What is the evidence that sobu dmx1m8v(9e66y wjm und travels as a wave?

What is the evidence that sound is f -)lqt1q)x jp5vh pu*a form of energy?

Children sometimes play with n,.aot qmt1uuz(: y9ua homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound , uuz9to(u m1qt. :naycan 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 air0m jmii;-mh ic-iff(8 into water, do you expect the frequency or wavelen mjii(- 8mcfhf; -0imigth to change?

What evidence can you give that the speed of sound in air does noi tq2gia4w- )n,z sr+syze;n.t depend significantly on frequen-qzz4g2 yntin) +ie sa,rsw ;.cy?

The voice of a person who has inhaled helium sounds very high-pit 2wpo..jcg 9w f,dvx6 oow+1uoched. Why?

How will the air temperature in a rooaq-:k.vg- ldx*pvkx g ss:h-( m affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of -dzp2ile/ 8ep+ueh7csounds in var2e-lie7uz+d8 pph e c/ious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer toget1o0,uu(k ,c t aicp4p:bj .xvjher as you move up the fingerb:pp 04(v cxo,j1uaj.kcu,t iboard toward the bridge?

A noisy truck approaches you from behindsaaom:t.036 wb ffs) wgl l2k2nsd.z0 e33rrh a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [s0 3w6): ms sl2eg0tafzbd3fkwr . nal.hr3o2Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to f.8o f z;xcrm,“interference in space,” whereas beats can be said to be zm f.xcr8f;,odue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wereuuh (. shourc9v b718m lowered, would the points D and C (where destructive and constructive interference occur) move farther apaumu(srv.9o7cb u1 8h hrt or closer together?

Traditional methods of protecting the hearing of pei6gu, e-:d0ly yv8i -x bu3m4ceeq1 vjople who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts-dxv:01y-,e8eejvmq6y3cgu iu bl 4i 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. Ekno1 ui+f gmhs,h8b27y;km l(ach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whic1hm,gnlouh;2+8i m kyb f(7k sh of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dirl-g2 vr:885z r:ts6k gbhh cxjection, with the same vh868grl gj:brc-2hsk5x tv z:elocity? Explain.

If a wind is blowing, will this alter the frequency of the sound bxvcb nbd k0 5s)7dlsa ()rt09heard by a person at rest with respect to the source? Is the wavelength 9ks c75 d)l)nbdr bxb(00ts avor velocity changed?

Figure 12–32 shows various positions of a child in motion onq1q0a*b ,th dcm+d+; 5ycihvk a swing. A monitor is bloit*chb ;d 5+aymc 0q,vd k1hq+wing 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 your reasoning.

