What is the evidence that s5ycatw7-r;tm5 u dhbbh9 7zs 9ound travels as a wave?

What is the evidence that sound is a form of cbe r(6+xzyvk)0 1iyrenergy?

Children sometimes play with a home4d e2u0rs citq-qba,6made “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 sound can be heard at the other cr 20sac-6t4 ,biqdeuq up (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, dofr*o . pnvqb7i8lf3.dd;zbc8 you expect the frequency or wavelength to chano;88b dflbp3d*f v7.n.c qrzige?

What evidence can you give that the sy-ui /yr 6x h46dzch:qlt9-nw peed of sound in air does not depend significawuhx --:6 rihctd 9qnz/y4ly6ntly on frequency?

The voice of a person who has inhaled heli5wab-zwf6 hl d v7rs).2j;bno um sounds very high-pitched. Why?

How will the air temperatcqa , g(9tbfc*ure in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter 0d(i*cku.h/ lw pns(b to reduce the amplitude of sounds in various frequency ranges. (An expl0nsdic/ h* b(.kwu (ample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30)dmxi+yme7 15j spaced closer together as you move up the fingerboard towarx djy1em7+5imd the bridge?

A noisy truck approaches you from behind a building. Initially yl(*gls9 svfvza le;:; o, ).ocmbk 5gxou hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear maoxlzge s:;sblv*ogk 9, f;lv.)m5c( ore of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference i* 4 e**.;hei(qfadar wu1 xxe1 br9jbtn space,” whereas beats can bewqax*91jbeh .ar;(i4 t ub*dex 1rf*e said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequenhfc+336d(tiei af4dx cy of the speakers were lowered, would the points D and C (where destrucfd4t f+3xeh i3(6di active and constructive interference occur) move farther apart or closer together?

Traditional methods of pp6j8 00px* vzmt polk5rotecting the hearing of people who work in areas with very high586mxlktpz p *0jvp o0 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 reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can beyl2tymr t mgf2;6s 0qgqe n/)4 thought 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 fre m qe0yr t;42t 2)smg/qngl6fyquencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shi .+ br ;tis;tqsfmdty54(a-yqft if the source and observer move in the same direction, with the same velocity?4q-m5ss.yb; tt qd r i(yf;+at Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pcw 3v/ukl7,i oerson at restw/7ukvcol 3, i with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion ontzw +.j .0fdmrhf(g z: a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the rfd 0 mjzg( hzt.+.:wfhighest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo bqbn u,8 0t8zoof her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting.t0,8bn oz8bq u Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side txiy:r78 zvm8 b 17wqyof his ship just below the waterline. He hears the echo oq z87 ti:rmb7vy1 8xywf the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths 2pl*bugzze 5tu tue42nv- b/) in 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 d. dv l ,+evb9 nr 0m4vj./kmcxiiaen/7rifting just above a school of tuna on a foggy day. Without warning, an e/./ va xik.ni ,jlnrmdc+ bve409m v7engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it fdx7g 5 csp3*kmakes when striking the water below is heard 3.5 s later. How high is the cliff7*g d3xcsk 5pf?    m

