What is the evidence that sound travels as a wav/h *hlx6x:kome?

What is the evidence that sound is a form of enerqs87z) bvjx+a8zpn)e gy?

Children sometimes play with a ho.-:y krp9eyf ot3kkzw.+ e)tememade “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 travels fro tr3y .o e.p)ef+- 9tey:kwkzkm one cup to the other.

When a sound wave passes from air into water, do you e qjoeoo7ev)5q s 0h+sw5 h t01tt/ cxjy+k/9llxpect the frequency or wavelength to chant+ ) 0k qt/50cey9os7lvseh+qjjth l 5/wo1xo ge?

What evidence can you give that the spedi :5j:t+zdtjp8a9+o; kgbmwed of sound in air does not depend significantly on frmpdt+aj;wb 8: k9j:5i g+odtzequency?

The voice of a person who has inhaled helium sounds very hi6f gjff01z /frgh-pitched. Why?

How will the air temperature in a room afqvq4kavf,5 2l d p ahz8v8fpjj*ch583fect the pitch of organ pipes?

Explain how a tube might be useoc 1) y6lq z)qfd,.nfn*ypt i4d as a filter to reduce the amplitude of sounds in various frequency ranges. (An ex oyp l) nic4fy q1*.q)n6fd,tzample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced an43 dicshfy:;if85wsgb:hsqd3q; : closer together as you move up the fingerboard toward the : c; baw i5s;qsh8:fgf 3d ds4inhy3q:bridge?

A noisy truck approaches you from behind a buildincndy+5 hai+6*vwul6)zk8lklbxi e ki 4f,; p+g. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequenwbki 5ud +4ck+nealz l;xp*6l iifv 8+h,k 6)ycy noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bp y38nf pmmtc-5xyk*t uan / k+/kkc7)eats can be said to be due to “tnk)um5x f+8acp cm*/7 ykkt-/ny 3 kpinterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,7zg(*(sje2nw pf) nfk would the points D and C (where destructive and constructive interference occur) move farther apart or clos fjg)*k (z2w 7npsenf(er together?

Traditional methods of protecting the hearing of people who work in areas with vwxzum2l)9g -.r60a q wys7m8rs x,xj yery high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addiy gxwy)rw2 j m9.mxsq,luax- 8 7s06rztion to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves showna4ng4 bkhc;)b in Fig. 12–31. Each wave can be thought of as a superposition of two sound wavesa;b 4nhg bc4)k with slightly different 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 shift if the source and og/xux(e7. p,m/ ;lu ch gcayg.bserver move in the same direction, with the same y. a/cg;gp.uglc eh, x( um/7xvelocity? Explain.

If a wind is blowing, will this +q-y+wz:,aa4 .x*wp;ly6tad t5wk8 cl vds ojalter the frequency of the sound heard by a person at ret od-4q6 ww5taxdl+zv.w,y pak*sl8;yc +j: ast with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions w;j2my-l.qxxof a child in motion on 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 whistle? Explain your reasl;xy- wmx 2q.joning.

