What is the evidence that sound travels as a wave rxpl w .xn2c,qg+*he(?

What is the evidence that sound is/ n 7gba*lsl (pgvt37fd5al b/lvzd8 4 a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thqp9 dx woo8 k6k/ y0mexjm(g/(e bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound wjqgko(mxk0e8o/ /p9dmx6 y(can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expec,2s zg: j(d4 z+gxntnao0fehe; 6spb1t the frequency or wav b2nf( tzp:hsxe6;gs+ 0 gj ad4,1zoneelength to change?

What evidence can you give that the speed ofb88tg(rhp, go: xg +o,ix cc:l sound in air does not depend significantly on frequc:+8p8 c: g i xtlrbx(h,o,gogency?

The voice of a person who has inhaled h )doazo 3ch ,kjdoh o :-qf5qntyw 5./j*36pcrelium sounds very high-pitched. Why?

How will the air temperature in a room affect tm/yf +g/l6ky1mik f;lhe pitch of organ pipes?

Explain how a tube might be used as+isfsud. yvp7 :1aes; a filter to reduce the amplitude of sounds in variou u7:yased. vpsi1+ sf;s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up*n 5cnamptliq8z0* f, the fingerbol*t iz,fnan c5m0p*q8 ard toward the bridge?

A noisy truck approaches you j*nley96(i yt / a*tttfrom behind a building. Initially you hear it but cannot a9/l* ty yetitn* jt6(see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference idf9u v7)ig crk /;c;d3wnbin: n space,” whereas beats can be said to be due to “interference in time.” : c;incrdik dg w3f7n)b; vu/9Explain.

In Fig. 12–16, if th fvs i/icjir m012q.gk),+edul7 dr8oe frequency of the speakers were lowered, would the points D and C (where d,i0c8 j v ds+erdl/rfugm.71o) iqki2estructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people hp3bd5ezg d i-37x yj8who 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 deteci5hdp-byxz337ged 8j ts 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. Eachic8;qvsgks1um/cf .r 1l3 .yb wave can be thought of as a superposition of two sound waves with slightly diffe.gl kcmrv. u8c3b/sqi1 sf;y1rent frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shiftfz (grb-v7qh +(he r6w if the source and observer move in the same direction, with the same velocity? Explaiq+ ((gfbh-z he67rw rvn.

If a wind is blowing, will this alter the frequency of the sound heard by a perao 0kh :a3 -emp,aby;json at rest with respect to ape,ya;- bo3:h a m0jkthe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mono ,g8*avq8mb u-h 1lbs/ggh9z itor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child h -8vs8b*/1z g m ga9qluobhh,gear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines thnw2:p4t 6rcfhe length of a lake by listening 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. Estimate the length of the la whr6ft24c:pn ke. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bxe nd1;qk 9 8lk+)zobbe.ps6 zelow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater )e8bez klp.no9bk x s16q+d;zis 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2sc,)o vptueyjc.c.4+0 $^{\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 foggy rra 0yta6w6)n day. Without wtan6a 6y0rw )rarning, 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 top of a cliff. The splash it makes when striking;k:335 jn/madurr wr gu3z 6ea the wakr arwg;duu n:6 a3 5zje3m3r/ter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strik 5tpp pa13y j1j;4 ya:wo*4)czgkwrlce the concrete pavement. 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 sw5cry z1kwo t ) *p1pj:44agpyajc3l; apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secon a3g4)hnz sls4 , nzxz3d4ii.td rule” for estimating the distance from a lightning strike 4n.at,zgl 4zix)3n d 4szsih3 if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at t52;d o5ams ogfhe pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a so rpi p:8he/ru5und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fire/fizvt 6hdifn 3xp9-3 d simultaneously at a certain place, wha 3dpfhf 6/3 nvix-9ztit 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 with four equally n) hq 7iwup p)*l50qgqioisy jet engines is experiencing a sound level boq5)0 h)lwi gqp7i qp*urdering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is sai vbpu;wr3hue hf i*.5+d 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 background noise for each+5 wp3h if ;.e*vubruh device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound an (wu:m j(oj5x1ptff7a 0- slfrom a person speaking in normal conversation. Use Table 12–2. Assume the sound 7 5(jmu s(afolfat01-: jx wnpspreads 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 eardrum whose area is ;4-b3djljhc c $5 \times10^{ -5} m^2$ (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 v c oh 2i7u)bc7b6d-sfis rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudf dsbc)7-iv c 62bou7hspeaker 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 metercxrj:2ue(u *j+pcslpe(4 .h e registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. je.u*pxls p2ruc+hc (4eje: (
(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 leve 2zed:rndev93 l of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?ed29e:nzv rd 3 [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) b-m/anuwq x8+ 4afg:rl,vav+h y what factor will the intensity increase? Increase by a factor o ha al +nv+,qu/av8:-m4rfxw gf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitude 8 nlyrm ,7gk*c1sh9gqb e5dlb6l uk-1s, but one has twice the frequency of the other. What is the rati 9lcs -6ebgkmd5ny*k 1gqhbr,1ull7 8 o of their intensities?   