  A person, with his ear to the ground, sees a huge stone strike the tt**8crch(0 mn(hy sy concrete pavement. A moment later two sounds are hyytt8 ( mn*0rcc(hs*heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile ofv(b d3 g.4cgo22msltaz:8 5 la.ktuw g distance by the “5-second rule” for estimating the distance from a lightning strike if the .a5c2.:tak8s3ggvtmo(w l4lzb dug2 temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a hr bfm-,5:9, v8a7 y ijrrmxqtsound 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 sound whose intensity iv.i6v4k 6jpa i5an2d g, chi3es $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level ofx 9if45op .pdf 95 dB when fired simultaneously at a certain place, what wo.x49df 5fpi pill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain(07es kr t(w 8 sekrspq:mep09 distance from 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 shut down0e0 s9esk7r(p(pqkr we8s m: t all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wherav awhy3gl44b9r1d3 a eas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background4 l34hvy39a1ag aw brd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal1b e/2zg, yu xvql1a:z conversation. Use Tablegx:zl,1/1bq e uzv2y a 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardaph o8a;vfu/: 1 iz:juz a15a zo9q7bcrum 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 2 cwdw07i(q w0r50 W, while the more modest amplifier B is rated at 4d r7(0qww 0iwc0 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when plac2v k2 a6-rns0dg.r)vbvm cd +ked 2.8 m in front of a loudspeake nd v-v+60v b2s)2ramrgk dk.cr on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Wfu n8:xs(gq p/tbht+. hat is the ratio of the amplitudes of two sounds whose levels differ by this amount? g:nh.fq+p/x t (utbs8[Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound w3r0fm(zgxg ) gave is tripled, (a) by what factor will the intensity increase? Incr3 r(f xgmggz0)ease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemen vbr j+7/x-s7rofk m7at amplitudes, but one has twice the frequency of the other. What a- /rojfm+7 7v7brsxkis the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave ).nwkibpqum5c0)7wd4.t8 k rl8hefx in air that corresponds to a displacement amplitude of vibr8)48twd0ux7nbml.ke.ph rwi5ck ) qfating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must t ,laieh yl.z859fnl76/fknqgy r.6q have what sound level to seem as loud as a 100-Hz tone that zqa r .lkf 7lt 8f65liy,.yne9nh6gq/has a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when th8phga fqvi/ )/cmb-9c e sound level is 30 dB?afmb/c- p vhgc8/q9)i (See Fig. 12–6.)

  Your auditory system can accommodate a huge ran2m6+ggra /uj rge of sound levels. What is the ratio of highest to lower/ uj ga6+grm2st 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 d+9-wo ;qqzlqte7y 457kjg 4(f;2i aggf b uwfthe vibrating portion is 32 cm, and it has ikfq9a g 5 j+g wtey g;duqzf4;7wfl2q- b7(4oa mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundej4/; onbaz6b7(i3 (fqplomd7shd 2iamental and first three audible olaj(74(z fb;ni/b6 h3so7im2po d dqevertones 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 gp d328 z 1bs 6q0slnlyg./ 5t2wsli7so5erp xblowing across the top of an empty sod ld20sp 6eg31y gq sr/wixbss7.ptl25olz5 n8a 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 spannik1jdin j n 9w;g38pf9fng the range of human hearing (20 Hz to 20 kHz), what would be wg pjnn f1j89if39kd;the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fr :/x9;xf 6hefwype) gfequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingerexf:6gp9; weh)/fyfx ed at a length of only 60% of its original length?   Hz

  An unfingered guitar string ik 3y : r7,-.blllphsyfs 0.73 m long and is tuned to play E above middle C (330 Hz)r-hfb,p:l 3ly7. ly sk.
(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 open6b9d gspo )uv7rlt3-h organ pipe that emits middle C (262 Hz) when the tempep36-sgu drlh 9tb)o7vrature 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 ; 4atc;ckyf4;pchfi- $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exawyx qxpoap2b(v4 .j37 4cc.c emple 12–10 should the hole be that must be uncovered to play D above middle C at 2c vbx ..2je c7w(34ppyacq4ox94 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 atku 6+ g iblyi42l2gg4o 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between+i24 ig6b uo gklygl42. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates a,p+ehpvznhkd i z jg76q)7ff ke)48.et two successive harmonics of frequencies 275 Hz and 330 Hz. What is , ijz))hngf 4qeez 7vedph7 6.p+kk f8
(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 romo q1mo c2lg+r6)i8$^{\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 arxf6 -zyrc1pzolp(b7rz/sop 4.9cg9m e present within the audible range for a 2.14-m-long organ pipe apz/r(zozp-r c x p6s49ygcolbf .1m7 9t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to thkzarn6 g +v; zmmqa2-;e 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.kv;amna 6 zmrgqz2-+; What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s whvkk0mi(q6 vv;ep4 v 0ien trying to adjust two strings, one of which is sounding 440 Hz. How far off i0em 0kkv 6qp(vv;4iivn frequency is the other string? ±    Hz

