What is the evidence that sound travels as a wavjwn1 vomp,lyn3w-tsls fo2 2p 5:je65e?

What is the evidence that sound i .(:7hl p)qspht ebd4ss a form of energy?

Children sometimes play with a homemade “telephone” by attaching axjvfg4758 obh string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can behjo8f x7b v45g 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 frequency o6 4b:j+pxctx pr wavelxxptj pb4+6: cength to change?

What evidence can you give that th+ s(:gu62wwjez d d h7.w1qwrbe speed of sound in air does not depend signifehjwsd z w bu 7g2.wq1w:6d(+ricantly on frequency?

The voice of a person wh, jbk*xxx di0f,hyzk:l+f. x(6j)w dmo has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orcn)fpme5z2m:6- v1dlmx y o/rgan pipes?

Explain how a tube might bh(dyn.x44 wlpw*1 q6j5by.g zhh; ybg e used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muf*qd wy4yz.5pg;hgh y1 x(4.lwjb6bn hfler.)

Why are the frets on a guitar (Figpyq 7igzf 2:4k t,ag1j. 12–30) spaced closer together as you move up the fingerboard ,2jg74tfakyzi1 g :p qtoward the bridge?

A noisy truck approaches you from behind a building. Initially yokw4oj j4 3;lc oyb;ji3u hear it but cj i4coyjlokj;4b;3w 3annot 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 on diffraction.]

Standing waves can be said to be due to “interference i /uf5g* kyouxpus2/0vn space,” whereas beats c/oy0*sxvg52u fpuku /an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wl.vk8 s /z,gpxere lowered, would the points D and C (where destructive and constructive interference occur) move ,/.8ksvzpx glfarther apart or closer together?

Traditional methods of protecting the hearing of people sa906vs ,gx*pd(thx y7j kzb1bgj*:pwho 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 that do not block the ambient noise. Instead, a device is us 0k9 y67phg ja*b(t j,b ps1x*dvgzx:sed which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be5 jnx. phu ltpuh2/n59 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), are the twp tx2n5ulphu/ j.9n 5ho component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obs vdfauyxq .42 gatros1 0ah7mrdp*1-) erver move in the same direction, with the same velocity? Expld1vpdraqauo1 mr.gy ft 4- 72hs0a) *xain.

If a wind is blowing, will this ii,7)v ydwnedz8.w)n alter the frequency of the sound heard by a person at rest with respect to the source.ww)nzeid y87v di n,)? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on dqu2 llu i,50ha swing. A monitor is blowing a whistle in front of the child on the ground. At which positi52 ih,udq l0ulon, 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 b: 8bpd+se 30llxbu k4he.4egyy listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0x.dy se3kl80e lbgh+:e bp4u4 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hearsyii. jbeputbic3lu(y/; 0lp,4u:7d w the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assum;pc 0plju.ulb b(u/y: 7e,iwiiyd3 t4 e 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 20-bx6/t ft py.f rg5o-c $^{\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 schoolr553 vfcj2 0eocuofnmx ,b4b/ 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 backu3,bocr/xf m5v2njcoe 40f5b fire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it mak*jvktfv (0 ,zves when striking the water below is heard ,t(*v vzkj0f v3.5 s later. How high is the cliff?    m

  A person, with his ear to tn0.bvziv oe qqh*b ej((:;wd*he ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How e 0:(d*vno*;(qvijb.eq zwh b far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over ones2 u/ -*egm*fsjoa2t t mile of distance by the “5-second rule” for estimating the distance*stjf2a2 gs/eutm-o * from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a kq(pcifigy)v; nw4,8 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 o*t w-qe uz,a4wp-;thrf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lek+g6zx- +ajds vel of 95 dB when fired simultaneously at a certain place, what will bx+zj k6 gad-+se the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain ls w xkkqw14.4ed.erk ,wo 4jbp6 4mnx:f1j8fdistance 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 down alle46q wde wnr.l4x 8mk 1pfxj1:kf4o, jkw 4sb. but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-1 ;xkj+jzmo, trlgiq)xf +..vnoise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sik)tql.g z+xjvm; ,. j+of 1rixgnal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakinvhs9hif1f j0ezz 2gt32e8vo25*x i v/x rk ,fag in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centerzofx3ifzje sh 10hfvtk,rx/ia28e25 2v 9v g *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 eard8d9hus :x.rnr rum 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 rated0ncs8. g rb/ foj/s7sg 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 / cog.g sr/bsn0s 7f8jpoint 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 plafok9 zxaqty+ t6y 6g)9ced 2.8 m in front of a loudspeaker ofotag9 q 9xk+yt66 yz)n the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sy *2vxh2v ory1ound level of 2.0 dB. What is the ratio of the amplitudes of two souyyvxh2ro v*12nds 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 the6y/4sh4;j n hlro8t nk intensity increas y4/ntsl;48o 6nh khrje? Increase by 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 fk hb /9-uhbic1requency of the other. What is the ratio of their intenckhu1-/bh 9i bsities?   