  What would be the sound level ( bxqf0h)cb.l ,awur 4*in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz,hr*l wbucq4xba 0.f )?    dB

  A 6000-Hz tone must have what s*/ zyf aqhh- f rju:b:qg*7z5wound level to seem as loud as a 100-Hz tone that has a 50-dbf *r 7:hh5y *f:a-zjgz/ qwquB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest fre8q ph*,a p0j9nxzzr (kquencies that an ear can detect when the sound level is 30 *jpnz(,z0qx 8kp rha9dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huo9c-1k3letkto ;o:iigr5) epp6zs i)ge range of sound levels. What is the ratio of highest to lowest intensit ip;ko-er3o:i zi9t1gep s t)l kc65)oy 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 l sz mrmy ;6nw;y+a3bl7ength of the vibrating portion is 32 cm, and it has a mass of ns7ywz 6r;3ya b;+mlm 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wha)zi ql( fpgs5: 8s(zqqt are the fundamental and first three audible overtozl: z(p(5gsis qqf)8 qnes 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 e 5enw/ /pwrg)dxpect from blowing across the top of an empty soda bottle thanpg5d) wre //wt 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-;rt;b t ovv4txzj(eb9q ju ad,-p .;:stube pipes spanning the range of human hearing (20 Hz to ue;;vqb:z4t;9j porx abv(s ,tj-.td20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its th+p5 lc u),wgp,7qvbe9kw6c(c 2ci a qwird harmonic. What will be c c7iab (6g , q529,wepcvlkqw ucw+p)its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and isv7kyms j6 0dp4+3g0y dvr8ax2kp eo*h tuned to play E above middle C xr04gdsdyav*o 27 8 pe6ykp0mj k3vh +(330 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 emitsui0ojd*1l ofd7q0 .dn middle C (262 Hz) when th7jd0fdoon*0 .l ui q1de temperature 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 vc6il 0yn16du20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole mf y. 4p(usx-dbe that must be uncovered to play D above mix(y4fmpsu- d.ddle 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 resonategvadle hfi5qz 4cfl(3da:3+ qgwb d 8)7( eq4l at 264 Hz, 440 Hz, and 616 Hz, but not at any othe4fz43 f e):(wgav(ge5d b738qaqlqi hll d+dcr frequencies in between. (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 resonatryj-wsxf -:w+v 3g-ftes at two successive harmonics of frequencies 275 Hz and 330 Hz. W t3-f wyfjvr-s-+x:wghat 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 .kvneg xmf,s 9qjlh;lxi5v. k09; da,$^{\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 within3cbd aa./+g km the audible range for a 2.14-m-long organ pipe at./gkmaad 3b c+ 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal i1x;58jm xqn ve(seqk;-g kcv0s approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible 8mv kq jk50vexx ncgq-;;1es(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 every 2.0 s when tryin- x 53cgg1kx9zfkbjyaaw ot(22d j6o8g to adjust two strings, one of which is sounding 440 Hz. How far off in frequency i2kw 58jz(a1kxby-g d cta6 3jg9x2oof s the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anyqsdo ga xt10tmp( 7)8d $C^＃$ (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) qho cqrz:;b0p :e6c9aoperates at an unknown frequency. If neither whistle caq6pb zrq: c:0e9hca ;on be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whe 3cijrar c,n(rc1h ria3+ 1xgk j0)k+yn sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Wk1i)k0r r ryj+,jgn rcc3ha(c 31i+axhat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in onemkz - )repxl22yy6nn2 ku4l m* strixyumzy2 nk m -26klnrp)2l* 4eng