What is the evidence that sound travels asdjl anr- ao8 7cr:yp gsq:)l(8 a wave?

What is the evidence that sound is a form o40dmut )7vc r8i s;)t ,zlywnvf energy?

Children sometimes play with a homemade “tboff*v / lo4o+elephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be hea+ foo*/ob vl4frd 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, +t 3s twv 9yt(oov* l8;-h4mvuqwq.y odo you expect the frequency or wavelength to chmvquyot qvto8v+ h-to lw;. s 4*9(3wyange?

What evidence can you give that the speed of sound in air does not depend k xjdkzh c9 :sma/4*o uq)35xgsignificantly on frequencmqsa 3zo9h5gk*dkx4 c:ju/)x y?

The voice of a person who h qdms+.sn56n dafrc/(as inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch s )is(b wpdel/-m t9s7of organ pipes?

Explain how a tube might be used as a filter to reduczb6wn3 cl96ve e the amplitude of sounds in various frequency ranges. (An example is a car muffl6zn3cew bl9v 6er.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mmcsv 8-byj 2-*+xeij uove up the fingerboard towardxjjue +ci *by8 -ms2-v the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but(ies,b b cl*e /9c-sop cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Exicpo-be e (9c/blss,*plain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” w7bo h(x(p vu)r)0 :kt(5ea3go rtc ssghereas beats can be said to be due to “interferebg)hrvtg xt s:c 3uoso((epk5ar 0) 7(nce in time.” Explain.

In Fig. 12–16, if the frequency of the sp5 2tz ah8 rzzx98fy*vpeakers were lowered, would the points D and C (where destructive and consp zv*258zrtha8x fz9ytructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in area5 j1qjzver ton5 n. giq;b7.u/s 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 headphones in addition to the ambient noise. How could adding more noise reduce .bnrgq;vj .i ouzjnq5/7t e15the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of8(v:p c ta/xpqtbzy0.b4r8a z as a superposition o4y/cp8at.p(vbqzz0 tx:8 abrf two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mo4buy6izm:rdh f3 8 am es((xs4ve in the same direction, with the same velocity? Expla6f:ui e4m(8sdbamx 4s(3y z rhin.

If a wind is blowing, will this alter the frequency of thjjn:bw94e q7se sound heard by a person at rest with respect to the source? Is the waveln 9w s7j:ebjq4ength or velocity changed?

Figure 12–32 shows variotem il*3li45rx91 ni ttthn66q sm;:lus positions of a child in motion on a swing. A monitor ismii9tl5; 13tiqe6tms lth6lnr*x n:4 blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of qoigze og(14ct1o; +mher shout reflected by a cliff at the far end oeoo1z4 ogqc+;m (gti1 f 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 w3zl.di:sz9e k 4x/f vuaterline. 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 e9zxikflv s.:u43 dz/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 at6d/o fbb:at0 l 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 drifthuk20l4 8q t 8mdmpwar b6w-i9ing 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 isd806uhwmw-ipq92 tmrlb a k48 heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fro y)-, , m2ytw,(b/jx r v2c-:gpse hdah4veajtm the top of a cliff. The splash it makes when striking the ea2xv 2jj,yrwd 4,-th ,:tbg-mae c hpvs y/)(water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strktz7+ ) a2 6om7e;rqmxer+rpo *gh9xjike 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 Table o+ 7m9ojh 6* qetxr+x) 2ram;gz 7kerp12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distan u 9-w9ih5n5zkun+drpce by the “5-second rule” for estimating the distance from a lightning strike if the temperatur nuz55w+-hi9nu9dk pre is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a8r b;crah(.q :fgd ep: 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 level ofag tcqo.k.k0f *pwza3( o k j38jlr0/n a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9fgdg46slr b-byex 3275 dB when fired simultaneously at a certain place, what will be the sound level if only one isr3xf ybde42 lg7 6bg-s exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noimb9. wg8rhz,c sy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensitiewcbgz.,9hrm 8 s, not dB’s.]    dB

  A cassette player is said4oh0 z z7m 8dzzk.skl4u4p64ldvutl8 to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio s0v44 87dlmzu6p 8uh4zzok lz k4.tdlof intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ouxz5 y8hv-j lblp4s(kqah5l; 3 tput of sound from a person speaking in normal conversation. Use Table 12–2. b-h xly 8k5sa lhjp;v5z(l43qAssume 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 strikegqckw2cd jyhis u8m-l7 7226/bkjv-z s 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-5 l6lzx,net d at 250 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 nlel,t- 6z5xd 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 130k pg( v:yjdj5r1n bg3* dB when placed 2.8 m in front of a loudspeaker on *g1rd jbvg :kjp3n5y(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 aby: )55 6w(ogoq wsuh;qygu+detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?q5u(: why ;)6ogsg5ayo+uq b w [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what p55t+ nu vz8z3/goe+ y2vlqgofactor will the intensity increase? Ince2vov+z/8z+5tg qo ug53nylp rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but zbxr-75inj+dtau5du19iz s/ one has twice the frequency of the othersdaz r15- ujz i75+ tinuxdb/9. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in4q19hu ctcyv-*mlp2q air that corresponds to a displacement amplitude of vibrating4vcqq cu9pt-hmyl 2*1 air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leve+ esm 5l8,bgjpl to seem as loud as a 100-Hz tone that has a 508j gsbel5,mp +-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequejzg n3x .ngli(.ti.(e ncies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6x3ilg ije ..tg( nn(z..)

