What is the evidence that sound travel5hrn9p 8ffj: es as a wave?

What is the evidence that sound is a form of o(val0n 1(3 kyep)fi henergy?

Children sometimes play withm/2 e77k 7nnbzejr .tr a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a chilj et72n7rmb e/.rkz7n d 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, dq x7u)hj;o,zm6 8pbhco you expect the frequency or wavelh; xz,pju67mc8hq)ob ength to change?

What evidence can you jfsc53h .exggq7xj8 +give that the speed of sound in air does not depend significantly on frequency?xe sx+f5q .ch8g gj7j3

The voice of a person who has inl,z+0qz ;bqpyhaled helium sounds very high-pitched. Why?

How will the air temperature ix+ea(dl*7 qramqf5s2d5roh2 g5 l2v in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundsha9t;x+zia ktsv j 9dyj7.,;t in various tx+y jia9h tads7 ;zjkv t,;9.frequency ranges. (An example is a car muffler.)

Why are the frets on a guw3oz4e4 :/w; qgayn7c u qkr4litar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge?y an;/lukw44:4 3 wqgzeco r7q

A noisy truck approaches you from behind a building. I (fe u4)/:v:mu yd,ygzyd 5, hbgq5tehnitially you hear it but can)eydg:,y z4v g bmeq/h(yuuh tf5d 5:,not see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whe:g*iwpj)d2 in reas beats can be said to b:w)nid*2 jpgi e due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wgy e v;uw8ih07ere lowered, would the points D and C (where destructive and constructive interference occur) move farthereivw0 yhg;u 87 apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with vwm bnzy5;w 7(r y2ad+ktp1x j:ery 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 m+;ap( d7 wtm5r y1b2xyjzw n:kore noise reduce the sound levels reaching the ears?

Consider the two waves shown in iooqs5q ci0+2 Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different icqo+02 is5oqfrequencies, 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 ;w*zb61w kdz i9uqq7zthe source and observer move in the same direction, with the same velocity? Expla9bw zziz1 *qd u67w;qkin.

If a wind is blowing, will this alter the frequenztluy :j1d*wx (8h q5wcy of the sound heard by a person at rest with respect to the source? Is the wavelength or veloctu yjhl:xq(w85*d z 1wity changed?

Figure 12–32 shows various6qkzk.5l:zkq j 1uf( 9h) klis positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the i5l : zszlk6 ukqjkk(1.q9fh )ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listed :s(+udaw tr2sbmzx/8o, de9ning for the echo of her shout reflected by a cliff at the far end of the lake. She hdabwdm8 ,euro /xss9 2:zt+d(ears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just0 poisp4qy1g9 +f:2d0obfvfr 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 seaw9ofv1pogf bs +4 ri:dq0y20pf ater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 4jy nms t/h4it1dm;r-2b0 fmo20 $^{\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 a8 xr10eqvjf1h bove a school of tuna on a foggy day. Without warning, an engine backfire occujrv8 x01hfeq1rs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikinf wosu7p2o10;hdqr- ug the water belouqdpuho; so7f12 0w-r w is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grouny3tz 482i kom+6s fcsgd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and tifg2zcok3t6 +ss8y m4he other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the * gkta1*cu-yl “5-second rule” for estimating the distance from a lightk g*a*lt uc1-yning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sou+sn0cer * sa xn :li2dvcu2u9-nd 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 of a so i.h1;q++llaaimh wu,und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leveyw4sk+v mtz ;+l of 95 dB when fired simultaneously at a certain place, what will be the sound l+4vk +y;wtzms evel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance dd9j 1n4n 8s(p;zfyw tfrom an airplane with four equally noisy jet engines is experiencingnz1js dw9ft4dpn8(;y 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 have a signal-to-noirj7zv e3n65: h2u-t hisvxd/wse ratio of 58 dB, whereas for a CD player i/ dx2tviu5h r-nv6 jh:7we3zst 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 2c2 u*n( z gv(sqvbad8speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the moutbazu s8( vgv2*qdnc(2h. $\approx$    $ \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 stri45tcrqzi c2n) +z8tcx9sx zg /kes 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 h mr t.t ;g2qykz(i8*urated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker( .rk2 my qh;zigt*t8u 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 registere(k krnuwc9y :u/ukr18y fj03 ud 130 dB when placed 2.8 m in front of a loudspeaker okku8uyu 0n:ju r 1f(y3kwr9/cn 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 s+7n d;nji3l7oq lkiq+a 7ad -cound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hi+ 7a q anld d+l7;7jn-qio3icknt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wha.vqbmu j-s nz+a+:t3rt factor will the intensity increase? Inaz v+-n u.+jt :rmb3sqcrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amb 7.k+kx *g-d xmjog7mplitudes, but one has twice the frequen-bxkk*gmd7 .m xg+oj 7cy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) o tase.jz8 y,/j ( wvk(1:yfudef a sound wave in air that corresponds to a dispw,jva(u.yd tkfj:8e sy(e /1 zlacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tpx6 /rxoy)2zjlu v*n3one that has a 50-dB sound level? (Sjx)xr / z63*n lpyvu2oee Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whmnawa*kp -yvk (2 (*8oaslvp /1 bo;gben the sound / b pv 8 g(a(ob-ks* ow*panla12m;vkylevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soun4ab irk6fg3;e8/nbr7o ne4epd levels. What is the ratio of highest to lowest intensinb6bak e 83i/e4rng 7e;4 orpfty 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. Thehb5)v-r kf ej0z mc) y)u8llg+ length of the vibrating portion is 32 cm, a y+rm- j ge v))ukl8hf0b5czl)nd 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 fundamentam;n95bc 6:i.yl6gjep. b jj 7u-hftzll and first three audible overtones if the jl- b zu:jf6ygnpjimt.5 7h96b l.;ecpipe 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 across the tb. -)s+g uijcwop of an empty soda bottle that is 18 cm deep, if you assumed it was agi+ wujc).s- b 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) iv tc:.vqxfe4w+wp: spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipesv+cq:):e4 .wi pwvftx required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency oddwr/8-mgvt9xvn bk 7 6/4uwsf 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of wx 4u9rsmb 6wdkv/vd/-n7t8 g its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middmtv4p2mo k0m2y 3dml9le C (330 H4kyo m 0vtdpm23lm9m2z).
(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 t1w1gdt a vx1 7g8iugpdct1a*6 hat emits middle C (262 Hz) when the tt11t * cuga1wxd1gdvp7iga68emperature 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 20i oqtj1y2. khxlhg20 1 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exn ;isil. (;jxeample 12–10 should the hole be that must be uncoin s;; e(ilj.xvered 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 y)w- mjxwgrn9,z . u/+n/qs viHz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is jr9, uig n.mqv)+wny-sw/ xz/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 affd 5p.9byxu6-t( jd6co* rmnt two successive harmonics ofyu5o d.dcj f6b69xpnmt-f (*r frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 -301lgxzw4cjwm/)l7 m *tl de eh6xsy $^{\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 2 *9yx9 mfwodvd u;pgi:*4 9vwlv)dgyfor a 2.14-m-long organ pip flym 99duxyvwv)gg:do;29*w*v dp i4e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appr):tc a) tnz:wkoximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer t tza:cn:wk)) to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adju)3tu-ysg25 lz-wx iwa st two strings, one of which is sounding 440 Hz. How far off in frequency is the othe)wlts -w5yi2x3u- ag zr string? ±    Hz