  A hiker determines the length of a lake by listening for the echo /52 ld/u6oqr+tp6mbvp g q 3oqof her shout reflected by a cliff at the far end ofompgvb6 r+ /qq/u25 qop3t dl6 the lake. She hears 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 just b t kvo749rjm6telow the waterline. He hears the echo of the sound reflected from the oceatkr 4m9 7jo6tvn 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,f8 z:-fwnk c(3sm lql 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 drifting j.bsdoq6+3g u7p/ k ytkh nn-/uust above a school of tuna on a foggy day. Withouth+6.ou-n g7qbknd/yu/tk p3s warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the ttir8ppof (f4r n87b m/ng1f/uop of a cliff. The splash it makes when striking the water below is heard 3 8/gtpb /frfi monu1nf rp784(.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pav+wtn y,(lpcoscv s0:+ement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the im+,s0cspyv(to :l +nw cpact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mil g hen7(t wx0pdvnl.qm.3gq5f7p0;s ie of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperat.0( eq.7t gsp 0;g5invmp l73qxdhfnw ure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of aw-7h)wiek y7raf9n 3t sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose ilj3mru u (*(0;k7 x hdaex6 i0)yplkrdntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soue0)a n9ba*veg0o9 lrr nd level of 95 dB when fired simultaneously at a certain place, what will be the sound bgne09*)9ar e o0varl level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplaelu14qvx)2 z;fjk n o*m92b ghne with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person e*o kh e4zqx2mj9u) b1;vf2lng xperience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to t3e0 d+j(ju4hhld*g hhave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device?(hdjhu+d03ej l*4tg h 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norusts7y;( irp r*3v6z vmal conversation. Use Table 12–2. Assume the sound spreads roughly unifyr6v37p;z ur(t vis *sormly 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 stri2 a6vjr,by3 dikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250i0zsk06qoaod3 bg, /k 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 a6/kkdoq 3a0ibs zg,o0 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 registerehu axsg3,a7u(lvanqks-9 0 7o d 130 dB when placed 2.8 m in front of a loudspeaker on the xl a0s37uah9-avgqsuo ( 7n, kstage.
(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. Whakvw(drpmx5;j a9j9 a yh/wg;(t is the ratio of the amplitudes of two sounds whose (wwk/vm pa jrg9(x;y9;jh5a dlevels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a61g:wgab4ddr+)ep(e q /xcy i sound wave is tripled, (a) by what factor will the intensit+(/ie1)wd: qcp e bga6g4xdyry increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the aw sph9nr5i6 8-yq6cvfrequency of the other. Whs -9hq w vipca85ny66rat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thnue1fwawgwfmo, 02, yk ;d*2 nat corresponds to0nn,y;f2a2uw w d*f 1,o emkwg a displacement 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 tortc pfn7 /h n+ctkrthbe;*jw4;6+qo )ne that has a 50-dt p;wnn*76rct+ k bj);ft 4qrh+o che/B sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequen-6c s0u,wxlkvq3 a k0q9k) bsvcies that an ear can detect when the sound level is 30 dB? (See v k6)a3vkkb90l,xq0q -s wcsu Fig. 12–6.)

  Your auditory system can accommodat7,txgy. rc4y he a huge range of sound levels. What is the rati7.g4cx yth ry,o of highest to lowest 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 fy; 1f asam ib*h16ht:irequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has t:s11;b ahmi i yhaf6*a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental aoa8 aoxh-z74sa; r9ecmmu/q-( c 3psand first three audible overtones if thma csre4 ;7q3( sp x-oucaamaohz8 -9/e pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency lsun w)gce:6 lin0r7 0would you expect from blowing across the top of an empty sod6swge0)lunl7ni c:r 0a 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 pipeez2tx 9 et(vlc(ynm50s spanning the range of human hearing (20 Hz to 20 kHz), what would be the range ofev0zy ( 25tl(m e9ncxt the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has ail2oqx exl,q/) n,7)bob,zm v frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its orq/bm7,lio o)bz xx) 2eq,, vnliginal length?   Hz

  An unfingered guitar string sqre; fm+af ( opnr idi b /7x1o:eq6b,4g-fl1is 0.73 m long and is tuned to play E above middle C (330/,r an seqoiog16r-fp74l(qmdx:e1 +bffb ;i Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle-bi15dkxo o6aqx )p s6/ rzya( C (262 Hz) when the temperature q-kr5z /p1o (yi6s)ba6x xodais 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 6,revgw vs mb/fel4o db 54gn.7h-z :k20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiec- cu5ggq* (jfve of the flute in Example 12–10 should the hole be that must be j(f v 5guq-c*guncovered 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 26nhm svdx +t)41 kyu ,5/9)grgx nm;dsa4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clx xdm s9dm;ug nty / n5rkg+hvsa)1,4)osed 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 two 3vfx/oztb, tb.n;dd z n.;m4 xsuccessive harmonic .zxd f b;x4tvtn,o3b/d.m zn;s of 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 d -y8ml f85h:i+smnt6wla b3; eef*jn $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long orga: sjd u2 2yvd wc7s*qyis(qsdx:+-qb/n pipedyc7iqx*s/j vs(:y:s q-sw b+2du 2qd at 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 the outside and . g2rv3mh.p s4nj(snn is closed at the other end by the eardrum. Estimate the fn(s4s.p 3jnm .vr2hngrequencies (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 ev(t1 qxi d *5umg*6fxvmery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in*t(i *fgx6vm1mux d q5 frequency is the other string? ±    Hz

