 6 / e3qy2kyh it makes when striking the water below is heard 3.5 s later. How0 k3fykl// ,a6tm xz qw42,n in hy:eyv*f2kex high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concretej8/-6aobd grk pavement. A moment later two sounds are heard from the impact: o k68-ord jab/gne 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 mnecu 8*rr;-w hi/ak q3ade over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the rwue8kh3na;qc-* i/ rtemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lev+ purb1 79sr sbih+6zxel of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity 0w8lpi j( ;zr0e*bkuy is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of t*:j( d26 vhu1spv dki95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dBvds2t d6j1i(p* hv:k u’s.]    dB

  A person standing a certain distance fr8nujmc e34* -/eawltw om an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shutej 4 l8-waen/w u*ctm3 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 v,029pbp5g mpd7tbunlawk.0 58 dB, whereas for a CD player it is vp 7ndp9kbm020w5l,tb g.uap 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 c8ti 7awqld 1.mqc0r+f onversation. Use Table 12–2. Assume the sound spreads roughly unif 07. +wqfcartl8m1qidormly 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 eardru b6 jihft;iu;b0txg46m 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 g 5u;x4moq8wo(cnw qesuz2-)m5g +wkrated at 40 W. (a) Estimate the sound level in decibels you would expect at a p+gxew o;5 ok)5m q-cm(s4znw2 8gu quwoint 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 when placea, zxp2)mc.gl 6is4aud 2.8 m in front of a loudspeakerx,zi a.p)lugs24acm 6 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 di+ 1rvg (u*su 59 es-gmp/phvcq 0in1lufference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Seguph(+-r0vuvs19mu ipcs/ l qn 15e*gction 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,t(m9sc1fdwk70b j pd+ (a) by what factor will the intensity i1(mkjds c0d79b p +wftncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but o fec(dn5rbq:vp (3 4zp ,evvt/ne has twice the frequency of the other. What is the ratio of thpdc bv:er,epv/ 3(vft5n q4 z(eir intensities?   

  What would be the sound level (in dB) of a sourzugr47oc -5 hnd wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13r5uc-ho7g z4r mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz a0s/ . z/d vksr xmq-ir*9n:g1of1 llztone that has a 50-dBs v:/d lifor zr9m lgz-0*kn.a/1 xsq1 sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies jxb 5)kr 6c0)a1mbhfk3 c ptij,bx(h+that an ear can detect when the sound level is 30 dB? (See Fig. 120b kim p,5fctj)k+hrb(xx61h)ba c3j –6.)

  Your auditory system can accommodate a huge range of sounuv t/smj(ql t5,nz .8cd levels. What is the ratio of highest to ltszl(j/t nucq,5m v.8 owest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin o0 tip*v8m l94cvwv+ y1+kw+w wkhn *qhas a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stringcp 8w*0*41w ymo++vwhwq9nvk+kitvl be placed?    N

  An organ pipe is 112 cm ltt2bma8v2 b3 0bnbr1.cmcyf 0ong. What are the fundamental and first three audible ot00abb8t3vncr.2 12 cyfm m bbvertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blod hj8x6vokn9dn:dr8;u/gpn7tc kj6h 1;pa1rwing across the top of an empt1 9r;vpj c ondk;t/xgdurj d6kh:p8 n nh6a178y soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning vo1mc fry- s+0)1rzz ethe range of human hearing (2-s fcyz)vrm1zr e+10o0 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz8 vbnlr82h4/boxmkfj +xw9h( as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original leohh/82x 9x 8fn+r wv bj4kl(bmngth?   Hz

