What is the evidence that sound trd r)m7dyi:d4ut4 x7 qkavels as a wave?

What is the evidence that sound is a form of energy? 6ye:h5iajqvgh0ocq6m3i-0 g

Children sometimes play with a homemade “telephone” by attaching p 7yaze1y+g;ei 96vmi 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.izyym +7gpea9;ve1 6 i 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into wa pxuhji3.g;1zter, do you expect the frequency or wavelength to31pg.u;h zj xi change?

What evidence can you give that the speed of sound in air does not d;:h 0y;zsf wzwepend significantly :h;ys; f0zwzw on frequency?

The voice of a person who has inhaled helium soundslt(txhe; ya13 very high-pitched. Why?

How will the air temperature in a rda40,pw*83gj l a gl;9 zulyiyoom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplituz-r:e1l2vv0u) j4zqa .ze9/fqv oc li de of sounds in various frequency ra .e/ur)lz :1qjviovqa4 - zv9lfcz0e2 nges. (An example is a car muffler.)

Why are the frets on 4qhb9u:7cadu/e29am, nsdp v96uauy a guitar (Fig. 12–30) spaced closer together as you move up the fi4a9umhde/apqcb6 ay9d2:uu, u7v 9nsngerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hea tp /a98iv(ry/ed) 8;qh l9 +myvehzhzr 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 oztq /ey9hvl9)i ;8aeh8dp y(+hvrz m/n diffraction.]

Standing waves can be said to be due to “interfermiq( 6sft*4num 5 cax9ence in space,” whereas beats can be cmf(a*minu 6 95q4t sxsaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequenc ) ,4ev)gyidysf3h/ ydy of the speakers were lowered, would the points D and C (where desydve/,3i )d 4sygh)fytructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the heari at;qlhw., ht8ng of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn hthw ql;at. ,8that 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 f1wgb v7gu i0z3.8aje Fig. 12–31. Each wave can 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),b wgeg3z.0i1 u av7jf8 are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thil u4oo9vb(; he same direction, with the same velocity? h(;4u i olbov9Explain.

If a wind is blowing, will this alter the frequency of tbmztrljg5 :y h6:**bshe sound heard by a person at rest with respect to the sos:*lb: t mz*bgr5hyj 6urce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monixec -lhg-rofd y+: 207 hsycg*tor 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? Expla*: gch0s7xrf oche2 ydly +g--in your reasoning.

  A hiker determines the length of a lake by listening for thedc0jbtuqo,5 2 aq4 o9b echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after0 tbqcua,b j2 q49od5o shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wate5h brk 4hdhwke.16,qw rline. He hears the echo of the sound reflected from the ocean floor bk5hhq h4kw1de,rw 6 .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 wavelengths 5h+: hnak p*t2mmvho -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 boa3f+sb7av+8 r:+ -i h o6auxzppjq)cfo t is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heardapv )s8zf 3iuor6+ox +b:-a+h7p fc qj (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of fv4ek *2b pd8kf.)kb qhz :1x2wtjp*wa cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliffe2 vjw4k1h8 k bpxkf)*2*tqz:wp b.df?    m