  What is the beat frequency if mi ijwl;h hpu6v.w 3,qf.ddle 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, w/+sx(on hr;e:gn0ms 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 simultane(s r;gx/sh:eo +n mn0wously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuni r dd0x6/-pfg+dx nl7cng fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is/l r0n7fp-d 6g dxd+xc the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequencye 1p.2 yp yb-nr:xh.an, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall p1pa h2nr:b-x . .eyynEq. 11–13.]    Hz

  How many beats will be heard if two ident- c* u;ibttvt9ical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0t9*btu-i vt c; $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 47;m rh(ug1v1;x; wtnqf0asxyl0+ nuc 41 Hz; when A and B are sounded together, a beat frequency of 0wt n1us a7;+;m1g u;fxv(q0rn lhcxy3 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 sq1z(klpbpl9g xjcjk8 4fp 9 ++tands 3.00 m from one speaker and 3.50 m fromb+fllxkjpq94 c89 p pjg(1k+z 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 sw9e 4z1q v6jzqupposed to 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 vibrati4zzvw q6jeq 19ng 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. oy/rfarv-o e-ts 09k4 How many beats per second will be 0/e-4rkoa yotfsrv- 9heard? (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 twi)d7 6p l;tuwhen at rest. What frequency do you detect if you move with a speed of 67ulwt );tidp 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginx-xwy8)9oqg lt:qs: 0ku3 rcue whose siren emits :r0-tq)x u yu3kcl w:ogsq8x9 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 freqto + ;ie/ks7yz l49yrzuency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly rsol ; t79/y4kyei+zz 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 2t*ob-:c v*.gnxu;c.xl bib vis at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat fv.tc-lbbc2xvi;*:n *g o u .bxrequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves05fj eu;flqfq rv l8.as ak5- r-7z.ws at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the r ;j-raqfv-skzfwfs.qea05.5llu8 r 7eceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, t/9+ fb pstj5oknn*n9ghe bat emits an ultrasonic sound wave with frequency 30.0 kHo k+s59 b njn*n9tfp/gz. 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 f, r. xwo8aji;xlat 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 frequency was heard if the train car approached the station at a spe.o; rj8 ,wixaxed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasouahkor7 8ngyb;o )/xr;h4l;hk nd 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 dirxga/b;4 l;oho h;hyr) 8k7 knrectly away from the sound source?   Hz

  The Doppler effect using ult+ 8hlrg7t). ,xypp hkrrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 1) pehnw -l2)nw(y ,gjw2 m/s from the north, what frequency will observers hear who are locg-ynwwjw lp(2e, )h)nated, 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 spee y /xh5tcj4b+td 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 310 m/ssym8nnr4w 6 ty2z.j+a (a) What is the angle the shock wave makes with the direction of the airplane’s mt6.n2a8 swy+yr mjzn4otion?    $^{\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 e yrtdzgy 5w)0o:e:npw ;z) vt 0+fc.hatmosphere of a planet where the speed of sound is only about 35hz df;w+zcr. 5w0 )py0: yetnevto:)g 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 oc2 lzb )rb(omf.ean. Determine the shock wave angle itzbm(fr.bl 2o) 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 xbq6nbmnt/p b/ ug d9 y1./v7c$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead aw gu,j9s 8m kx2jhw**c0jd;uand see a plane exactly 1.5 km above the ground flying faster than the speed of sound. aum scdj8w * g2;hwj*x0,u kj9By 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 sends 20,000-Hz sound pulses ;htwslz4l3cw h-5 pev4m u79b downward from the bottom of the boatpl lwe uvw3-h s49c7;mh 5z4bt, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hv(j)vo3b5,z )epeud i uman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manyf3 *egisxeu 1(yjog w+,h2i1l plastic pipes of various lengths, which are open on both enj 1+xeg*2l3i h sfuy, w1g(ieods.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of hup18s :xf3be yoman hearing (0 dB). What will be the sound level of 1000 su3:e8fysoxbp1 ch mosquitoes?    dB

