What is the evidence that sound travels as a was,t1dk*z(st*mr axlop . ;d.ave?

What is the evidence that sound is a form gt ,-:sh:gkxn:5t:jtcmjk u0of energy?

Children sometimes play with a homemade “telephone” by attaching a scdoj7ml:3akxu64lo *tring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, *cl7a dxoo6j:muk 34l 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 frquv- oe44 mu 8oon-r6fequency or wavelength r v4meun oufo-8-46qoto change?

What evidence can you give that the speed of sound in air d/:z dkco ag0/poes not depend significantly on frequenc :dkoca/z0 pg/y?

The voice of a person w+xc0earqi+- n ho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgalo ryhk)ea( h5hm :t+p gm+)d7n pipes?

Explain how a tube might be used aoaq ;e*mc-.bajl4e v0s a filter to reduce the amplitude of sounds in various frequency ranges. (An example ib-ameo v;.c4 j ealq0*s a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you movr3wpx33 mf4* qik exq ds 6)zopf)72gne up the fingerboard toward thegq7i3o6n ex s43*3prd k)x)fpmwf2zq bridge?

A noisy truck approacm;r- 2jrtzn ygy qnj; 8t1ehs 0rw287xhes you from behind a building. 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-frequency noise. E7 sr ;ny-hrr1jt22 8tnqem zgyxjw 0;8xplain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferencxj9ei :m ,(g( ikh8nfoe in space,” whereas beats c,f((ko ienh9x 8ijmg:an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wee546t i uxq 3*am,n8ltte2 blould the points D and C (where dei 2q4t t3em6*8ae5nube, xll tstructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work9 fkbb3x: wf p17ps6v*m9zse d;q -iun in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphof7 36mksfbsx1-z;b*v enu 9qpp:d9iwnes in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shm42z d8 ozeh+z r/7zndown in 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 wavez4 +znddo2/ rh zzme87s, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obse; cenvezky 5+,rver move in the same direction, with the same velo5kvc,; z y+enecity? Explain.

If a wind is blowing, will tatl9(krp 4 xrepih11d1+e55p 6 a zzplhis alter the frequency of the sound heard by a person at rest with respect to the s+5 kr1 1tpizx 96d h erael5p(zap14lpource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions rqqe94yvlkg14 ffep8(d8 ef) of 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 heaey)19pqfg4e8 dr8lvf f4e q( kr the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a la.zqasa8s.k /mke by listening for the echo of her shout reflected by a cliff at the far end of th k./ assz8qa.me lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the (3g+dj;w* ncf)oe j+zgf+8v 6 i+tvta/irm f tside of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is gfvett+) +t d;ij+rvfin38g/ca6mf *wzo( +j 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 in air at re- /-lz/imrr 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 (f6 /)lagb 2om 9ubfnoof 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 heard (a) by the fish, (g fb bulon 6m/aof)29   s (b) by the fishermen?    s

  A stone is dropped from the top of a clif4jqi5k ( vt,yuf. The splash it makes when striking the water below 4j(ui v5q,yktis heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, s64 jq vxhq9r6n bhh7i:ees a huge stone strike the concrete pavement. 6i 4hn9:b xr7hqjvh 6qA 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 Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile oqh z,r2f2j.syof2st-1 mt /swf distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 3 .w 2t-ms j12sq,f t2zoshfy/r0 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain 4r -t08nc3pbk,oc uu3goklsu7qe*xy7jeq - ;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 levelrrgeetmov y0 i6 e0-5mds /87p of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whee5 jsnz1 j44iwn fired simultaneously at a certain place, what will be the sound level if only one 44isjjnz51 ewis exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distanq.re5kg n-pg4)f8a db t on6d)ce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on p n5 k846bdd. aqfenrpgo-)) tgain, 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, wherea3)xka q/a ieu.s for a CD player it is 95 dBa uk/3.ea)qx i. 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 from a person speaking in normal cun br ed3v)p8pi2xyae;4h: 9dq .e)zv15ceyb onversation. Use Table 12–2. Assume the sound spreads roughly uniforml3v.ir2 ned4;bb15 d)upazexcv8q ey y9e h) :py 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 sti+a65c* rdje6qzs (q .od.y ekrikes 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 )dedf)nz*x: ub,c5le250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaddc5luefzx*,)e b n:) ker 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 plat8nzlk t)gv dt -89ym+ced 2.8 m in front of a loudspeaker on thetv88kt9t+z l )d-ngmy 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 of5n3cbo.l fc9e 2.0 dB. What is the ratio of the ampocbnfe 9c 3.5llitudes 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) by what factor will tja1zvu. 5 ib8:al wnh.he intensity increase? Increase by a fa.zba jla.8h5i v u1w:nctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twico4igqq 2hscsx i g:eaplt:t)3 4u*; a4e the frequency of the other. Whatio; eu4:2 :iqs4sagqc3lh*t t)4 ax gp is the ratio of their intensities?   