  What is the beat frequency if jzc0+pga( 7 k:rko d*lk4th7 ee6c8fwmiddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anoesfrwd f 42ef+j1,bog- 0(t dither (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 simultaneously, estimate the operating frequency of -(+j ofrgfe2e ddw01sbi,f t4brand X.    kHz

  A guitar string produces 4 beats/s /yfgr2 drgm w 8g(qm( dpzj6l..+gv y8when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequend.gvfg ym(lwr g(d8y j6mz./28 r+qgpcy of the string? Explain your reasoning.    Hz

  Two violin strings are tun9p 7.gx6pop of,gzf.zed 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 z pgg,o ox9f67f.pzp .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 k6 d b70pzp2+h)i7gmfsv3ui 2 9btops C (262 Hz), but one is aphsb2i0+6mbg3) o92t fid vup7kzps 7t 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freqjq lw rpx.ea+r;42 p+fg7s 1puuency of 441 Hz; when A ar+fj;apqru42 +exp1 sp l w.7gnd 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 3.00 m from one speak:e a t;zj 7i cl7b1.d5pgsjbh)er and 3.50 )h1tp lj77ceajb: 5 .;bds zgim from 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 (iz*yq*qj ,og be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ? i ,qg*(oj qz*y  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 w.z6hw6dz *sx 8rwzin8 avelengths 2.64 m and 2.76 m in air. How many beats per i68 z xdnhwz86r*.wzssecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sc9w;2nj 7 ((; glxohq(sdnb a0a+lbnairen is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 3;jwaa a(nxs b(l(02dh+; l9 cqb7on ng0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if /exz6x/zp (wcm0z(1 h qs nrw5xmh):ja,1 man a fire engine whose siren emithj/wx z m n()z ew6asxx0q mn1rmca/,15(zhp:s at 1550 Hz moves 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 towu n(,od 6-tbh69gxsov ard you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly tu6n odg x6-bv,9(othshe 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 ):hwy* l vza*uteh6r/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 5.5v z wlht/yrh6) a*:*ue 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 r;e13f rq1p sv6juq,zreceives them returned from an object moving directly away from it at 25 m/s What is the received sound fr frej1z31;qrqv s,p6u equency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed or9x6) ol* bwjgf 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30lw69)xro *gbj.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 played1fobxzg (ze.;wyy0.;)d4m bf q -8vrzi4j crp on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played t4f.rx0bqc y mgv;j1ip d.4e;z8r zy fw (-bo)zhe 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 bloeut6nst7)d /le 5)vttg5mgq-od-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the soundg56g)e ett7vd)qltns/5 ut m - source?   Hz

