What is the evidence tkbid+s5 .+( ydk6c snbhat sound travels as a wave?

What is the evidence that sound ,n duqutcg6,1 is a form of energy?

Children sometimes play with a homemade f5l20ig+jl-y l 7au;n*o yzjm “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 soaj zlil- j7myugylf *n5;20o+und wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency oh4cmo wr vad5d3d(w 2+r wavelength2+ 5 c3dhvwdrm( 4aodw to change?

What evidence can you give9w3hkrzcs1 j02 hkf7p that the speed of sound in air does not depend signific2 0h wkrjh kp17z9c3fsantly on frequency?

The voice of a person who has inhaled helium soundsvy *j(2bdxe f6(ncn;m very high-pitched. Why?

How will the air temperature in a room affect the pitchannxl /a( sr;7 of organ pipes?

Explain how a tube might be used as a filter to reduce the amplid.ww6 9o7gsudtude of sounds in various fwd sg67.u9dwo requency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethee l iga8o9i43sr as you move up the fingerboard toward the bridge? ols83e9ii4 ag

A noisy truck approaches you from behind a building. Initially yoyk w7ytu.+ q /4ow4oaxu hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brightek+ 4to.ux/y7 4 waywoqr” — 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 “interfer2bukal(4,c ewnly0v4ence in space,” whereas beats can be said to be due to “interference in time.” Explain4n,lk0blue yvw ca(4 2.

In Fig. 12–16, if the frequency of the speakers were lowk8.qyn9 v)/:,y9 ewloj eam skered, would the points D and C (where destructive awy /s .:eeaq8kk)9y9omn, j lvnd constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas-yl9kx( f6n x2-mmeo .bczps8 with very high noise levels have8f. eyzk-xxl-nm(mc obp 6s29 consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave canw9e /shro/; y9ubm en*7pd3lu be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain9*w u7u s h/d/nebr3yom;el9 p.
(12-31)
(12-18)

Is there a Doppler shift if b 5g lki yo25l;frn0v3the source and observer move in the same direction, with the same03l l boy5r52f;niv gk velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pe5iqb9 aau 0 b6rmhw):rrson at rest with re0)9awiqb r6uba 5:h mrspect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on eryt n kbw0g,7b (fyxz:93dx(a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whis: yb7d kxg, e3(z bnf09w(ytrxtle? Explain your reasoning.

  A hiker determines the mnn60ul*qg 7o w2-)f yw xhlemy5m6m. 5hxcb+length of a lake by listening for the echo of her shout reflected5 h0 gwmxhwo6bf7yn25lmyc.nm-e*ux+ql 6m) by a cliff at the far end of 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 belo2whn5 f9hj ;hnw the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep isfnwnjh;295hh 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 waveleng: h b(olfvghv 3yz7-7wths 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 foggy day. Wi 8h 1o. nuj,7/cv 4yydjn+budethout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard jnj v e/du8 7yd+1u4o .hcny,b(a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top osgza r9;*rm6 h70rnfef a cliff. The splash it makes when striking the water below r9az ns hm *fr7rge;06is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge sto k(re,v1-om1wk c a wth-lkxw(+i.h)qne strike the concrete pavement. A moment later two sounds are heard fr-eik rh,vtwcwa11.q( hk)(lx ok mw -+om 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 mos1l(-, g fe-hsx7xao b*s jb,ade over one mile of distance by the “5-second rule” for b,o,s7-1 j *-(xfxsoe lga shbestimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soundb 2 etl s/kh6k,s0)t es-6e)9dpl uhzn 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 lev-kp1s-a.q szqlnvda/z g2, -fel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers proh w)o pz g+ t5;jihp0a8c9(bgkduce a sound level of 95 dB when fired simultaneously at a ce t()gk9ai+z0jwpg h;o 5ph8bcrtain 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 with four equally noisy je/o,ytpks( 6)2qwngw+y:lu82 o mxjpet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [y(+ o kmoj8g/2w6tyqsp)xp2 w,nu:el Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratioi/x1a sf4.dzg 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 4dz 1.fa sxgi/for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking m9zagr3 f8fv9 in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mov389zf9 agmrf uth. $\approx$    $ \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 ad ,,d (uwb1xm.vc z5k0swlif-n 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 250 W, while the more modev3obz,(x cl t.st amplifier B is rated at 40 W. (a) Estimate the sound level in,3zc.( o vtxbl decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB er auwf 2)l*vs .jc,7pr6m r)umeter registered 130 dB when placed 2.8 m in front of a loudspeaker on t)) .6,sr7fuvawrmec *u r pj2lhe stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level ofj5 cogl,,7 u,a:o vmmm 2.0 dB. What is the ratio of the amplitudes of two sounds whose m, uomlgmc7oa: j,v5,levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fa6qz ag fjica *;g2dr+)ctor will the intensity increa+6 zgq faj;2r)daig *cse? 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 d75 yv pl*7-; ia*kblgakua r)has twice the frequency of the a ;-idk7vu 5rpl b**gya7k al)other. What is the ratio of their intensities?   