  What would be the sound level ( *(mgboqaar)+p:7 jofin dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air mog)7*:oj rqpb+ofm(aalecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must havexo*bv.dt3 / 2 ojgtlq8qo.u 9c what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Seegu8c d32b.to o/9x*.oltq j vq Fig. 12–6.)    dB

What are the lowest and hiq8.k 6mmurir7r) lh, lghest frequencies that an ear can detect when the sound le6kl87rrm) ,u. qlirmh vel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommom4 gc x.xcief .50y(/ :kpo)bma y+hhndate a huge range of sound levels. What is the ratio of highest to lowest .a o )x5p.yxi(kh/hy0 c4 mf+:egmbncintensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 4qz *:w2epv- qb)qzm (b40 Hz. The length of the vibrating portion is 32 cm, and it has(eqw*mpz:- ) 2zbb qqv a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thecm da 9mz+p5:y fundamental and first three audible overtonezmd 5+pc y:a9ms if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blow+5(q)g wzvkzging across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a )gwq5vzk g+z(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 spanni d 41gbzmfn*0/jz10giv rd9hlng the range of human hearing (20 Hz to 20 kHz), what would be thb941mz0vd0ild /rg jzfn * gh1e 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 thi6zze(gksjv7 el)4 tcc/i- g-yrd harmonic. What will be its fundamental frequej/ 7 -zve46ggc-s(le k)t ycizncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tund1mq n.6hm vv+m*t9cped to play E above middle C.vmvq9h m6d1n+mpt*c (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 H2 da g3hx) klc2d4gi0(lnv6bbz) when the temperaturid v) b4dl6acn3xbh 2( l2gg0ke 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 he9u 7.jy4:bqp ) imbxat 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 be th:+c* tlqd iz3uat must be uncovered to play D above middlu:t *+3iqdcz le 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 re1mgy 16 xwsdsd(7rwn8 sonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an dr 7s1 8wm6wnxgdsy1( 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 isnn1 7td(pz u* hvu8/tq1f7rxs open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What t*7x(qpv nz/7r ut fn11ud8hsis
(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 fzhp*.5ba8*y e:vysg$^{\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-m-lonvi c 1rk 4-bv(vyfdc0i:z e0)sg organ 0r1e4ydc 0-vb(z i )kifcs:vvpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to thm614q s/k pb1dylw-zee outside and is closed at the-/1s6qmb p4lzkye dw1 other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of 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) jtjx mzyij bzyw )7+vd9pl5c//9.z f strings, one of which is sounding 440 Hz. mxp7zyld . jfj9jv )w9 icyz+t)zb5//How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzp2/alxz7c ar7 ) 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 operat, q (pnx+a-/3 s/ut)za49ntw kjat vhtes 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 occuwttn)tq/asnp zaht( u4 v 9-ak/xj3+,rs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats//jb63 lsfz3i y, o+gess when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stringj6o+ sgl/ sb,3ye i3zf? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The te;k4j;cx qs 7vension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–1k;74vc;qx j se3.]    Hz

  How many beats will be heard if two identical flutes:kij1z4 dqn5 i each try to play middle C (262 Hz), but one is at 5.0°C :kznqdi1ij 5 4and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441hc+meb0:2rx+ -pjmv s Hz; when A and B are sounded together++: pv-s2emxb jchm 0r, 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 1.80 m apart. A person stands 3.00 m :e l e6kgt/ti7from one speaker and 3.50 6lt 7tie:k/ge 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 vibrating at 132 + - hd()6jh0lxmmbkmdHz, 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 the d(mhxm)6 jl0 h+kb-mdother ?   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 a4ba yzp5hvtf16x;a9keu( 6o r nd 2.76 m in air. How many beats per second will be heard? (Asb6kr a y;(taz fhuv 94xo5pe16sume 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 ro1g;h3, + u6x-z f cm1ja9-hk/ lcoobtecseq2est. What frequency do you detezl-oqhx-/oe9tf+1k2m ,e6cc;s bu31 h ocjag ct 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 3evp5 x 3 e3ee 6fv:cb5v)fjozif a fire engine whose siren emits at 1550 Hz moves at a speed ocv653bpev53 z eefvxf ):3ejof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifben; i bku799fb,tm 6;3 -ifallox zn5t in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they , 3uaxnf9 tk9o7lz5ibbbmnlef;i; 6 -close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When oneba7 7:dh9;mm6km 9nc1w fw dic 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 ibc1cwmw fm ddk6am799n:7 h;. 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 and rq4oohrwm y4y1 f/ z11neceives them returned from an object moving directly away from it at 25 m/s What is the received sound ym z ro141ofn41w/yhqfrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat embga.dcv( t z/*65 ojpa2:wz ggits an ultrasonic sound wave with frequency 30.0 kHz. What f2wvc :a5tab6/.*z ojpg( gzgdrequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat dg0hrs .i 3l1:pcqmk*train carlg :q*c .k1s03ihdp mr at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-foa/*- lz bzjrb+-fhi10fmtj7 q +sq)r low speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is take blm- *o+f+r 0b-jh qa)/ riszqzj17ftn 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 frequency sbio 56)*nbeidv 1v /z;sj8m v;dhm(r3 q,xci$2.25 \times10^{ 6}$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 freqca9c77do 4xqvo2xzz:.w9vll uency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obsero7lxclw zqdo4 :2va79cz9xv .vers 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 speed at 2i)6 -oir;gl nv0 $^{\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 m 29imjc:bcb y(0tn 3mjm(rjd;v0;c g is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’sbivj :2jgc0jbry; c9mm3;0tnmd (( m c 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 where theh7(q17btqksz k ,iprv12fi -e speed of sound istkf,q ( 71ph- ziqrb i21e7vks only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine teu)w. r czmg.8he shock wave angle it p )m 8w..zrgeucroduces
(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 w2*j*j be 8ex3pe+m rxd;abi5$/theta$ 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 flh x nr0/hxi/o)tans2+mq )my6ying 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 Fis)m )a2xqx6t 0/ihyh+nonm/ rg. 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 pulses downwv r*j gx25c1 f8c v2brk/uf34zz.n tzyard from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fre br23jvvu rf1zt 84xz 2*c czknyf/5g.sh water)?    s