  Your auditory system can accommodate a huge range of sound levels i blgch*g993l. What is the ra*gi39g c 9hlbltio of highest 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 violin has a fundamental frequency of 440 Hz.z6 sdf+2,sm qu*8n aqa The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stri n+mquas*6sf2 q8 da,zng be placed?    N

  An organ pipe is 112 cmo .p1j1yslpon; a( *2sc r4doa long. What are the fundamental and first three audible overtones if the pipe i4j( ;o2y*s1pdanr1saopo.c ls
(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 freq .;jz e4xvww 0nvu.z(vuency would you expect from blowing across the top of an empty soda bottle thazvvwvwu (jne.x.4 ;0z t 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 the range of hum6 uo9agzh 9g4fb.p i,m5qza3n)wu b+ han hearing (20 Hz to 20 kHz), what would be the range of the lengthsb.wih)oz9 9uzhq b4am au nf6,+3gpg 5 of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz ah2kjps uzqhy*do;, d d ,90d+zs its third harmonic. What will be its fundamental frequency if ;u kjzdd*s+d,20py,9qhd zho 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 .24qgng 8p2t 4rw z5j+y ufcit*kv1 entuned to play E above middle C (330 Hz)..c14g vt+n4uj2* f5 krqweg8pnyti2z
(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 H: gur4) g*nlmw gj57kgq .izjzp7):llz) when the temper*ugjlkl pm )z):q4j 5gwn gl.:gi7 zr7ature 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 20pnqtlq9 nbc, hr63n; p 3)r2vo 8.bupa $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute018mos2xa2 oyoy f3) slqqh1p in Example 12–10 should the hole be that mushyq2s1023omo q fl8)1 sy oapxt be 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 resoxtx) zhvo4g6ni;m + u,nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or ;x in v)hx+4t,oz6gmua closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 8ovup( *dmif91.80 m long is open at both ends. It resonates at two succe( d8i9fo* vmpussive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 dovok/w9 y87 )vtj s;u$^{\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 )u4mymu)e7p sg0ic+6wysev 1 rm+3muthe audible range for a 2.14-m-long organ pipe a )+ )gmu4m6emps y+yum 7ui30wesvr 1ct 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apji :vr 2x9:l(spn5q2njd5bu mproximately 2.5 cm long. It is open to the outside and is closed at the otm (sirn5vdqx5jp 2 j2u 9::nlbher 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 onejf12,hyv4 *zkcfpc ; q beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off inqpz*cf ;yc21h 4 vkfj, frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) -pr l e4 qi 4ga3wml3wwl4rqi)28; tbzand $C^＃$ (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 gshp k4 )de18vkHz, 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 played simultaneously, estimate the operating frequency of bra4esk8 dpv 1hg)nd X.    kHz

  A guitar string produces 4 beat+*p d f(k9v ny-m l0hxa hu77mvdk4(pbs/s 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 st vl-kf*74nxd+bp( yku hha9vm( pm7d0ring? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tx6; fgpj;wwjs;)+f ckension in one string ;6sjx;gfc+p fw jk) ;wis then 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 oq uq1vx eci* j/g8u/4middle C (262 Hz), but one is at 5.0°uu *84ge/c q1ojixq/ vC and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fora* u4;hh 0js16cwps9foti zt* k 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 a0a;9op *c s1 huiztj6hfsw*4tnd 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 pe)ko+wh0cl+ tbrson stands 3.00 m from one speaker and 3.50 m from the othet+bo)wlhc k +0r.
(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 piamg7efqn1)a47:r l afjno 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 n:g 4el1amfrjqf7 7a)of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How mxi37g u )-.psbtj/eneany beats per seconde3s.p beg7u)j/ tn ix- will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ce,pqgm4l -j7/ l nor(aurtain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if4ar(j ,m og-qlu/7pnl you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Whas) ) myoi mafl)i n:ja8w:2/o..hfv oht frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32/. jnm oai2faho:vy:hl) f8 sw))io m. m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving q h*n ssq:;r k+19nab(ppzm0htoward you at 15 m/s versus you moving toward it at 15 m/s Are the two freque b*(s;ks:qznpr+0h9nh1qp ma ncies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with tjbjs ,yg(cf)b my+:+bd7l a 4lhe same single frequency horn. When one is at rest and the other is moving toward the first atb+ +ym(,l:a)sj f7j cyd 4glbb 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 and rwr/tu h b.w5*jeceives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency?*ru/ 5jw w.thb    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, ttt74 fagxh f2315c vhc0jmf+ whe bat emits an ultrason3f4+hw j x270tm5ftv1cc fgahic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba;fgutx8;2 d(fvtj 4i d was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car apvt gd2; j8xi t(d;fuf4proached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure 7zyc *a ,9soigbxe :j(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 freque9ie*yo( bxjsga z,7c:ncy 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 b v0hns5swwz8h79 waol b(g8,c95mqeb1,gzm 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 5//zm khp*wb1 o) k8kuu70 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hwm*1u)8bk/ zkpk h/ouear 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 movibr-,i nsv6t*a ng on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speemat2f y5gp (.yy- x6*i bdqgj8d of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the 25figjxap-*bgt6y ( 8y .ydmq 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 where thev rvyv2c hi*1alf e*l(tb; n;1 speed of sound is only about 3(*;nlbic2e;* l 1tvy vfh1vra 5 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. Determi:1lhb a+x jqg*ne the shock wave angle it p +h:* 1aqjlgbxroduces
(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 a:;yc e7kht g0$/theta$ 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 exactlybr-qoq er5f 41 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travelq4fo-1 rer bq5ed 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 sendd /y((ad nsof5s 20,000-Hz sound pulses downward from tha d 5(ds(yn/ofe 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 there in the human :oml6 :h.lkamr z -np)audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonyn eb(8r uunlf rsebm543/7c*0erqx (z. It consists of many plastic pipes of various lengths, which are open on b(30 uceuf7rb8nq* m erelbs/4x5r( znoth ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thr g4aei;myvl94q7 s8i yeshold of human hearing (0 dB). What will be the sound level of 10qyia;lm 478e 49sgviy00 such mosquitoes?    dB