  The Doppler effect u 5unn7k 6omo0ksing ultrasonic 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 winosl15fga7. bg d velocity is 12 m/s from the.b aogsf5 l7g1 north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object movj+cbcj6yz jw /q5 k8;odxk0* tudk.k+ing 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 4zq hh( c8jmex+4u62pb fh0jx sound is 310 m/s (a) What is the angle the s4f 2z8+ 6hb 0u(xe4xhhjjcmqphock 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 8k f i24j vd7n+xoaxp9of a planet where the speed of sound is ooxk9fdn2 v74x ji a8p+nly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determinebhr. 7uoo:n0p(9tls g the shock wave angle inlt79go pho bus.r(0: t 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 b*fa7) juc7bs$/theta$ 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 exactlya, z5(1cpidn sv6l1o35 ch aoj 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has tcls1(j1hooz ina6,55v c 3dapraveled 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 so y8bcv3rrdbj:5icaf2+lwm w 1*+yj y-n8 mtw)nar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200n)j5d y 3+wb-*yw: 12c+trlicyrwvmf8a bjm 8 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there i en0v sx71jkr5n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Iov8fv x;384slxepoba 4v2e 15u6ts hf t consists of many plastic fe1b x24 o 64sapvuol;3f v5v88thesxpipes of various 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 to the thre :7e1*ejuafj,ld 5 p8pxx+ 0dd8pqwcdshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoe,58+j 0eldxfj8wpp dqe:7ud p xc1da *s?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound arph n, syh*we.j0s)2 ,jmwmlcmr1,j c0e hea2j. hjw0 0 m,,wy 1c,) nremjs*mlphcsrd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed im 5pkxu yiqm.feb- l c: 0gi:/w9f8;hqn the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming f ;/p.f 8qbqic0ghmm -x5uy k :e9:ilwit radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dr ,:ik 5h:klpugops by 10 dB at 15 ph5:k: ,k giulkHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft)5koblcu2 gw* typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane eng5bl)kugw o2* cine?    W

  In audio and communicationsasmi.v0e :2r x systems, 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 frequencl0e aq17 +njxty 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed po/j,ig;l q,zyynuc8g 6 ints with a fundamental frequency of 440 Hz aij ,yc6 g,z/q; nluyg8nd 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 ino +:flish *xrsi*2.vf5rtz lmhom,./y ,ld6 kto vibration above a vertical open tube filled with water (Fig. 1. m,vyirz+tfrk l l2/6*lof ,m.ds:s oh5h*ix2–35). 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 fork?   Hz

  A 75-cm-long guitar string of uzng* wc .dk/(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 tu.k/*n c(gdw zhe third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate asm q6jr(z 39p-s2g:k q/m :. nilpnomvc one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming fr0r xs: -),1kjq rfibqidsg1* v7bf 9dxom two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is mj7qv ,) i9:x*q rdg1ib-r01fk sfsxbdinimal 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. Tv54*n uhn h,mhhe conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speedm5h4u, n *vhhn of the moving train?   m/s

  The frequency of a steam train whistle as it 39a 13w+oz y73 u.xsnebilhe wapproaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? 1 33bysa+.wxl9 nhe u3e7zo iw   m/s

  At a race track, you can estimate the speed of c l ww 9+xp/)y20pyi:xm- tpfncars just by listening to the difference in pitch of the engine noiswn c:m-py) 0yltpp9xi 2/w x+fe between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The m-e5jfh 2xut9 shorter one f2emux jh9t5- is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppo5w6 ftbrvvj3g w/q92dsite 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 frequency heard by the observer when (a) he listens from w26b5w vrqtgdv jf/93the 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 thew(vo0rs ; rpxu mk:b,3 aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50- 0xmuk:, v(;wob rps3rMHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a m.53etggnjt 4noth at speed 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 the frequency of the wave detected by the bat after that wave reflects off the t jget345n.ng moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moo3,1 br(p vcwqth. The pulses are approxiwb(1 , op3vcrqmately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38)0kd.s/jp(0q e 6:cd gy lmp0bldl: to3 was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn.p: ( oqjed0lly.mbp:dsgc0/k60 t3d l 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 comh.ske;fw)w 32c t;r lci- v3dypromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental freque.3) tswfyc v;i-; 2d3cerklhwncies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singi/+c v6jpm u ()xdszsbdnaw8):ng rods,” involves a long, slender aluminum rod held in theb+ dvm 6 px)8/(nuwsz:s)acj d 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-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 fdkst d e z.i47zgd 5e*aeq.12.i;ppycor the human ear at a frequency of abo2t 7iazcd14y.gi .edpedz*q5. kse;p ut 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 Mach 2.0. An observer on the grounwuws 383uxp3i bi0-:5hr ptjgd hears the sonic boom 1.5 min after the plane passes directly overghip8iwpu 0:b35x-t rsj3 uw 3head. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is gm 9nv/n j17 4gt6gzzj15 $^{\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