  What is the beat frequency i1qizg5.j(fr(vz jmr (q +3p kif middle 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 opera1 bgw vsre; 8zjj7:vyl*g:i44na/r ectes 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 50004rbg*we a :8grcsi j v/z7e;:ln1yv4j 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-Hz fktx5 54uic ijl pd6hqgv;(/;tuning fork and 9 beats/s 46h d5/;kc;ix(p5lv igtf jquwhen sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tunev jgp q iw.)o1vq5b e5p1.c2ond to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%v b2o p.n1owc5jqpei5 )q1. gv. 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 tl7lax *btq4;d o play middle C (262 Hz), but one isxt4dl;a7* qbl at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fork4aw-j)83mnsmt kzeyr i;2zo 2gig (j /s, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency w/gjzr;ijtmeo)8zn2ay (3gs 2i4k -mof 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 4:opgm 78/3tfh hsjvhns 0h/ pone speaker and 3.50 m from the other. 7j308toh:/4vpmnfh h/ spsg h
(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 vil637gwbox- m3n yjcw,brating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratij36oww g7xc3bln-, my ng 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 i qxc9ppo+3y8okzli7-q mmx9 ,/7ehg mn air. How many beats per second will bek3qp+ yehm8p-9 xzcgo 7m ,/x7iom9ql heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of /jw59rl.5u *,tx .v rbr dqxvba certain fire engine’s siren is 1550 Hz when at rest. Wha .r.v5 xdu*lb/xw rv5 r9bq,tjt frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fr 11dm-kt; ywkvls;6wh equency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s 6;s -m1lyvkdt;wkh1w
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift io.;ndushhy33ikj ld*hm 9, ee i b)1q/n frequency if a 2000-Hz source is moving toward you at 15 m/s versqdj 1us.,m33i9e /o;lbhk )i e*hdnyhus you moving toward it at 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 frequency horn. When one ijm .wx,.jc;s.tk* uvis at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit?mjvc us ki;*x.wj ..,t Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends oi6cgmf hjp 83+ut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequen8fj3m6gihc p+cy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speeds,l0 0t k5cf-vuxlji6 of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear l00ti56 ujx l,k-fcv sin the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuaj+ 1hm)ocw25m 51:hs dr,u jkins-ez ba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat so+-jm52zr jc m,:euak1ihdwn)1 h5s frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses hnsmj;gi t( 5e-jjyk)d2 o1(hultrasound waves to measure blood-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 dihkg nsi2 j(my5d(th-;)jj1 oe rectly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency au :6xo/sjxe)bx ;b7f$2.25 \times10^{ 6}$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 win xh ;u .0haqw9q3wky:ud velocity is 12 m/s from the north, what frequency will observers hear w. xuw:9k0yq;ahh3quwho 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 its speed at 20 1ir0 2;ebwtdb$^{\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 310 m/s (a) Whavfi8 k i,x2/exuwk80g t is the angle the shock wave makes with the direction of the airplane’s motion0/xu8 k v2ikeix8g,fw?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planetvsqu95bs-2sl where the speed of sound is only s-uvs 5qs9 l2babout 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 the4(:g1h d,nts .nd1rz v /klnsu ocean. Determine the shock wave angle it produces gndnn4 v r/s.z h(l1tksd:u1,
(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 5 *qvqfbdhtx)*kd1hnmom k d.)v3q .4 $/theta$ 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 above the gro;)emx yhe+aobuk 8vr+;:ro( ound flying faster than the speed of sound. ure ;+( y8)ro+:obhxvkoae; mBy the time you hear the sonic boom, the plane has traveled 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 q8fwrvk,w ce+o6 * tg.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 time between pulcfo* w+6, vq8.t wkrgeses (in fresh water)?    s