  A hiker determines the len *w8kl bo hc4tqz q0p6z6k(2kxgth 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 tq6o82hp w tk(zlkc0*q4k zx6bhe length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the ,s62 , rb;vcnknx-bzy i.4i .-gbslvswaterline. He hears the echo of the szbi.n2 . s;r,sxl-c 4yvgknsi bv- 6b,ound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave 4kus+ t*ja*b*/exyy8f ;ru kmlengths 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 an. ;leks uzknptl ( 4:,h mnnkg0, sruw7,,ei8 foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before t0umk ;gn knn tuihz4l,7e, 8 :s,wns(k,r le.phe backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliim*pzdl*7(klm(o /b5z p9f ii ff. The splash it makes when striking the water below is heard 3.5 s l(m5b*dollzzi 7i ipp9 m/fk *(ater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the:yk kvnf6d-p74s dm;b7sb h6gxihi5lx)3 7 r a concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and th :p76 x7ba vg-k xmdy)s3kd ;n5b6ir7lhhs i4fey 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 e ;m+tq*q(jpf over one mile of distance by the “5-second rule” for estimating the distance;(jq*fqt m p+e from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1.k7*q jx hjzg120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose int840a0lc o+xjfwf4k x fensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leva; kl3(mxm ac/+n)2azlz h5iyk3 tom8el of 95 dB when fired simultaneously at a ;k3ym al +nahm)ma (l 2okcz8/tix3z5 certain 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 airplah 4:z mr5)vm) 4ckq3 8 n,zpxanug+pdkne with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captc)x4n) mzr4z8:gupmk k+ 3nhp qad5v, ain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-eqh/pjehc . 6;to-noise ratio of 58 dB, whereas for a CD h6ph;q ce j./eplayer it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fromtip n gm-(ql66 a person speaking in normal conversation. Use Table 12–2nm6 p-tgqi 6l(. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strizu3 5ozqx/x xw638c-ssqa 1xjkes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the mos 4rrt 7s) 6m+2jrjw sol,v/pire 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 loudspeaker connected in turn tor2)w isjtorrvl mss,j /764+p 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 place7zsv:ew pr: * nj9;cded 2.8 m in front of a loudspeaker on the ste7* :nr 9sep :vcw;jzdage.
(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 inihuvr 9rznc 0 jjz0dbxo,+v41 ++ypf; sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by thr0z+y 0n4o9,ivr;v+ jud+p jhcxbf1z is amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of sw+6x 8uwyf ujnahy)8t, pn4 (a sound wave is tripled, (a) by what factor will the intensity increase? Incr t48pxnhw) janyw, +fys8 (uu6ease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenjow:e*x(pc2 k t amplitudes, but one has twice the frequency of the o:p( xc2kowj e*ther. What is the ratio of their intensities?   

  What would be the sound l +f k:dw(w ,dagv6 ,xkt4zvh3qevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air moled6qk daw( 3z:hv kwfgx ,+4tv,cules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem asc)2 8u4pph za2 gxzlu p0-gr2h loud as a 100-Hz tone that has a 50-dB soundu0 x28 2pcg u2lprgzz)-phah4 level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thqz19f:)0iz3by6 k(ize d nxi uat an ear can detect when the sound level is 30x yq3(1nk)i zz69 iefui dbz0: dB? (See Fig. 12–6.)