  What is the resultant sound level when an 82-dB so-2led 4f+owd rund and an 87-dB sound are heard simultadf4ld -2er+ow neously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the ope1cf d9 )ibo t cv;i(n(.0slfmun, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directionbis(1f(m c ct0)ldovun9. ;fi s?    W

  A stereo amplifier is rated e .1,tavce2tu at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outc.,t ate2uv e1put in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deviceshzp 7sf*os1:e 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 ai7s*1hofs:z pe rplane engine?    W

  In audio and communicati rnx8 9 xub eyk1(qv4,jf3njn,ons 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 t+g-z z(+ 7lndw5fhou 0pqq g ;p/1oqzmuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points wim xi-a,hzrjh,wv(q1-v2 : bpvc5-mgh th a fundamental frequency of 440 Hz and a mass per unit lengtx-i hq,rvcmm- p h-a,wv h5bgz:(2j 1vh 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 a *umb 3jcd86ic v5rx5 7-wljenvm0r+bbove a vertical open tube filled with water (Fig. 12–35). The water levvidr n635c*urjjwbl780+mxcvb e m5-el 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 mass 2.10 g is near a tub) 1 c*tz6qhaacr*ks0cs .7xzxe that is open at one end and also 75 cm long. How much tension should be in the string i)cx skq0x.a rt16*zsza ch c7*f 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 adf21yo -p ;k*ed a7jzts 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 500–1002-2 ,tg:c,m j ;a) yjrubuwtmx0-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 moves about and finds that the sound level is minimal at a point 0.34 m farther from one source tha,u-g:, ;m artxt)w2yubj cjm2 n the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The;(w-idjip 1cfy4x;p1yg .sd k conductor on the stationa.kixf14;wdd yjps1;c( -gypi ry train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaco* xi oro*a:9auw/wi3w9)dt28zo u lmhes you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train trom w iw8o:2u*xua/3* ilz wd9)ooa9 moving (assume constant velocity)?    m/s

  At a race track, you can )l9m qevbd;8yal99e 3 ,hlmjqestimate 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 certain car drops by a full octave (frequency halved) as it goes by on the strab9 h)qll3a,mmv99;yl j8 ee qdightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toge bq r-+fw.8xei+xv-5jvtr ;r lther, produce a beat frequency of 11 Hz. The shorter one is ;-x x+ f5lqvb r+tie8jvr-r w.2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a .vto7l zhn4 he2mu2v,+2 gwli stationary observer at 10 m/s as shown in Fi2., v w+i2mnzlo thl 72ghu4veg. 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 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 normal)ob nk;mkz hwa 0u5,z;ly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the w0u)kakzwhb;,o m5;znaves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed dg0-bh;m vq5ob8xsw. 6.5 m/s while the moth is flying toward the bat at speed 5 m/s T0b.sd -;w5mvb qhog8xhe 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 his;8a6b n.bbw3e ym v*ygh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, ay3;eyb* bm 86wnba.v snd 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) was once used to szfv7++ sc)ia gend 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. What is the fundamental frequency of thi + szfc+7vgi)as horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the p th0of0x v:p3pagjlf b:4/i;8uct 9hwresence 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. Calculatu li ap/8hxog:bfpvct j0t:0w3 4;h9fe the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long,49 l yq8 vrnpv uk9t7bset;;6g slender aluminum rod held in the hl6y 7esk99pqb r8gtt;u;vn4vand 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 ofvwm ( j*fv:49kv :swgr 0/fjpo hearing for the human ear at a frequency of about 10jv m:spfw0*jvwv (o49/ fr:kg00 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 the soii. * 5nigb3:8(jki d/wibivonic boom 1.5 min after the plao3 kviig5wj bb.i(ii:nd *8i /ne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1r74vlv+c7e vvv16bo8g x9wkb 5 $^{\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