  Approximately how many octaves are theqdz,6hby ;1dd5(5lwlm tj ,qxre in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dispagm; r,3jz-ct :bqb q7lay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whichqqbbma:j rc;3 ,z-g t7 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 fr rflml4k g+br85k r*0oom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 sucfrr08+lgo*bkk 4l5mrh mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and r fi 8h0-6i x4yio)yucan 87-dB sound are heard simultanehyiciou4 -y0)x r8 6ifously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1onabc 7k( m uav/qz;8/05 dB. What is the acoustic power output (W) of the speaker, assuming it /qab 7u o8vmnk z(c/;aradiates equally in all directions?    W

  A stereo amplifier is er4m z5k*kukd)1 y9 ydrated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power ou*d)yme4u5k 9kz1 krdy tput in watts at 15 kHz?    dB

  Workers around jet aircraft typically w pkzw-v;h5;p y1nnm(+iwr h;year 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 distapyh(+ 5p- 1vnr;izm;nh kw;ywnce of 30 m from a jet airplane engine?    W

  In audio and communicathi56ryds0o8h 2h xb( vions 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 auzl. n, 7ck lx:.jje4is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a viogp9i ho*l,v d(b,nw r/lin is 32 cm long between fixed points with a fundamental frequencyrp9,li dnb hg/*,vw(o of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set yl-owgm u65kt e; m)x9into vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and -tul 6om ;5ekwx)m g9yagain at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar mk fjy1on62 1ql q*za4string of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should beokq *f6a2q ylm4j1 nz1 in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lo6s0scdxdbj )fiqpo 5 33ch8 p(op ($\frac{1}{2}\lambda$) 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 toly b:/sn0jt. wne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person mb0n:wsyjt. l /oves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is sj;6 s:+w+zf9.8 hmkybxn 1b (m1cm6pkp ycczmtationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the o6:(zmw8 c;x6 jn h1m+1ckymfbm.pszy b kc9+pther train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yorbsdl4gj vufgp l9lc84y 0 306u is 538 Hz. After it passpr483d9 l cs4l gf60l ubg0vjyes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars justnn,h kgk9t) 6d by listening to the differentkk6n d,hgn9)ce in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togethep -p*(eopq4f2 ggd)xlkrf / j.m/1of xr, produce a beat frequency of 11 Hz. The shorter one is .qko2e*(-po1xj df 4 m/l/g px)fgfpr2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movgig 5m1 n4 ,ss x9jj uks04(ha.0ktawves 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 the position A, in front of the car, (b) he is b0j w4, 9.usjivx0m g(5tshk4 s1g aaknetween 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 norma 6jsmv* qd4r0hlly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound w* h4rj d60vsqmaves 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 moth at speed 6.5 m/s while the moth is flying toward the bml ngb/q(;ju ti05hp7z :a*qgat at speed 5 m/s a qm7qpb (*;g0 h n:liju/t5gzThe bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of hrdq04a +6n p +7 ggctwy/g1fvwigh frequency sound pulses as it approaches 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 next chirp is emitted? wya g40+qg wcg+ d1vr7f/nt 6p   m

The “alpenhorn” (Fig. 12–38) was once used to sen 8;) kwhnff4+jyfd qg t1peh0)d 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 resonatqdh1f4n tk0)jyh fe; p8+ )fwging. 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 rmx)) l2uyw +q, u1ajlbe compromised 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 fund+w u2)yru ,jaxq) 1mllamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing roizq h+ pkl1 .sx4sip3u0le.n)ds,” involves a long, slender aluminum rod held in the hand near the rod’s mids+.ks1q lxn04l 3e)h uzipp. ipoint. 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+k no0;:jf7 n rbqk-q2avzg;l threshold of hearing for the human ear at a frequency of about 7gqb0rq;fa kl;jnnkvz+-: 2o 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 x ch*;y 8/a so3pegbw2xa6wi: Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whatx 8cse ;3 :h/yo6pbw2*g xiawa is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat*n0wx ,nv/mrr 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