  Your auditory system c dfkn-3 q6y8tban accommodate a huge range of sound levels. What is the ratio of highest to lowe6- yb8f tq3kndst intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violinwk 9erw,,z4x1yunf,o.t v kuy 4n:e 5t 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. Unkv1o4 ezyw x u,wy5,f.ekn4:t tu9nr ,der what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible oq*vtvx-yn:ztwl ;1 3gvertones if the pi vtzqg;xyl *:-t1w3v npe 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 woumi0gce8a. j x.ld you expect from blowing across the top of an ecm.8.jg0ea ix mpty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube c);ue +klh3tupipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes ceu)+3tk hul ;required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string 80 q+guqy wru6has a frequency of 540 Hz as its third harmonic. What will be its fundaqy8rgqw+ u0u 6mental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.:u61 8hq7yob1ttfmb p73 m long and is tuned to play E above middle C (330 H6tt 1bohq8bu 7:fp1myz).
(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 C (262 Hz) when:v5xs ;f oyzb21b9bini(hd,gt0 ,sa q the temperature is 21t nqhbs a:zgd,y(b;v5f2 ii0,xb 9s1 o $^{\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 20yqkb(7) nse j9 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ofp :p-/ rs48glm(ehsm h the flute in Example 12–10 should the hole be that must be uncovered to play D above mi pm(s sm:h 48e/rp-hlgddle 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 61es)l7ia cm2a56 v0vr 4ou2 azj6 Hz, but not at any other frequencies in be0czraa5 vlmi4e2 7ova)s6j u2tween. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates avrp l:zxt n);b;p;q*w t two succe;v tpq)*xzr;w blp;:n ssive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 9p6n*6npb,5cxs sq( (z xr2fun wn *wi$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14,kjr-wtm 3g8u-m-long organ pipe at 2-w j,u3k8rtgm0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is op mx.xm 2:vy(h0gv:afm*cprmp)t8y l + en to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationshtvmxgv)2:m mla0yr( m.x*yp c:+p h8fip 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 whe zt*i/gvc85k wn trying to adjust two strings, one of which isv*ic t8g z/5wk sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middlvo9 5jzfg1 bg,5tfm*f e C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (bran5 p3t z9i./yngstjq5mdav- /pd X) operates at an unknown frequency. If neither whistle can be heard by humans w5gtz/v9n/j3ay d m 5pqp .ist-hen 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 when sounded p ;(fnpesyexvv,0;f v- tke39with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequ;,f(3y eskp-vfp0t nve9;v xe ency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The te8g4 c1mbb5 gabs;h,kw-nv 4uknsion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings 4s1v5 ubhbgm4,ka-nbgck8w ;are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes c 08 (2gojbbkaxf ..edeach try to play middle C (262 Hz), but one is at 5.0°C .kgo2jde(0bcfx 8b.a and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A,;m7xdu sv351yvl d qew).n9uq B, 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 fuw x1d5lqu d.; 9)vsnqyvm37 erequencies 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 aparta lep8cd(f)9) jb6navm r0m6t. A person stands 3.00 m from one speaker and 3.50 m6v pa0))lbeac n m(jdf9t8r6 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 bk,yyp4i9mr v9 qk)0 cvibrating at 132 Hz, but a piano tuner hears three beats bk)9 ,y kpm9yvcriq4 0every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How md h 8;va(ln98icydv6 gany beats per second will be heard8 ldvg6c89inh ( ;dvay? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 r.; 34kvh zlglq cjaghc850( zHz when at rest. What freq rva.c 4 (;hkzz385 0lghjqclguency 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 l2uwv6)ie9 xxa fire engine whose siren emits at 1550 Hz moves at a 2u x9ixwv6le)speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is gj r w-eamfeuq7:a0)6moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? A-uew7jm)qf 6a0ag er:re 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 0s2 a q5t7soufthe 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 Hz. What is tsfs2 570q uoathe 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 c9c +tyt 9r)/upa kq.ythem returned from an object moving directly away f cy9y9.ku/a tr+cqtp)rom it at 25 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 it fls(ql6yc4o biw )fkf 68ies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the ycs( )fl8io4qkwb6 f6bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pla/s12alrflf p h skxx49yzg(,-yed 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 appx1kasx g/l(zs92p4 ff lr- ,hyroached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to 3p;;6 xtd btcvu*kqs 7measure blood-flow speeds. Supposeq;3bpvs7u d 6ct;txk* the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frdj /1.h1iu()w a, k7ziqg/dtto tr(enequency $2.25 \times10^{ 6}$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. We9i0+ s2 v:y tkqz1m gz,ko(ztscocru0l-2a8hen the wind velocity is 12 m/s from the north, what frequency wiczl -+ s qz92to kt:i(cvg rmkya2s10o, 8e0uzll observers 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 objec ob;. 0p-+cb-zlabbdq t moving on land 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 vb dho(z 3ab9i:pby+e4 xb,w7( bqur 62.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction ofb3r (ow6d bax9i :ye+v7 z4,(bbuq bhp 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 thin atmosphere of a planet5t*;*8 iircp)ygero *csd 0x m where the speed of sound is only about 35 xe tr*cyg*8c0;sd o )pmi*5irm/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 vjunh+t*+uv - 5 mip8ashock wave angle it produap8 tv*vumi j-uh5n++ces
(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 .jxvafgq:6o1o6 mpy +.q6ucv $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground fl n w8f1o:zjiu3yin:3oiz81fn uj wg 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. 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 puv+;ohc kd:sg-/,u sljlses downward from the bottom of the boat, and then detects echoes. If the maximum deptsk/c s, vou:dlh ;-+jgh for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in tvyw;( 4vhm.m,un0l. nkyjz e-he human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display callew. yk -.mkywv:d a sewer pipe symphony. It consists of many plastic pipes of variouyw :..-k ymkvws 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 ma4aepj *bcm 5u0kes a sound close to the threshold of human hearing (0 dua4 j e05*mcpbB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sew;1lngkb3esx7 g +k9 ound are heardn e+w ;g9g kxlk73e1sb simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placeh hs8 xo*j btm9nq7azc2( 28ced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equalacq9 8 he*x2bs czmjht87o2n(ly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The p r5xtwuq/:bm( ower output drops by 10 dB at 15 kHz. What is the power output in wattswt 5 rbq:mu(x/ at 15 kHz?    dB

