What is the evidence td;h ycl,ej/imk)a xgjg6;* i )hat sound travels as a wave?

What is the evidence t7s2lxps ,8q s3(e)v)j7m1zyfbj u dlq hat sound is a form of energy?

Children sometimes play with a home/4 x s fe-xduxlge.(pf sv5h--2pry;fmade “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 cup (Fig. 12–29). Explain clearly how the sound wave trave;.glxupxs fyxd/-(f -fs2 -re54p vhe ls from one cup to the other.

When a sound wave passes from air into sn eq)czf:4r9 68ba 2xw*o svtwater, do you expect the frequency or wavelengt2:s aw qvr xfbo4 *sc)e896tnzh to change?

What evidence can you give that the speed of swb yrvuwcvh5zd1* 5 wv6,: 8fbd -h6zaound in air does not depend significan-5drbv z 6u hw*cdf:h1v,y85vwb6zawtly on frequency?

The voice of a person who has1i kj(h-:u aws inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room.cp2f6gh t4b6 f1 9l9 ,b nmkcc sqreb+mlk1)n affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitu2bnaff32 xetqml420 lq u1qe5de of sounds in various frequency ranges. (An exampeqfa 2txe2 4bu lqm0l2q51f3nle is a car muffler.)

Why are the frets on 2-sy6ph-).ypc2 e eha 9fgdcqa guitar (Fig. 12–30) spaced closer together as you move up the fingerboard towaese6-9cg yq 2hfh ay-d)pc .2prd the bridge?

A noisy truck approaches syi/65mgq rdu0+nrsr*b+k: qyou from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound irrd +gkmys 60 5r qi/q:+n*subs suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sa 6 ),:-vi3mttl;r yl ;vvczr0nu za6waid to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explauiyz:6zrc-l;lvv03);tw n , 6 vrmatain.

In Fig. 12–16, if the frequency of the speakers-fnk0j -cxm g+ were lowered, would the points D and C (where destructive and constructive interference occur) movk jng0c--+mxf e farther apart or closer together?

Traditional methods of protecting 0 d5e3e9+d 7bycddksjthe hearing of people who work in areas with very high noise levels have consisted mainly of ebeysd0+c j 7k ddd3e59fforts 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–fa:5 5.pqmo fa31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. Imo5f .a5f:paqn which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observd/6+tuf0 ffld/i q5fe er move in the same direction, with the su it/ef/dqf6fdf l 05+ame velocity? Explain.

If a wind is blowing, will this alter the frequency ol; qvc7/t9us r otl 2xs+vfs-)f the sound heard by a person at rest with respect-ss v+xq7)scr;9 2ulv tfot/l to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swingu( gv(1a:tn zb. A monitor is blowing a whistle in front of the child on the ground. At (bvtn ug1(z:awhich 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 listeningg 3 (hde7b:so1(y5 jz* fuyq)- miekrh for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Eeqoy3m)( h(- h fds51yz jgek iu*rb:7stimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echn/-jz-v9 cbe i /zm;ouo of the sound reflected from the ocean floor directly below 2.5 s later. Hz v--nz9ij b /muoc/;eow 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 wavez86 t yqcb5drlhf(fy+ dy+ua xm()3 m0lengths 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 just above a school of tuna on a foggk x7cv 3kb,wwhtf k-+5;dgx7py day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 1;xwxg-75tf3v kdhc7wb,p k+k 2–33). 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 ma3mtg, isc el;d .39qcukes when striking the waies tg,3l;qu ccm. d39ter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the 8h8q s 1c,jmnpground, sees a huge stone strike the concrete pavement. A momencsm8p18,q j nht 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 impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by i w97me-4 gj9x5sncf cthe “5-second rule” for estimating the distance from a lightning strike if the temperature is (iegm9c f579jcx 4s wn-a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound e * ple,zl+17b*oin gxat 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 o htmjalj1-/usg)8kt*f a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leves9pqlfj6kfby7(-oij h 8j h*;xb* d)vl of 95 dB when fired simultaneously at a certsy7 jb f6f ojkib(p *q8l;j)h-9hv*x dain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wyblwt9tsk(i0q a : 3o9ith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level:qiy9k 9(l0tw 3oastb would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is saidmh0z(ykyf45 k+ i.wve to have 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 backgrounw4y0( vke z5miy.hf +kd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person wjofb),str .0 r 3kf9wspeaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cefw3rof rw.s 90)jb,k tntered 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 eard1 b5oxl0zrng6rum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the moro tn(k9k.wy 8h*ybz4tkr/vlc(r .8vze modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expectbkn/ykotyrwh*.zz 8 4(lc 8t vk9(.rv 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 placed 2.8 m in front e iv,1nxl41vkfmvq4lbz ,;m(of a e11nfk4iv z mvq;,l,4 blv(xm loudspeaker 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(3+7 t7wye naytfk:kr in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amountwe7rfy3at n(y+ 7:kkt ? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (at/8 /spw-s/bkx z5u db) by what factor will the intensity increase? Increase by a factor ofdw p/u8/x-kssb/5ztb    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal disc z)gs7 y6twsxwobr4)859el cplacement amplitudes, but one has twice the frequency of the )cy4t) rzwlx9s5g7bw8e s6c o other. What is the ratio of their intensities?   