is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be7hj4no(f : u0m4z i*oxucztd2 heard if two identical flutes each try to play middle C (262 Hz), budjuxih4 cz(o0tn mfo 2:4u7*zt one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a f)i )-w0 4 e)rlu4z6*4fldawffnqq jdu requency 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 frequencies are possible when A and C are soundedzq)*0ane i4l4qr6uu 4)lj- wfdw ff)d together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.54sp 3t0a48s g2,eiopmwf kee80 m apart. A person stands 3.00 m from one speaker and 3.50 m5e pte 3wa44f208pse,mgso ki 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, bu. it9p 5n2caxct a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ? nx9ctpa2.i5 c   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. Hjy(wui8 hdck6p f2kvj(j+, 59f qgw.iow many beats per second willk6 c +i 9wk pufjjq8hgj.ydw f25(i,v( be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ,j4 sbg xwvw:;ency of a certain fire engine’s siren is 1550 Hz when at rest. xvsjw, bgw;4 :What 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 vw*8rgh,/d o9a ; fo+fi 8xjoi( yc y0vgv37rma fire engine whose siren emits at 1550 Hz moves at a speed of 32 m0(cii8 g;+ 8yvrj r o fw/9f,h*moyg7oaxv vd3/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movia93tabmya6 d. 1ows, yng toward you at 15 m/s versus you moving toward it ats61wtab,od my 39a ay. 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. Wi:at7inhmfbj0p5; 7 zhen 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 Hz. What is the frequency them:n7f5ji ;07phai tzb horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recrx*huj;* 1,ud8g1svj 4f ttip eives them returned from an object moving directly away from it at 25ursuih**x4 t;8 g pjjvt1d1f, m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As b mvc6;y bh a03ztxx0cobw0.rk7- gu. it flies, the bat emits an ultrasonic shu-3ycz.0b 6gwxt07a;b 0k o.v rmcbxound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimlm7th 5629xha zw:yevents, a tuba was played on a moving flat train car at a frequency of 75 Hz, anxlt6v2aw:5hm z 9h y7ed 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to :lklid3bm ym40e , n1ve4w9zwn -pwq9 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/sky4mmz0i- b3 ,l:en wpe9wqw1 9vnd4l directly away from the sound source?   Hz

  The Doppler effect us 5bv( g;c ))tw mbl3b(irnctu,ing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of f gxq2pbp/ ynkub8:y8uf;, o3trequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observ:q ;uu,o yk bpxg8bt2p3 8fy/ners hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if i-czid.4v/0br bpp/pw u1e7x.t 3zeofts 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 M e8 g6dln, 0q-s+qdgyc7tue h+ach 2.3 where the speed of sound is 310 m/s (a) What is the angle de7uq,+tcqgg n+s eyld -086hthe shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thi bd/+l:ms . w6v8yfaokn atmosphere of a planet where the speed of sound is o:ldymvok./8a6+swf bnly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the sh0p4,y6g4 eunmekh2 mwock wave angle it produceshe4p2 4ew um60mg ,nky
(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 8as5vkx-z(qq $/theta$ 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 1.58+njghi9i6b f km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determinh9 b6jing+8if e
(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 devic dppf*3 ;.l (habk;ahje that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (i abh;3lj*p d(.pa fkh;n fresh water)?    s