  What is the resultant sound l(zeejtpzyl3 . d8nn6 2evel when an 82-dB sound and an 87-dB sound are heard simtz63jnel8ne(z. y d2 pultaneously?    dB

  The sound level 12.0 m from a loudspeaker, u o9xf1 sr32r x9r56 wpvs8bueplaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally owxr5sprv16u3f2ebxu 9r89s in all directions?    W

  A stereo amplifier is ratenxy1y/k zkpa- 5mg:4ad at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts a-xaz gy:/a4p5kk ynm1t 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earsmj/rm uv+ds2 7. 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 intercepted by an unprotected ear at a distance of 30 mrd 2 +/vjsu7mm from a jet airplane engine?    W

  In audio and communications sys0e8 gje8atcx e9 6ux8c6dttaadh 9u ,:tems, 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 violinb3 l3(pt-znxs/h rk2m)qtxny1n (wi6bdq )o3 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 c-i d:e34j kgotf .sz m3lsk 9qp392qbfm long between fixed points with a fundamental freqqbo 2z3psj.i9f9k:gf3lq dm4tks 3e-uency of 440 Hz and 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 vibration above a vertical open tube f ljw 90mhwb69billed with water (Fig. 12–35). The water level is allowed to djhb 09wl m96wbrop 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 oks(1rb4 l/ qj 5ci2 *dloctrw8qy ga:3f mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the lqq* bct(l3yj1cksi/5 aworrg:d 4 82third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wasf( dw sfr 9kd,,,e.ios observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz ;f5ncm) uphif7md ;5 nrange coming 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 sound level is minimal at a point 0. 7 )u c;dmn5;fph5ifmn34 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 on thev5*thcni)v9p u z8cp2 stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the sptcc v5)89 z* vipnhu2peed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Ahsl49*nun6sw fter it passes you, its frequency is measured as 486 wus 9* ns4hnl6Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the +jarx 5dr,cp 2m9nsa8 difference in pitch of the engine 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 goingp+axd8j 9,m a 25rnsrc?    m/s

  Two open organ pipes, sounding together, )9cqv5 aw/dw yproduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is t v 9wayd5)cwq/he other?    m

Two loudspeakers are at n:96k;togc5)xsxmh3 bbmj :u opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have ixjb c)x9 t;o:6gs b5hmun3k m:dentical 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 normally about a3e zl/g/v hf4zt;:.hg smuwr zb/ ;p70.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were de/phb;r/f ; wlmu:hg4/ vzt3g z za7.sirected 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 while the moth is z-uf ,; mpc:lvh0f1cdb 6q -swflying toward the bat at speed d61 -:zlm,ucvfwf hq;c-b ps05 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency soun+1 irvva :f-qad pulses 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 dete-qv+vr:1afai cted by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was rj u1 bj;fd+,sonce used to 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 fu jjdr1+bs ;,the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can c)gd0nxk y2r4 be compromised by the presence of standing waves, which can cause acokrg 20)cn dyx4ustic “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 long, slender aluminr ww).yy(n-4sr us :pyum 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 soyy sr(r)w:-4y.swunp und. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold kx t,0+ut 3g+ 8r)r6fdk2zqu 8os osirof hearing for the human ear at a frequency of about 10+gdoutk r su +8ktr xsq23ir6z80,o )f00 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.i5gt -c: 4uqwwbxl)./ab tcq60. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altituag6:x5cl)/4 q.tbci- q wbutwde?    $ \times10^{4 }$ m

  The wake of a speedboat is,9q:pp; wuuys 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