  What would be the sound level (in dB4hagh)r4 )0ofd hcm) e) of a sound wave in air that corresponds to a )0h4h 4 dgmohfr ae)c)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 tone that e*k- r8i wmd j .zkh1+3u;i;d1f pcunxhas a 50-dB sound level? (See Fig. 12–efhn .c- pk * 3d;umixu+k181 drjwz;i6.)    dB

What are the lowest and highest frequencies that an ear can detect wh.paw6rb0( n90w y jszien the sound level is 30 dB? (See Fig. 12–6.)0(j6 syzib9rwpan 0w.

  Your auditory system can accommodate ihhzvzrg ro.5.s:-b.ev.;tha huge range of sound levels. What is the ratio of hi hro; t g.szvei.hz-..vhr5:bghest 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 violi*vy iy,yc+0o:76s :jvp wg cmhn has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string bgc*vy hwy 6:ys ov0, ijc7pm:+e placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fipbsg5s c lyn*gde2 ks61a869nrst three audible overtoneny6bsc815kedl62 p9n ssa gg*s 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 blowing across the top fo5vnyn g*2 p0c t2y9gof an empty soda bottle that is 18 cm deep, if you assumed it was a closed fv0go2 gny 25c tpn9y*tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of h .ucu3)u jzcp:/( z ygyyg7za(uman hearing (20 Hz to 20 kHz), what would be the range o u/(7zgcyya.gzu :)3 juy(czpf the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third haddfe* -md2d3c5 +q zhkz8g4qyrmonic. What will be its fundamental frequency if it is fingered a*4ezddf2h-cz d 3m85 dgqyqk+t a length of only 60% of its original length?   Hz

  An unfingered guitar stri7-f1 pz2vi m wao50xwr4x e8rzng is 0.73 m long and is tuned to play E above middle C (330 Hxw7xpzrz1f 842 vm0 or5-waiez).
(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/bci r+va0f4k;vif w + C (262 Hz) when the tempercfiv ra+k0 ;/bwf+4viature 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 20mri, (l, zs/yy $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampusv(ur7w z-7s le 12–10 should the hole be that must be uncovered wu 77zv(ssru- to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but; m7.d *pe(z;agobw fj not at any other frequencies in between. (a) Show why this is an open or a closed pipe ezb(j7f .;p*dwoagm ;. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m p:iyha*)3l7b) c5nd glv 1viwlong is open at both ends. It resonates at two successive harmonics of fyb hv5c1llpiva 3:g))dw *7inrequencies 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 ;hi ,x p2hpp)p$^{\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 tw 2nn1pfvr cc2ow4or (+6:lkh he audible range for a 2.14-m-long organ pr wrnh:lwk+4ocpcno 1v f2 62(ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is awvgi c+f2cn-.-bwt (ky/b+nj pproximately 2.5 cm long. It is open to the outside and is cl2kj-( bwct gyf +.i/+bwv- ncnosed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat eve)ag:m-0 :lzsw g f xpfmf5lo8)ry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. g: a)xp85-fw0mml) fof : zslgHow far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)* *db iu)m*khz 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 another (brand X) operates ;ov , x;aqa8e6veoz6lat 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 th v;xl,a86q6ve ze a;ooe operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hzpb dtw(:.(oyb tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reas yo:bt.w( (dbponing.    Hz