  A person, with his ear to the ground, sees a huge stone swo(0+fb abh1if 6rdze amz.09 trike the concrete pavement. A moment later two sounds are heard from the imp96b of(0dzzrbm .aifwea1 0+hact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dista3-d(sdimvw(wb pk,4 h nce by the “5-second rule” for estimat4db3,s wpm dwv(k-(ihing the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity307vynmfb *ggatga v8:9r xj- of a sound 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 levem)ns 9dv:xub 1l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prpi5bk-r.r8pgtm v;n7a+f p6d fy 1pm 4oduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound levpk1ma.+6;5mnppb rgp- 78tff4dy rviel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a cews*+k k9s c-n ck 5hagf:j(u3l9 g:rsyrtain distance from an airplane 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 captain shut do3 u9w+g n:*5g k:scysrljhk kf-c9a s(wn 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 d 5 yi (mds52bx( nq*5k3hcgethB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backdi3 * sm5x(5kecg2q( by5n thhground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakin, lhov*b2;jo jmud3h 4g in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere center4ul,o2 hhomv3j* bjd; ed on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area ijn/of mqom191 yn;k+ws $5 \times10^{ -5} m^2$ (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 apgwi),tm) /8ogndq3 e(que9rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound lee/qno)ei9utwp (g,da8q m3)g vel 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 meter registered 130 dB when plf(:ey0:oc vw zaced 2.8 m in front of a loudspeaker on ey o:(wz :vf0cthe 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 of 2.0 dB. What rau/vx8 2y+u4cabe6e t2,k6h ajp 0xiis the ratio of the amplitudes of two sounds whose levelax 6xec/aut06jp4h8+k vau,2iy re 2 bs differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fa(z.w3 *n- +rxrkmnvwm ctor will the intensity increase? Increase by* rmmn wwk3 +nx.(rv-z a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freqffq +de82qs/wuency of the other. What is the ratio of their intensities28f+es q/wqdf ?   

  What would be the sound level (in dB) of a sound waveclmv r- fs09(w *ye- 7.uytdld in air that corresponds to a displacement amplitude of vibrating ai(yl9 cdde .w y-v-lmu*frs7t0 r molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that 98 k) kgckwvy8has a 8 wk)ky89gkvc50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highestk)samp 9,l:he (0 +tjylky o+e frequencies that an ear can detect when the sound level is 30 dB? k+yymoj, klt9seh+0ep:a) ( l (See Fig. 12–6.)

