What is the evidence that sound travels as a wave owr h(i m)w;0+b/5;ssilab rq?

What is the evidence that w7d5zq b9bamhju.)/h f0a7lnsound is a form of energy?

Children sometimes play with a homemp68ryqfvn+l17b:l uuade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretche8: 7uy6f1lv+unrq plbd 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 from one cup to the other.

When a sound wave passes from air into water, do you expect the freque-hoe+(.mkt 0 bv yah7cncy or wavelena kmh- c7(o0ebyvh.t+ gth to change?

What evidence can you give that the speed of sound in air does not debmg- ,4wqdq e2pend significantly on fre-eqw ,bgdm2q4quency?

The voice of a person who has inhaled helium sounds vbrxv yz/+*cp3 ery high-pitched. Why?

How will the air temperature in a room affect theg0xm xmo *,8y7ec ix7j pitch of organ pipes?

Explain how a tube might be used as a uufuo4i.nt4 lwcs4- 2 filter to reduce the amplitude of sounds in various frequ-44lscuiot4. 2 fnwuu ency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–3ax jucz51)4ed 0) spaced closer together as you move up the fingerboard toward t d ajx5z41c)euhe bridge?

A noisy truck approaches you from behind a building. In1c7zz)w 5jw qpitially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 op)j c1ww5zqz7n diffraction.]

Standing waves can be di 5el(so6lt )w4nm r wrj.h+;/,/ls7ru unzgsaid to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” E(ir ouwz/l;/lt.m6jl7 4s,grerwdns) n+u h5xplain.

In Fig. 12–16, if the frequency of the speakers tw;5mn d )ew,do lc34vwere lowered, would the points D a edtn5wowcvm4 ld)3 ;,nd C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas withz deab)c6c 4t8qgl*w x)r.qft9 ac. 1x very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are wo8 g*.b9 r qx4 lqc1.t)6zf ccxdwea)tarn 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 wj hs9;mp tlm12ave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. h1ml t92 j;msp12–18. 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 sourcee+jkr 3hwfb ) x(6,j+2pvlc vm and observer move in the same direction, with th3cf kxpj+,rv mh(6)wle jv2b +e same velocity? Explain.

If a wind is blowing, will this alter the 76hs fch* //qgyu*p* qjfzw(dfrequency of the sound heard by a person at rest with respect to the source? Is the wavelength or veloch/p7c / s6jy(qz* fw**qgd uhfity changed?

Figure 12–32 shows various posi5dj* kly 4c2zktions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the grozk5 4dy*lc k2jund. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo ovk tp91y )q*f8vm, qywk u4bn,f her shout reflected by a cliff at the far end m qq,p1f*) k4ykbn 8vvw yut9,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 below the waterli dqb6:g(c)x dw jpne6uap531j ne. 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 is 1560 m/s (Table 12–1) and does not vary significantly with depth.d6djp exn)wu c5aj13 :pq bg6(    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2z63 g:n7*x o ygx6zrh0y6dcxv0 $^{\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 cb: t1xol7f7lthout warning, an engine backfire occurs on another boat 1.0 km away1lo c 7ftb7:xl (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 strik4gd3d*3 y3u kowvp*2v7mefar ing the water below is heard 3.5 s later. How high is the c 7vrm g43pwak yo*d33d*v2uefliff?    m

  A person, with his ear to the ground, sees a huge ston1s,xs: 7vxm5 bl inul-y*u a.re strike 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 s apart. How far away did the impact occur? See sn:*ixa7yx -br 1, vuusm ll5.Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent errw: aqe*n g g,u7d1gp*sor made over one mile of distance by the “5-second rule”w7n*:ge ,qu1ap d gs*g for estimating 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 sound at the pain level of; eo:,tfd5xq wyo(j1 f 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity*udjx++ :)aaism)u wmg5stu9 is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producekhofcke3 j)vz5t v0m *1se; -k a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,3;tk khe vf ze0c)v- jm*k5os1 not dB’s.]    dB