  Workers around jet aircraft typo y,tyy hi*,e92h6 fwyically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would 9yhiwot*y,2hy f,e y6 be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communic .nwu+gnx :1boations 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 violi ckbk+;s , 2vvh4tzr1nn is 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 fundamisf947gei/:3jpu *u pbw mq*mental frequency of 440 Hz and a mass per unit lengthf pi4 i*qmep9*wu s:/ 3ub7jgm 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 open tube ogz( fkr(o ,i3filled 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 resonatefi r,og( o3zk( 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 stkdt+kfo7 f/t4 pv+x2s /e 6tqqring of mass 2.10 g is near a tube that is open at one end and also 75 cm long/+ qtpf o4 /2t76d+ktksqvxe f. 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 ob2ybi zc lf7fr:os)48z served 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 in the 500–1000-Hz range coming from two sourcesua,h;/vf*xw, w+gko 5 oidq2p. 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 thghiqkpw/ oo;,* u2f+,5xdv w ae sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. Thespc* 5og+um (y,az+a m)y+vp v conductor on the stationary train hears a 3.0-Hz beat frequency when the other train 5sovyym+ +z,*apv gc()mu+ ap approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as5v1+zylj)q+ sn(bykm it approaches you is 538 Hz. After it passes you, its frequencyk qnz1m5l j b+y()+vys is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate thej o4*-a9icqj-f 9ofmg speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a -*gjjof ifa o-m 9q4c9full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, s y)0h 8woot2:*poij p;izi z-zounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othezzz8) ooiw ;tpi2-yj h:*ipo 0r?    m

Two loudspeakers are at opposite endqlh09mly6o)p s 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 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, anh 0pymq l9l6)od (c) he hears the speakers after they have passed him, at C?

  If the velocity of blo6 ;h:jsmf :ycyod flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wav sf:yj :6mh;cyes 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 c ayte np.2lnx7l2j/0(x8tt j 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 freetxj(/t7.ynjt0p2 l2 nc xla8 quency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches aab0ipc k3tpp74iq.4 p 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 bacbppt 37iak4i p4q0p .t so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from onts qvh a.v3:qqow:)g 4e 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: q at34sqv:wh.ov)qg 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 pre 4v,gtacfv42gs/ 0uy fp, 5gvqsence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies forf,t y gag sv/fu2v,4cq g4pv50 the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calledr8vznh l8;3 4fqi-sextml85b “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. irsmt-h5x nvz3 blef 884 ql;8The 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 hearingr60u83b gljno for the human ear at a frequency of about 1jgol b6n8u30 r000 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 gg2cge/ ro mufgkxp)72 2(d7erround hears the sonic boom 1.5 mf7ermuro)d k/ g7x pgcg2e(22in after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo r1d26ghc+9n r1lw xtw,9z pfnat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h