  What would be the sound level (ine ,as :z;t g0+g ppat5u/om0lx dB) of a sound wave in air that corresponds tosa zttg0oa e,xpl;u+0g/ :pm5 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 louvt/i9djqf il *x301zp4/+mtbc mk )c dd as a 100-Hz tone that has a 50-dB sound lmmq34txjpk * 0 c/d9/c1+i bdit z)flvevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detecmcgni32b/snz(ag5j, ; 1bh mtwpz 9d0t when the sound level is 30 dB? (See Fig wd; 1b2 5z ,9mgpi3hzcs/m(n0 atnbjg. 12–6.)

  Your auditory system can accommodate a 1jasyhl7:, ivry0 h 9jhuge range of sound levels. What is the ratio of highest to low7 0 :j,jvy1y9ahshrliest 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 fundam s9oe)7d.j( ennlpvoo*q4w x4ental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g.n .ej*o)e4wns9(voxoq7 4pd l Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundame z*ezaw:ou6f0 -r s9rgntal and first three audible overtones if tha:gf0*zos- wu9re r6ze 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 bl1r1l4p d919a wj rlwxeowing across the top of an empty soda bottle that is 18 cm deep, if y we4lrpxrjw99dl 11a1ou 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 e qzz,90h bck(/oh hn13syi( bpipes spanning the range of human hearing (20 Hz to 20 kHz), what would be theb(o13y zc,q0ihhhe( n9skbz/ 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 third ha) ;w:pwz(tyoe rmonic. What will be its fundamental frequency if it is fingered at a length of only 60%y () ;tp:ewzwo of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tj **zrowr2 cd9uned to play E above middle C (2rc9o zjdr*w*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 pipegirun ,r8: ;hd that emits middle C (262 Hz) when ur:n8r,;igh dthe 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 tyb0zu+yu 2)yf6sp8 rjoh: 2o at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampxxle73hcp9u2wvc+ n rtcv6 *2nso; w5le 12–10 should the hole be that must be uncovered to play h6;nxct* +scxr9wce 5upn7olvvw322 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 re,j u11gcvv/00 w5nlxipjg9b w sonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequ1 ng0c up vgv0ixjblwj/,1w5 9encies 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 endsweyt3;x1t*kj . It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What wx 3 *ktyj;1etis
(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 2zvl 4yh,dg4c $^{\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 ra.sxm)u8ikg.xv a0 p1ange for a 2.14-m-long organ 0)smik u1ax ga..x8pvpipe 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 evca,x3 aaj0t2 9p/pzes 4oa. is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of /z2,e4pxco3a.s aae9j pv0 at Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adj v7u6tnkomxn-p t;r .0ust two strings, one of which is sounding 440 Hz. 6k p-t0t7; nrnuxv.moHow far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz rdif (bf:1gk3) 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, wdwcgl-v 63o orkxi1/8hile 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 simultaneously, estimate the operating frequency ofoovklw 1r-dc8 /36g ix brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz 6 s6 w5znb,dqbuy0rym):fhk+4 suy7 q tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of thedhqss5b k :0,b mnu74w6+yuyz )q 6rfy string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tencgif n5a :5 g3c..f.fo lyoby-sion in one string is then decrease-g.:fl c5.ycgoy fa ob5.3fnid 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 be heard if two identical flutes eav- j:z-:j,ikr;l(/c9s riitp7.bee 2og p sljch try to play middle C (262 Hz), but one is at 5.0°C: (loj ;/7ge :bi ers2pitpsk9-,l.c -jzjrvi and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, Bav5th zz(r 8oo 009szbn- 6w3oauu2dn , 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?oz-zoa0 (rvz0u82n9 sh 5wn3 6baudot What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker an4irah 5w1g1r/nswl .jd 3.50 m from the other. s51rw ln1ga h/i.r4wj
(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 hee34ny v0gtou n2b6z5 gars three beats every 2.0 s when they are played together. (a) If one is vibrat g0z6t g4 vu35y2bneoning 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 wavelz9(h/wbrlkm / kmu1kq3v c68)xitt*7f coue1 engths 2.64 m and 2.76 m in air. How many beats per second will be heard? (A t3l ev) oumch (wk1z6/fuk/1x 9q*kmct87irbssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire*(mrvy :er cu8 engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s :ycume* (8vrr
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequ9;c phlz yswx+li2jldq (3 bd+b*h.-lency do you detect if a fire engine whose siren 3j ;d cbl dlby*qh-lps 9+2i.wl(h xz+emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if k31xv ) khptxg+rs.x 8j.r3mta 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenci xr.1xhkj gp+8t3tm)rx 3kvs .es 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 sinfb2wg7oy (+ nu6 tc(klgle frequency horn. When one is at rest u(2gk oywtln bc+7f(6and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ulterak( 0 -a) (rmrjfg 6 04idmywna,8zcrasonic sound waves at 50.0 kHz and receives them returned from an object moving a z 0mfimk6y(adrj,0r(en)rwcg -8a4 directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spee(o kx2v.cc.bo t3qs1td of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wav(o3t2cqb.ct vsokx 1. e?    $ \times10^{4}$ Hz