  Approximately how many h 2a)vwn8dmig3 1st. soctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displa+8rjw p- / rhe5gv;i/j q +5kiqbdjwv3 e(rh7py called a sewer pipe symphony. It consists of many plastic pipes of various len5 3i7h;pjv bqek/w++j-whj qri( edr8 /r5pg vgths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to th0 2.gizblr; 9sfnrk(me threshold of human hearing (0 dB). What will be the (n mirbr9; 2szf0l.g ksound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB6ds q vxlt)**c sound and an 87-dB sound are heard simult*qs6l)v* dxctaneously?    dB

  The sound level 12.0 m from a loudspeaker-w8;ki * vvpj3bcc t5a, placed in the open, is 105 dB. What is the acoustic power ; capwbj53-i*8 tv kcvoutput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powew /3trnc-az *jr output drops by 10 dB at 15 kHz. What is the power output in watr*wa3cj/tn -zts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ear lk3wx5- utep,s. 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 airplan35t-k,xw p luee engine?    W

  In audio and communications systems, thaax l,qh50(x vxvwau91 m7px0e gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fre9bf( . rbprmy.quency 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 betweej2aa46 zkw3gh*l f :yvupz/d(n fixed points with a fundamental frequency of 440 Hz and a mass per uni*/zpl6 3fa : zvhud2jay(kg4wt 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 viys 0:pc) abt. v5bu3wbbration 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 lev.)vta 5:b 3wbbs0puycel 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 cwd;i 8.eobn .open at one end and also 75 c..iwdon ;c8eb m 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 observezbz-s5 +kcuqvdb*fw j( u )f65d to resonate as 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 inzynd +d/ 5qamndf+2g( 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 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 t+zng qmn/ d(df2d+a 5yhe sound?   Hz

  Two trains emit 424-Hz whistles. One train is stati er9ei9mxxs.8onary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other trainxri.99 8esexm approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as tpaw .emu238l yw*(s4 +evw5i j 4yyjdit approaches you is 538 Hz. After it passes you, its frequency is me vds+( 2e4wjww5e4lia*y.m8upjyyt 3asured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of car h/xe,-kbp jdvbcib948,cqe )8m d4qss just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car dr8b/hep e bb48vc ,4d dc s9xj,i-qqkm)ops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundixny kxs4r 4( s6do(3e*yzi .bfng together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How .4x k(*n 4(foziyebdsx3s6 yrlong is the other?    m

Two loudspeakers are at4jo(nso0 vrkh(n1i)s opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound)(s ikj1oro nhs4(n0v 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 bl2 t0sd61ng0p r4fw c; z6qypsoood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound 0;nfd0c2zp g4ypqo 61rswt6s waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the mothvpm1v wg +c 8+l/y/ckc is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What pg/cvcl+m vyck8/w 1+is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of higvr 5e/u yufv3ud4 6e9xgb4pu:h 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 b3/ upve5brf6ye:xu4v d uug49efore the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wn 9g7-xql7)nm: (/oobz5eww,h ybt r xas once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most populn:yrx7tx m-n5lg/7w)bqb9( ozoh,ewar 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 bye2 :0sw:bo( cnwk.ffw the presence of standing w:e (n0s.w wobf:2fkwcaves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental 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, slender aluminw94, u,.igdypy e em(bum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can gi. by9 4euw,(mdpy,ebe 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 2kflctz)x /c9 hearing for the human ear at a frequency of about 102x)tf c9czlk /00 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 Ma) h bpah.lc,8;c*bqqtch 2.0. An observer on the ground hears the sonic boom 1.5 min afc *ltpcb,8h;ba. qq)h ter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15f*1-kp5+ seeo bgyye + $^{\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