  A person standing a certain distance from anw*2bmij2w/jmx 2ju7 x airplane with four equally noisy jet engi mwuj j2w2i2j7m*/xbxnes 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? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas foeehcr:8s2jz* cw mi-6r a CD player it is 95 dB. What is the ratio of intensities o:i*m h-rj2sez w8cc6ef the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power 4w2xu5p; d; bps8l cwu*j wd1ooutput of sound from a person speaking in normal conversat;l1 ud j;oxp8 w*ww5sp cu24bdion. Use Table 12–2. 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 strikes an eardrum whose ar1+1 umyhylu) lea 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 j:etlm1sd 2h 1is rated at 250 W, while the more modest amplifier B is rate1s:eht2 d1lmjd 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 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 m.x5 uaa+6/zo:njpry keter registered 130 dB when placed 2.8 m in front of a loudspeaker oa6yz a:uojx/ p .5+rnkn the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level oglw8aqbx8j *, f 2.0 dB. What is the ratio of the ampajlw8,x*8bg q litudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)qih2l(.z0vr l by what factor will the intensity incre2 v(.0lzlhqri ase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have e q tv/e5u:wnx eo7+,a6ntv,to:+hy wequal displacement amplitudes, but one has twice the frequency of the other. Wh+ayotvw 5+,eqev t/n exh o:t u7,6wn:at is the ratio of their intensities?   

  What would be the sound level (in dB) c )xog; f3g zr7--mfgm0*sdp qof a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.m)0 gfqr *3;mgp-z f-g dcs7xo13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lc-r o)l(sa8xe oud as a 100-Hz tone that has8)(l cso-ae xr a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thht+6hp bcfc 8yw.+4wwah , ln1at an ear can detect when the sound level is 30 dB? (Sew +fph6 h+wh8.4,ylcctnwb1 ae Fig. 12–6.)

  Your auditory system can accommodate a huge range o:tk68ctj;,cghip eq0m-ajb 8 f sound levels. What is the ratio of hig-kcg meih80 jjc;tpaqt8b,6:hest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a viownrd-j5gk; .,lb8 w-p*nfaf j lin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and w-f.b;pn kf*n d-wgjj,alr5 8it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible k3 + wqcms)qac25io4g overtones if the pipek2qiswg3 am+54)oqc c is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing a 72:bmkg glv;w03(9dw swl jobcross the top of an empty soda bottle that is 18 cm deep, if you assu 9dgmk;3o (b2wgsw l0jwb7lv:med 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-tubed,t k +zem4v84(z kcbgeud-dys6 .1ii pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of thedgck41dide6 u(e,8m-4+bzzs.v ytki lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frci ;rq /b*ini (4ic58wbbgdtb -9m8tuequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original len58b b *4mqgcbt /wc(i-d8ibrii; nt9u gth?   Hz

  An unfingered guitar string is 0.73 my 1olgr z)1reel 3s2ng6w1.hr long and is tuned to play E above middle C r3g. z1e2 syelo1lrgh6r)wn 1(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 te 8 ud1n 4 g07ra;bobi *qz4gjh),1odgo- cqnkhat emits middle C (262 Hz) when thh0g*zuoq b 7nednbjriq1)o g k8,cao;-4gd41 e 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 aov:a tttjh5-z3c02l ft 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 Example 12–10 should the hole b6 wdme7 ry)2nzw+eri:vgf i:7 )-gpb be that must bgfmbied6 bew 7+)ryz n: )g 2r-:7ipwve uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440tk 0cupy5:)3dh;fhoi Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is ;cih 3ut h:)k50dyfo pan 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 at t n.qmfm+/,mgcw . glx)x1y cpyjxg6) .wo successive harmonics of freq , w l1 mfq/jcpc6xy)+xm..nmg ggy.x)uencies 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 dd ujz1un n1;pmm.clg-1r 63b$^{\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:+e tace c4k--jex/p.ej d4oc a 2.14-m-long organ pipe a/.-cejd +x-4o ca:e tcjpkee4 t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 do1o -oao- 0zge9d m.ecm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in0eogdo1z-9-m d.o aoe the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one 7 5gcghxtryu(1u+f.0 tk(g f 7d:dbawof which is sounding 440 Hz. How far off in frequh1 x77yu.dfgudt+ :g(bgt rk5 w fac0(ency is the other string? ±    Hz