  Two violin strings a7kg0 q,3g:)sdcq m qyire tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency hey:dq,7ggm q3qcik )0sard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to plfz) wa *q2s+qqay middle C (262 Hz), but one iqa* wfs2zq +)qs at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, hud-1k jua,ox-16lwr and C. Fork B has a frequency of 441 Hz; when A and 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 frequenciaul1-uowjh1-x , dr6k es 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 speakernv3 a( d0vh5rekd3i.o4nn d,k and 3.5drkv knn on0dh3,ai 5d43v e(.0 m 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 be vibrating at 132 Hz, but a piano tuner h6xq+ 6 jikw jed*28dgqears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what+gd j 6w6jq qi28xdk*e 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 ( ) ye;cm5jlmhair. How many beats per second will be heard? (Assume T = 2m5y;c)eh mjl( 0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren wmi w,w/4b4un is 1550 Hz when at rest. Whatww bw4m,n4i/u 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 frequency do you detect if a f5oao rmha;)r8ire engine whose siren emits at 1550 Hz moves at a speed m;rr8 ha a5)ooof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz zcr-q e /.3yeqsource is moving toward you at 15 m/s versus your ye-/3q qezc. 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 equippeuxk4 / h(mbx/vp 9fb5cd with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 u 9/ kmv/xxb4hb5pfc(Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives thel49gugn5 +m t6( gf3p 0rfemkhm returned from an object moving directly away from it at 25 m/s What is the recf95 ge3nlfkumh 0r6(p4gm g +teived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 53nj0 nvb2x4 + lpauzd6 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected w6n 3xaz l2bp d0n+4vujave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, ,uf6id 5r )atka tuba 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. Whi6)dr,uk tfa5at beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supp m10hsf,i0uf nw2xbf*ose 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 wxhfu fm0*f0i,b2s1n at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequi2ymyna 1b 17aency $2.25 \times10^{ 6}$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 emi8 ,fu8wlaxn 0ots sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observersflxo a0nu88,w hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on lanfiw5uz1gz s;o6/ )kaod 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 th xx( ku/x2 xe .tkgfkgqrsdg3-(:4qm1e speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’sk sg k-x2tx e.4k3r/fxgud:xqm(( 1qg motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planey5.o, xa jt)aj58hrs9algg :z t where the speed of sound is only about 35 m y., g5 rxo9agazjt 85js)lah:/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 850:gm 81,upmrxv ; zfm6k urxb3+0 m/s strikes the ocean. Determine the shock wave angle it produvurmfgbu; 1 ,:x+6xmkr mp 8z3ces
(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 (-6 6fwhbv tq7hs y;gs$/theta$ 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 thegwfe 7+x,nc,y ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance cwg7, x,f+ye nof 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 dow/cflmfc 0s f:qzn . 5+dp5cf*xnward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designe+5 xfcsql*mfcfp:/cnd z05. f d to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are therek 432l(eyl-:swoczat.y j0qn in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pip8ei3 d;p pt(d gvenph , b:a(72zzbl1we symphony. It consists of many plastic pipes of various leng7zw:a 3d i tp,deb lpevzb1 ;hp8g2((nths, 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 48ro4m)mwrkia person makes a sound close to the threshold of human hearing (0 dB). What will be t 8km)4orrwm4i he sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level whemtejz z7+b0nfs7 vp u :xb*/n3n an 82-dB sound and an 87-dB sound are heard simultaneouslb73u+/7tj:x mpz *nfse b0znvy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, zxu c-2lbyt/.o pspp5 q/2k9f is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direction- .tq psc5lfpxopyk9 z2bu/2/s?    W

  A stereo amplifier is ratuo:l y3 sx)b//ld:k wuboid3q/0ka;m ed at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wattbi/ l0olb kkds; :qwuxda/ /u33 :moy)s at 15 kHz?    dB

  Workers around jet aircraft typically wear protmtx +ytd) (vvoh7 1uf4ective devices over their ears. Assume that the sound level ofo)tvm(+y fhd4t xu17 v 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 engine?    W

  In audio and communications systemt375+cf zle o aca19w/b swdyd+k)fu (s, 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 torx aj(hh j3tkk g:0+/mo ok02u 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 with a fundl-vr;hrceeyor 2y5 5/amental frequency of 440 Hz and a mass poe2/cl;-vr5r5eyhr y er unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical ope0mmam;+ :(r sw h3lyo,gd :gsen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so,gm+msew:y3;rha( ,gsmd :o 0l 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 tube that is op2+j icywrm70z en at one end ani 0ywzcjrm +27d also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate a .br kx-acxe5),phv0ms 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 pureka b4ew lv *me1*/x1nmjewf)9 tone 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, thej*fe4/mx1kwbwnl v9aeem )* 1 person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz wn)i;pll ; yq(qhistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaci(p);;qy nl lqhes. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachedyz q5w6 x+6n5ac3cfg s you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast gw y36n5c+ dzxcfqa65was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to t *a( -/xyqs3lbwars1gkq 0wb-he difference in pitch of the engine noise blg- 1waa bs0xq3/y qsr*-bw( ketween 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, s8w/figk-n(e q6pem- tounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lonnfewte-/68-qpkm (g i g. How long is the other?    m

Two loudspeakers are at opposite e )vs,kcb97.nj) sgxyeb(4bx)l fcf3k2 yjuu9nds of a railroad car as it moves past a stationary observer at 10 m u.e)v f(2klj7by jg3 b9fnb))x,xyku 4s scc9/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 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 aor tps83zo2zc7ota is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the 2osczpo8z37t 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 spe(5nq- qx.gnm7c t3m:b f j;jjfed 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 thec:n3q5. 7(f fjgbmqj;tm- nxj moth?    kHz

  A bat emits a series of high frequency (ltxxll a+o7wpj xps-91la*+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 (wlja7lpla 1sxpoxl*9 +-xt+ by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–br zp973-nwjzp8dk f9l. i1sm38) 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 dp-l i7zjrsfwnb1d z3km8 .99peep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the prei8z.4 j (dbud g5mnl-dsence of standing waves, which can cause acoustic “dead spots” at the -lzb(in gj5m dd.84du locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,,r9q: em a akx0rm9fd1” involves a long, slender aluminum rod held in the hand near the rodr da1r9: 0e9x,f maqmk’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear qrhxjn 5y3+ :iat a frequency of about 1000 Hz ij3x+ i:5n yqrhs $I_0$ = $1 \times10^{12 } W / m^2$ 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 pf7r dajz)*4txn hf.b r7iu/.hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plaub)7fin7tzf /a rdp*hr.j 4x. ne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is)k/ c,7ppc fd)xr urykbj)il m*g /a+- 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