  Your auditory system can accommodate a huge rajn.5onioj c .u2oxfa r7 b/g--nge of sound levels. What is the ratio of highest to lowu o25njng. -7-raxbifc / ojo.est 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 fundamental frequencyqyd.e,+i4vpj l )pzx ,v+bc3h of 440 Hz. The length of the vibrating portion is 3 +d,v. y+be,pvlqc x)ih4jz3p2 cm, and it 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 anhkqq78) ;czsh*p oa dt+. vsr6d first three audible overtones if the 8zv*q.+rhhp ;d ss6)aq 7cokt pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of ahdyu :2k;f; majfd w 2xui.5:gn empty : d; 2w5f;2im.jyud:axuh gk fsoda 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 pipes spanning th;qnaf.6lihrhmpsm7t )(2 x0 pe range of human hearm)ha; 6r2ph7.(fq pilsxnt0ming (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmoni0n,uwi6ude7 p:9 ybyj c. What will be its fundamental frequency if it is fingered at a lengtbu6 9yey:pn d70 jiwu,h of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to platt5zhsi tgi*7j9y+4 nt +alik- g/;l py E above middle Clj4pa 7tyt+9zs*+h tii -ngt/g;l5ik (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz (dpf(hr3g1yx ) when the tgdxyhp3(f ( r1emperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at(ajt:/l uh snv-l thi5- e/nkh-27aat 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 f n*hc;vks9w:e/jwbknq6y 9o+ea/ *h12–10 should the hole be that must be uncovered to play D above n6 e h;sfhno vwqk+9yj*e:wc9kb/ *a/ 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, 4gi 0( nif*lz zzam2v:(40px ef40 Hz, and 616 Hz, but not at any other frequenc*fz(4(zaz 2: if0 ilgpevm0 xnies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends.3x9xc9ake oeag4mbh 1.m17cl wlco 01 It resonates at two successive hac7a k xc.l10oo1b1 mx993lmh4wegace rmonics 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 b(f(d,76 jh5 uluopmc$^{\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 audib 1z*nyh 6la1wnle range for a 2.14-m-long organ pipe at 20ln1hy1n6z * aw $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is mmx37i kds0em wp-1d;d*lo:1bszd, jopen 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 relationship of your answer to the information in the graphmod*1kp ijzb ,s7md0mdd3- 1 w: ;slex of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.v7yfn/o9rpz k5slh*8+ d:h e8e hhgd 70 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off n9rh:7h*+k5 d/eh lf8yhgo7p z esd8vin frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2g,0v */ .tpue2y*bkv d(dfful62 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 whistlld z2elzl062(b02ht m/t ybos2crq0 sp+l7v p e operates at 23.5 kHz, while 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 playe tlols7lbql2dvm26/ tbycpp s(h00 e0zz2r+2 d simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 7epxs- 7 a6zynbeats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded wiz -y67a exspn7th 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 tetmx3+/r mcb ducx k6)/ec,ztokin)8 4nsion in one string is thenko)rk8uxmxci6 b4d 3,t czt/ /n)m ec+ decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mi vwqc/:47kqk en5l1j qddle C (262 Hz), but one is at 5.0°C and the other at 25 1 k:4/ 5cnkq7wqlveqj.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. F4ax ecx*lmnc.0v2, p* lyzm /dork B has a frequency of 441 Hz; when A anc,x0e .vmma2 *x4pydcn l*lz/ d B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80i(n:o,) cg yeq m apart. A person stands 3.00 m from one speaker and 3.50 m fro ency:,(g )iqom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano *imk4* ,zbco rtuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be tz*rmik4b* co,he 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 ai jlu x5;1qc en8z6 l/uhb.yvx--)jjubr. How many beats per second wil vjql nh.6 )j xxuu1uc8blzj-b5e-/;yl be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at re-koh1 hlzi m3hrxw4 f37rl.y71q rp-a:fh*lw srwl -qay*lxhh3o hi74r7fkfl3p z: 1 -m1hr.wt. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a 80+2j eq+ ijy ka;n2agss -lphfire engine whose siren emits at 1550 Hpaq02-j yies8+ha+s2lg; jn k z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sour8snl4ijhu u5t,1l. bqce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are4qus1bn 8j,llu5ti. h 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 they 1- dllu. .3ti5s 8ytkj8nldp1o) viy same single frequency horn. When one is at rest and yj1 u.tni-vioydtdsl15 8.8lky p3)l 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 ultrasonic sound waves at 50.0 kHz tv f72t8u 72yitic sm8and receives them returned from an object moving directly away from it tm882u7 t t icifsy2v7at 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 flies, the bat emits an u cj+9c) uqit. 1wxhhu/ltrasonic sound wave with frequency 30.0 kHz. What frequency does 1. h9t)ccju/i+qhxwu the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dod-kb hesoq03+ppler experiments, a tuba was played on a moving flat train car at dh 0-bs3oeq+ka 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 m/s ?   Hz

  A Doppler flow meter uses g*rk1w-+ shmf 9j5yqvultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flow5h*sf- w vq1kym9jgr+ ing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonis)w8omo(jk ;pc waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind veloci : yl4n5w8/;k txxrtvcty is 12 m/s from the north, what frequency wiltr 5lx8kyv4x:n;cw/ tl 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 object moving on land if its speedu5jrh- tm.dp5 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 ofnum )(m+x5q,sluw. v m sound is 310 m/s (a) What is thu m(mn5.w ,+lsumxq)ve angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet w;*ie. igk8ksyeazn: ( here the speed of sound is only abo*(.8 nseika;gz ei y:kut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Detyojv*z7 eb 0xqe f6u(u-,3hx hermine the shock wave angle itqhxej evofh,y *z0u(6bux-7 3 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 / 55rkl2gns kw$/theta$ 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 flyin7 ib1 6kv7jqrmg faster than the speed of sound. By the time you hekq67i mj br17var 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 20,8 xyjm14vfihe )2fwn (0 yyul.000-Hz sound pulses downward from thewhj(f0u4)ivy l ey8 1 fnym2x. 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 water)?    s