  An unfingered guitar string isn*ksw g0kg epj3-;gz : 0.73 m long and is tuned to play E above middle C (330 Hz);g0zk-gnpg jks* w: 3e.
(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 orgavqo iotu1x/l4yv9 p77 ztk42 vn pipe that emits middle C (262 Hz) when the temperaturep7 u/xio4v7 to kv4qy9t1vz2l 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 xeq3ynpq (p8)(q9i - we8cadi $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute b,m2mftrsgq * (yvf2,in Example 12–10 should the hole be that must bq,gsf ,v* r2mybmt2 f(e uncovered to 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 can resonate at 264 Hz, 440 Hz, and 6xv) tf).:,ket(ny vyq16 Hz, but not at any other frequencies in between. (a) Show why thi xky t)q:.fyne,)v(tvs 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 twoxj(j5.ehw 7 c1+69nmgw mf eo0r+k nxm successive harmonics of frequencies nx9mw+g.h0e+mr kjn(6mc wex 7 of15j275 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 dgnoz80kqy-i +b *y;5c v-.jo rx2x gv$^{\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 wit,-lgwlf .3 uxkhin the audible range for a 2.14-m-long organ pipe au 3wx,lfkgl-. t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is 7o1oji*sozv,l-z w 0papproximately 2.5 cm long. It is open to the outside and is1joo,wpl zov0 - *7zis closed at the other end by the eardrum. Estimate the frequencies (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 .pih,w:h 4uul every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the oth .wh:,pulih 4uer string? ±    Hz

  What is the beat frequency if middledh evvttl5r,9*4 /ylb 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 operat re c(bp9u*ip8 gfn8c7es at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultanb7 up*(8 er9c8gnpcif eously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning forkc2 xep,i /q (avmp+9jm;ux*+ic,dck r and 9 beats/s when sounded with a 355-Hz tuning fork. What is t iumqjp,+ c,2m+ pc*x9aiv(d erkx/;c he vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 dmzjgdia pstblt2:j9. -36h(rc0 qd(Hz. The tension in one string is0ptdl(t.sg3 ai 9qbd :jh6( djzmc2-r then decreased by 2.0%. What 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 middle ij e*hyn1qr4:C (262 Hz), but one is at 5.0°C and tq :4r e*inyh1jhe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whe3vwqb /n 64vtjn A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are s3 bqvw t64vj/nounded 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 peri+; .w:ur kivd7ru jdu*-x js/son stands 3.00 m from one speaker and 3.50 m fdui* +sj.dvx iujw ;r-: ukr/7rom 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 suppo:5t 3uo1k 2mxfmrnvr.i84ie 1bch 9cosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. 1extkb4c2cm53oh8 1mrfvr i9oin.:u (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many b 1mp4po;b-pxbeats per secop1 xp pbm4o-b;nd will 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 Hz when at;smc vq82af o;bk12z i(oa75eq9t vv:o dd d4s rest. What frequency do you detect if 2vd;zt4aq 5 17scv i v :d29mo;oabfkd o(esq8you 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 0tgy+aa 3g5j)oa k ;z:.kwwjodetect if a fire engine whose siren emits at 1550 Hz mo:+w aaozk. yjtkow)gjg 053;aves at a speed 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 toward yoy f3cl-xe+l/ejc9 e.8x4xzj8km j-m wu at 15 m/s versus you moving toward it at 15 m/s Are the twle+k8celex -y43/ wcj9jx.mjzxf m-8 o 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 frequ5p./5m +a9b yqhldli aency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5./9mqh aid l.5l 5pbay+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 thezeg ,):l ybgqjp0se 6)m returned from an object moving directly away from it at 25 m/s0 zg) eblj6g): sq,pey What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wallelda7gry,e7: cromxe -;nlgnj* 4g: 6 at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 3 y6 d:ogg7:l a-jxer mcr ;nleg4e7,n*0.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat aj859eyfy*ld train car at a frequency of 75 Hz, and a second identical tuba played the samd f8ly9ey*5a je 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 bloot ch5 3obw( brvx:cer-w (/5gud-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound inog t: r b/h5e-wcvrw3ub(c(x5 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 frewhae 0roo,y :7quency $2.25 \times10^{ 6}$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 velocity isd fdoxp6(k y8 d00m*hl 12 m/s from the north, wh(*o0lyxd6 d8pdm k0f hat frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if it37xgch/ dq / suz0kmamqg-u+;s 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 is 9wnt(-u, ll zpqsd0j1310 m/s (a) What is the angle the shock wave mak(lznl, u 9t-pq 1sd0wjes 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 ahs)vxzurg 1(;r w: z8dj4* grn planet where the speed of sound is only dwru8h(4) v1nzr :j *zg;xgs rabout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine th k,ye 1b:jaoc;.azy m*e shock wave angle it pro,1j:c.;yb amy*ekoz a duces
(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 v08czmj9h0lsrof x-d295 thz$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan yw 0q*pi2jx+je 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 trjx+iyq2 0*jwpaveled a horizontal 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 sound pulses do x*9ovp.:lu,5yiu iueu)o:bl wnward 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 u*5:llyi:ouu u)ob pix9ve,. minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible ralr7 iiym5z n k(ftj. qy;,m6*hnge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display ca2n.i kpogqnfi* ) 8zw-i++h colled a sewer pipe symphony. It consists of many plastic pipes of various2-oifn8pqz)kg i+wn+coh.* i 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 from a person makes a sound close t9myss8l x (2gko the threshold of human hearing (0 dB). What will be the sound level of 1000 su(x gskml82y 9sch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound or11q;psaj f0 are heard simultaneousa 0ro1;q1j pfsly?    dB