  What is the beat frequency if mide9oq)a qo:cr: dle 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 (brand X) operates dny2y 7sp((rnmpwr2 (at an unknown frequency. If neither whistle can be heard by huma7sr2ndp( yp (rm(2yn wns 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 when sounded w/duqis)6 zz ef*g10d1g xz(smith a 350-Hz tuning fork and 9 beats/s when som/6( 1zi0edg dq szfs xg*uz)1unded with a 355-Hz tuning fork. What 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 one s1rah xobf6 qs:0ng+ *ynl)w+ntring is then decreased by 2.0%. What will be the beat frequency heard when the two strings are no w)rqn ++0a:6nf1* x ghlsybplayed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicp/4e*asyqt x0 r 2s h0xo3r4nyal flutes each try to play middle C (262 Hz), but one is at 5.0°C and the 3qsn0h /4sre*y 0px24 xatyroother at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, andlwpvk+- x/l .v 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 b./-vlx p kl+wveat 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. 3jsy4jzo1 pr22jq6 /dw6xkdr A person stands 3.00 m from one speaker and 3.50 m from the o krs j6rjdz1o34x2d 2 6/jqywpther.
(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 H 5gfla 5r3eq(9okb.dae- 6 vridzi8-dz, but 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 th6 -ib5edid.9ad8(oe3vaqlzg 5kf- r r e 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 om c s;-c2.9rdtg3 pf2)otqxzp f wavelengths 2.64 m and 2.76 m in air. How many beats per go qs;9ct.m2d-3prtfx)p 2z csecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqvpl-l2eg:;epv t+ s 3wuency of a certain fire engine’s siren is 1550 Hz when at rest. Whaspl vtle-wv+ p2; g:3et frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a f w3 nx.u0lq 7;01iu+o u(jj r-onjjxgsire engine whose siren emits at 1550 Hgjxw37 n(+-qu.1n ojir u0jlo ux;js0z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency i3- (epuyutz9wg t xog*7lp:r+f a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/x*t- t:3geywuo pr( p zgl9+u7s 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 eqk w,+1npwn) p:3 lgxnazl70hxuipped with the same single frequency horn. When one is at rest and the other iswa1+k l:wlx37n ,pxz0 ng n)hp 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 ultrasonic sounl1p-tjpvr26wt:amftf b 69z44s sx(x d waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s wtf-ttxsz 1fp6l6 2spav:j m49r(4 bxWhat is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speevun0:rx ggxpu5,p )7 hd of 5 m/s As it flies, the bat emits an ultrasonic sound wavvnghpuuxgr :5x0, 7) pe with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimen(rdur a3o/ + .pzmxt8cts, 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 ru3(x m r8dp/+ act.ozwhile 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 measure blood-flow speeds. Supex+r40vwj um-pose 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 arteriesm 40w+eux vjr- at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect us 3d4bei. gju/98xatz/eljyw 0ing 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 soundure hcg7jt(8u uf87 h: of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at r7tj 8ufu gc7h8:ur(heest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spt+3 r lh*rou3weed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What iszw lhvnjq.oe7xg0 hf/5f0( ,z 6xqgj2 the angle the shock wave makes with the direction of the 7h/65v zfw. ,nh0fle(zjx qjq g0ox2g 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 t(7 bq19bz+9muomjbnf he thin atmosphere of a planet where the speed of sound is only about 35 9n(+bmjufb z7b1 m oq9m/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. Determin92djv) hjp*+ zgev1ge)i yle 1.8igime the shock wave angle j*eg)jeigi vi)ez1892+h gld1my.vp 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 bs f5j j)2bz/m$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and t b*t(z,cd5oj see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the pla ztc5dot,*(bj ne 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 devicrd38c-hts *f;fgox4 me that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects emsh x;td48fg3f*o-r cchoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the fuj 3p.1wucx0 human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dijcyytt7vv3 5(*6 cz:( e ht f6u+qhpqasplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open y q+6qfeuv a5 j3t tpzy*hchc67(t:v (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 togvvb g 0dg tpq)9n tj8.-zpe-z3 n-o2a the threshold of human hearing (0 dB). What will be the sound level of 1000 such mope 9anz tbtj-n o)-v-2 dvgz.gq 80pg3squitoes?    dB