  In one of the original Doppsnyb dg +-xw.;a-6qamler experiments, a 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. What beat frequency was heard if the train car approached the station at a speed of 10+sadn y6xwmq g-a-b;. m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo/c84sc4ke9shi1.w2npl 3 j7uqmpuc b d-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 fl9 8m13sus4ue 4c b2qp c7wjc.nkiplh/owing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves bapqw - ad2n, 16o7ac 4ikj *tlhr:z,oof 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 velocitnkk+o0b zh.x )l2 nu54scelr 3y is 12 m/s from the north, what frequency will observers hear who are located, at rest, n5elkx.+ nu b0cs42o)hz3rl k
(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 4ys i)b x:i-mn x5ld-xif 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 Macnyk.fhttfv, r8kq;47n b4 4ee h 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the a44t 47et f8fkkvh be.qn,ynr; irplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet.m+z aa4s mtmi(e b-y8 where the speed of sound is only about 3m+y.(ei4-m zat ba8sm5 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 shock wave angleq1 y-kc4p*9y.o rn lce c 4noy.e9ql-r*y 1kcp it 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 gc7:fg2ppqa, cq*e /f$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheu- 8p,qm4isilk*xx, xad and see a plane exactly 1.5 km above the ground flying fau-q8, si*mx, 4 lkxxipster 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. 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-o 2g vhyrs q4c8ex23j t;yr qvfrh)9hd. d45g-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 (in fresh wat 4defhygxjc25v o89qvr r;qs2-yhd)3.r4hgt er)?    s

  Approximately how many octaves are there i3 *rrg ( l1bqqv:a+ucja/qur::*qegi n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has546 rp rt)/g*dflnoef d:ha,c a display called a sewer pipe symphony. It consists of many plasti ro*5e) 6atdn4dpfh,r/:f lg cc pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to th 4cv*y3 q9xsjsiov+dfi s1 q87e threshold of human hearing (0 dB). What will be the sound level of 1000idivqx+1y*so7q f8j c49 s 3vs such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound .d vi*v0tn( b8n0 hkm+c iz1jdz1k5omare heard simultanm j(0+nz10*kc vt d5z.mk1dh i8nbvoieously?    dB

  The sound level 12.0 m from a loudspeaker, placed in mnwbt;(4o d 6cy;,d16vr nhnrthe open, is 105 dB. What is th 6,n; ntydcw1 ;no(4hr6 bdmrve acoustic power output (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 power output aig1 f 2rfn0.fdrops by 10 dB at 15 2arfg.0 nff1i kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically -8 fvyhd5ip u5wear protective devices over their ears. Assume that the sound level of ihypf vd-u585 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 communicamck)o.ay*4 t6, dod xvtions 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 q e+35 (vs:a*b cqqwjdis tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental z0 q c6a:rpgkwpu0 v2*ao0zl7frequency of 440 Hz and a 0p g6r20opq07 :zw*lakuv az cmass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration abovek);x bh )pmap; 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 wab h;);)x mappkter 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 nreq cz9(**0w8c apeomass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third*creqe* a8znc o9(wp0 harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as x2srgl.5:g vu4-1u5 aid ty wcone full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz ran.c, 41hefdwf uge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the fr1we.hf, cdu4fequency 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 the sound?   Hz

  Two trains emit 424-Hz whistles. One traike*ii m dm5 dg)h-b)golc, .g1n is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the)gmg.dmb),*idc o g-kl5he1i other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it a/0 *bs0tin yg0k.tpjgpproaches you is 538 Hz. After it passes you, its frequency is measured ag j.p 00iy/ts0gt*knb s 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to tt -jgzrp5g5kzx,yg, 8he difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car dk5 gj tp z,rg,5zyx8g-rops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of +;agp drr-gxe)f guhq:-f+ 3 3xlhc5u11 Hz. The shorter x+3x:u r-gh-hf dg3r e +qgc5ua f;pl)one is 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 i9j96tf(lnr( i ,;v3yoyn lux stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) 3nflyt(rn9u jxi6(oliv y;9 , 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 normally about 0.32 ml )lpziq zm 5*+(fi1fn/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directe z1qipml()lnff +i*z5 d 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 al ybinwi1h2un ir3: m;/(8usa moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave rw r(lnm 2yu/iu n:1s3i;i8baheflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it ac;(eqwaai e w+r0 c6x/pproaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before tx(a6ie ae0q cr; wcw/+he next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alm-w-l,x:o yjc pine 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:l omcwy jx--, 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 ccf hh, 5t;i6mcgq, q,oompromised by the presence of standing waves, which can qq,,c6fimc, thh;o5g 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,” involvesx,0g0j8fp,tz l x:iaq a long, slender aluminum 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 be made to “sing,” or emit a clear, loud, rin,px0 zgxa 8t j0l:,fqiging 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 thres4x3ovl2ujqy-(z 4qkuw*w0 ah hold of hearing for the human ear at a frequency of about 10004hl*wuqj3o4yw-qv0 2z (u akx 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 thgytog:g, e-dn8tw 8j 7e sonic boom 1.5 min after the plane passe yw 8ng:j g-8d7,tetogs directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 o g,y cjic*e82$^{\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