  Approximately how many octaves are there in the h89uau p7mmv )pvy8 gn;uman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display(: szj3lye6z i called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which lzyi z6( 3je:sare open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes:ha*:pca:;gx z 8o dkze-:e hn a sound close to the threshold of human hearing (0 dB). What will be the sound level of 100:g c:ph:zza-k;dh*8x:ao n ee0 such mosquitoes?    dB

  What is the resultante8grut: mjf 4/ sound level when an 82-dB sound and an 87-dB sound are heard simultaneou8gfr/u mte :4jsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What w1hhp+1i7tg o is the acousp1+ wti hgo71htic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150xz1g7c 57zw8( sfw bzm W output at 1000 Hz. The power output drops by 10 b7cmwf( 1zwg58z7z s xdB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ear/1.ty4li n;i9 dkxr0 lkm;lras. Assume that the sound level of a jet airplanr49ia0kmlll tr ky. d/xi;1;ne engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, oa(t1-,iw c,kd r lqth,5 rg9w)p1m gsthe 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 tuo lebm*5w+pq5 zi i1b*7 d+fkkned 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 fundamentalgoq1f ul3h+ d9 frequency of 440 Hz and a mass per unit leng+l fodgu1h 9q3th 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 filled with waxqpuk6 wkwy0:d) hm -8f+5usqter (F0 +ukfwqpyhm wd56sx)u: 8kq-ig. 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. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open a (p2hz3 nlx*ld77vqumt one end and also 75 cm long. How much tension ( 3ml* und27p7lvhxzqshould 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 resonate as one full loop (so j:qiukxda4+2 q5;rq3 kf5n$\frac{1}{2}\lambda$) 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 tw4 .kzeus:.i2rarbe s xn7j6u:66im pto sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the persrs..te j : 6zur:i7u6en4 26xskapimb on 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. The conductor o,9 iwuemc* 6lcn the stationary train hears a 3.0-Hz beat frequency whe eicu*wl c9,m6n the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After it )f ez+0r8avhypd-l8k passes you, its frequency is meal-rafk 8 p 0)8ezd+yhvsured 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 liow7 6io6ra32kqu/h rs0yuib -stening to the difference in pitch of the en 2uiw6boor03u7/r y6a -kiqhsgine noise between approaching 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, sounding 3j fo9jtih9n d;wmt26yulqa go* )y5:3by n 1mtogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m l a;mo9 yfy2 5i tho 39qb6)d 1jnnmwug3:jl*ytong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car a3txv( e(ewa4 b6x /oli6y smv(s 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 /(owtxvlbys6ea 34ei(xvm (6 is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s t9ru) jj9eu nu7y4os h+eei 7zb+s85 wwhat beat frequency wouls5ejtrh 9u 8onyiusu77+ jzw9 e)+b 4ed you expect 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 kq+krnm n 02s.hts)s2 moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What+ )qsm02thnkks2snr. 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 pulse :hp5 clqum:6z:ks6bgs as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp retg pu5hmbk6z:6:s:l c qurns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send f1j vx(jt( :qkd3qf1s 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 sharp? (See Table 12–3t( 3fd(1qk jxq1svj: f.) Model as an open tube.

  Room acoustics for stereo lissfu4+ l2 6r (vte+afhts8*uq xtening can be compromised by the presence of standing waves, which can cause acous+ex fl4vq (fus82+u tt6rahs *tic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long2 re*e q8dpqu3 vmg .+k1mjpt+, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hanq28pedujt m*+mr+vk1 eqg .p3d. 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 t2ybdp 6 is,)wh u.e;fahreshold of hearing for the human ear at a frequency of about 1000 Hhpy)e ;fa w,si bd62u.z 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 Mpd4 f*-/umzq9aaai7at 0unl7,v 8 qx kach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passqq*7u8t9ai dv4 -lpkxa/a7n am0,u fzes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i4 /zxoq)1u2xxb2qfn*u nm:ebs 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