  What is the resultant sound lev71 :y/.oy lg,oeweggxel when an 82-dB sound and an 87-dB sound are heard simu 1wxee go:, lgy/g.7yoltaneously?    dB

  The sound level 12.0 m from a loupzj xpgsp2z 88696egndspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directi 6gpj9 zpgpz2xne868sons?    W

  A stereo amplifier is rated at 150 W output at 1x f ro)jzm03d9000 Hz. The power output drops by 10 dB at 15 ormjdx)z90f3 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet airay8z 8s/rq;a rcraft typically 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 huma;a8q8/ zyrras n ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the g. bbdv2svthkh ::w;u .ain, $\beta$ 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 vios;umziv:+hc )7lu ( +xjky 1:w6zkunelin 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 poina bdsd9:k okuw *m05*sts with a fundamental frequency of 440 Hz and a mass per unit len dsds9mub:o50wk ak **gth 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 velnc:3vjpenet ,y. .x e;js .j0rtical 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 0x.j.. ;evj n cpet,:slen3 jyis heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 gyvt3sv6 y+)xl is near a tube that is open at one end ant6 vxy)v+s3y ld also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obser y+f6k3t5* + bkysjdhlved 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 tsgh / ;ah v1x2tk8) n:zv4dbjphe 500–1000-Hz range coming from two sources. The s sk/h18 z;vapnj)4 b:gt v2xdhound 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 the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary.2s0u hj/ m*ehe 8rv s,-sglke5 The conductor on the stationh/*ss hejvgkl mesu e 5,-r208ary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam po 1.rlnv.,az (l4aed train whistle as it approaches you is 538 Hz. After it passp. ,4an( ve1oz arlld.es you, its frequency is measured as 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 listenind +p2awe-3tmw1r u ;blg to the difference in pitch of the engine noise between approach2uwm r;w3tlbep -+a1d ing and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sx* ab pkgvh2;,ounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the otv;* 2bahkx, gpher?    m

Two loudspeakers are at opposite ends of3uv- ,z8 -)c a9k*awsddosr p:bkxr 5r 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* sd,-:prkbr5 3)ox89- c kvzaawsrdu 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 o8b.jupvwsy:/ t)2v rabout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume t) /.vv:wtbp8u2 y josrhat the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 62nkmjay a9dxx;d4 v)..5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a 4;y9)xdxa 2nda mjv k.sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high fr q/i6xm 2gybzw/-f+c/dpqml. equency sound pulses as it approaches a moth. The pulses are a+wydzq.c/q-6 im/mfplxg/2b pproximately 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 the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one A ; vnqld6o-6m-tpdjc 4lpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamelp nvdjt6 dm6 4qco--;ntal 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 x5o) 2 -mafz)serkou 4can be compromised by the presence 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)xz)orsmkue a f-25o 4 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,” invol*akb/ve4 84)vpi dw blves a long, slender aluminum rod held in the hand near the rod’s m8bw)/vbv4 aled4pki*idpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the thrvs n4dmmx8k 0yo s7g72eshold of hearing for the human ear at a frequency of abouto0 8my4s g2v77ksnxmd 1000 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.u9(6/s bfxke 8vywff(su :fjbff *x5+0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the sx:j(fyb 9kbvwf6fx8 +usu5ffe *f/ ( plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1laqey-.3e r63 gcvlb -5 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h