  The sound level 12.0 m from a loudspeakean *5p;6 ),ji ncpztsu:wosd )r, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assumin;)zs), 5apn no:*dptci jusw6 g it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outputrv1n+syn9bv t5e 9g )f at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHzrvy)+n5e9v tb9 1gfsn ?    dB

  Workers around jet aircraft typically wear protective devices over th:)ck j-v:-7sqm9x b 4 dzshvzweir 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 from a jet airplane engs:-4zwd sk7v bvz-c 9m:hjx) qine?    W

  In audio and communications sz4 niddz:302x ima8 zlqq(/qg ip/8gsystems, 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 lnmmsn0n 3o-ni/9 k5ya frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm lonthznhk /s l./9g between fixed points with a fundamental frequency of 440 Hz and a mass per/t/9hhzn s.k l 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 filledj0x0qdorao: j ye-w crn.+t+4 with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the airyono-w :.dtr aj 4q 0cr0+ejx+ 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 fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is nei4rw:3k d md1par 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 the third p kdi:4m1w3rd harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop (v- ht utpcfqp6y8 ;9/u$\frac{1}{2}\lambda$) 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 range coming from twopt2 ks41 vx6bf sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the2xkbtfv16 p4s 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 whistletm;+ i9mbd6 kedz2n1cs. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is tn+9mdme6 ;zk ibc1 2tdhe speed of the moving train?   m/s

  The frequency of a steam train 93b lraslf(1l)z:gnxgf d1ln +( q,gvwhistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity(r gax:flz+qv 1nfldg)b(l3gl9,1ns )?    m/s

  At a race track, you can ,in+a;p1m s,xu+lf qrestimate 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 cerp1xsinrq+malu,; ,+ftain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes,gj8iqi i ,)t4k/tj+lnqz:sy( sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lqisl:ik(t,n) y j4j zqg/+i8 tong is the other?    m

Two loudspeakers are at opp00ugess5 a,hh7rk/x nqm;86t:g jq unosite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat fr0s6 :smqh;kx8rtngnj auq 7u5g/,e h0equency 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 normaaezi 01(/lamgufz siu5(x5tq36sh / ;cb n-wzlly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected 5 hflteq-aszn;a ubc/6 m1/(ixzuswi3z50g( 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 tnz.(l-y*q d: 7d* hawretvn.jhe moth is flying toward the bat at speed 5 m/s The bat emits a sound wave owtd veqhryd(*lj na7.. zn:* -f 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 approacho-0-nq thsxg 0es a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the oxt h q0gs0-n-next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villja /: mk*t9mzg r4lci9age 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 called the F sharp (or G flat) horn. What is the f :/ki rt*99 4mlcgmazjundamental 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 l0ehb w5+se/co n5w-esz+ o8bcan be compromised by the presence of standing waves, which can cause acoustic “wen- bwho b / +5lzec08+so5esdead 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,” invf ntj8.z3 ed-( /kqmddolves 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 em qd/d.fd ejzk- (3t8nmit 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 fum5rh f w:5zp.61dy hwor the human ear at a frequency of about 1000.5: hwp 1u5zhmwfrd6y 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 thewoy)3/5xxb:ea gsbj x -ab0s5 sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? 0: e/awsbxxg5s3 abyjb -x5 )o   $ \times10^{4 }$ m

  The wake of a speedb4hs 9j6 o3hkgxoat 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