  Approximately how many octaves are therj- fg/o+g(q mbe in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displa,1ckmqcke6gu/.j9 nl y called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bo .n 9,kclcem1/6gq kjuth 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 make96-qv8aoq 1zhr gy9jj s a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? y8 v6gjj-r9qhzoa91 q    dB

  What is the resultant sound level when gebwg+bi,- qnjo6t e5gs*0 vw,h+ *1 ixoyet4an 82-dB sound and an 87-dB sound are heard simulve,og5qoh+*+ 4 ye-6wb i1tgjtb 0,igx*we sntaneously?    dB

  The sound level 12.0 m frod34t2ne r 69kvdx4gi om a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radia n2i9tv6ogd kd34 er4xtes equally in all directions?    W

  A stereo amplifier is rated at 150 W outnzn(fi-i r84 vorcg34put at 1000 Hz. The power output drops by 10 dB at 15 kHz. What 3-nirc( fvz4 rog8i4nis the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devm-0 injgko77yis2wj -ices 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 be the power interceptogk sy7ni-0ij 7m-j2 wed by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communication23e lbp g9tippyb.* t(l 59ipqs 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 is tuned to a frequ7yej5v v,or65fkal9y ency 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 fundamentalbfk* d xq906wy frequency of 440 Hz d9*q0 xfwkby 6and a mass 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 vibratiz 0p6 a9e;drxgon above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. Wx9e;a6 0zdgrphat is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of i,koit ce1 ean **pt3x b 3kj,zlx*35kmass 2.10 g is near a tube that is open at one end and also 75 cmi* 5 3kc31xoktn 3,**k z, ijxpebatle long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to ref1)e+xx/v 2x dqsw8nnsonate 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 comin64 f7aj rw rnp3vcxv):g from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the wr n3vrvf74 apc 6)j:xsound 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. The conductor onq(mh1( 9s6 ma qz+tsbx the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the (hm(qq+bx9a61t z sm smoving train?   m/s

  The frequency of a steam train whistle asn2(2ebp b 33e4 l)elldzkuqo*wb -/ lt it approaches you is 538 Hz. After it passes younle )k l(ldo3blp2b2eu w4/tqbze*-3, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estiqw3p,uz tmzn8slf0it 452u ;gmate the 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 certa,u4piq5lz2t;n80z m twguf 3sin 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, sounding together, produce a beat frequency of 11 Hz. b wl1a,q(izc0l h l*5vThe shorter one is 2.40 m longha qw l1zbil*lc(v,05. How long is the other?    m

Two loudspeakers are at oppoysbe.+:54 wi h g/dibnsite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speaye / ibg.nsdiw+5:bh4 kers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is zgwrvbe70wi2up:i.cvo7+ + j a:+abl normally about 0.32 m/s what beat frequency would you expea uv:crol 0b+ 7b 7vwa+w.+pgize ji2:ct if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s ywtx; 91 thrz4)e. ia:rdnx )b/ytxi)while the moth is flying toward the bat at speed 5 m/s Theia1)x w:;hx4 ie d)bz9 /xt.tyrrt)yn bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approachv zu)rf6 rr(r:es a moth. The pulses ar:zu)r6( rrrvfe 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 the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used tog/pu*irmv 0 a, send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most 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 /0r,apg im*uvsharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for sterex */(db-*vjdcs8 hz w2ntbqn0o listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of- 8/hd*nwx 0jt*cd bv(qbs n2z the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, j +x/*47ubtns thb eo3t,m3wbslender 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, ringing sound. F7*hb/ ot wnt3umx t, b4sjb3e+or a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear bnv+qu v1:1nm 1ecke )at a frequency of about 1000 Hz is 11cnuv1v mqk)+ :e nbe$I_0$ = $1 \times10^{12 } W / m^2$ 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 thbl314m rw apzw38ei k/e ground hears the sonic boom 1.5 min after the plane passes directly overhead. What 1/wlwi43e kz 3pr8m bais the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbrmd6xg . 4k kkl8j,z;qmq *fc5oat 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