  What would be the sound level (in dB) of a sound wavdg)i3 rt nrf-7e in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?i d-fnr )g3rt7    dB

  A 6000-Hz tone must have what sound level to 3soz6w;qkamkyt y *6 2seem as loud as a 100-Hz tone that has a 50-dB sound s*m3 o wkz62a6q;tkyylevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequxym ol oqyqj(b71, b-8k5+ zv/z3eepeencies that an ear can detect when the sound level is 30 dB? (See 8ljqoy17q o+mk-,p/5(yvbe3 ez zbxe Fig. 12–6.)

  Your auditory system can accosy3 x7 l/rua1/h 3ll-vdm(ko8 vgct: jmmodate a huge range of sound levels. What is the ratio of highest to lowest intensity- 8svovjl 3 ha:3u m1dc7k/y xlgr(/lt 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. The length of trt/l11f hq,2 ljn*in)jsuef 9he vibrating portion is 32 cm, and it has a mass n q/f 1j )lluejh*9if2nt1s,rof 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wh *7kflh2tlqxk) idd8 2at are the fundamental and first three audible overtones if the pipe is 82t *qk7f) hlx ldikd2
(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 t6v 8w)do4p mgrhe top of an empty soda bottle that is 1dvw4)6r8omg p 8 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 8+ayyf iz4z p9of hum fzy p8a9+ziy4an hearing (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 harmonix a3z4s*zsy1y c. What will be its fundamental 3yssx14z *yzafrequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar strinuxf b0t),v-dkg is 0.73 m long and is tuned to play E above middle C (330 Hzu0dkf,v x b-t)).
(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 middm ,cmdb:m1 q,fle C (262 Hz) when the temperature i,,mc:qf b1dmms 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 2 nz/7d rhy+ (;flbpab20 $^{\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 shouldc72hh;vj,do.+rz-6 d peqe vi the hole be that must be uncovered to play D above middle C at 294 Hzh iqvp2 dcz -67dr+hv;o. ee,j?    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,u7u t .xwe-5; zor2euo 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is aotu.5-zu;x wore2 7eun 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 ef6tfx v f: z b8zbj1uf;u9tge*c-)j)i,9i uae nds. It resonates at two successive harmonics of frequencies 27tet)j, 9fj 9*-gbzuuue z 6avf1);8bif:xicf5 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 s yw2th-t yk6on.9t.o$^{\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 au6 2e9ss:op hppdible range for a 2.14-m-long organ pipe6pe :spps h9o2 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 the outmlh-k.u2 u7 a1t b+yffside and is closed at the other end by h+u1-bt f f.lmyu72ka 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 bea gaj mv ,ontpgyxf t3a:/j3 .7p:c((sxt every 2.0 s when trying to adjust two strings, one of which is :gjt3s p3avxc/pja y( tgo: 7n. mfx,(sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2y89yb uzo; 95y 8 am*u3 akjjmodqj,k762 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (bra. eu/ok6-bg-9v gh ncdu k0q8rnd X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hzuhuegg8ko.cv0 -bd k-rn q69/ occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-H/ r7nmopy/dy4 py6ie 5z tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational freqymn57riy pye/o/ 4pd 6uency of the string? Explain your reasoning.    Hz

  Two violin strings ar j- :/7qnni5gtbzwf1 me tuned to the same frequency, 294 Hz. The tension in one string is thej7 q1wim:n/ ztb-ng5fn 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 ide1uvpl+ dr q9i(ntical flutes each try to play middle C (262 Hz), but one is at 5.0lq+ i9pr1vdu (°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; w kuvvjek6/xfp)0v3gbqij* 0( hen A and B are sounded together, a beat frequency of 3 Hz is heard. When B and 0q6xf u(g*pv/ ji3j 0ve)kkvbC 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 st o39mg0 gxruqowb3, t9ands 3.00 m from one speaker and 3.50 m from the moug xgwto3 039 9,bqrother.
(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 tuner 1kioc n8: 4+i*etqm.g y3aht chears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz+* gt :ck8 ei4i3y.mtha 1oqcn, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound t9e5dhwun0;m6abl t:5d ds /dof wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Auh6 /9d;5mnd dtsdwl 05bta :essume 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 am) p, 3ozyumo9v-* mw9 xf/rx0 egh0rnt rest. What frequency do you detect if you move w-0e,or/) fm9wvmx 09 yhm rpnoz3gx*uith 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 de(+ .m wbfoi5l2ol-ddh tect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3 lmh di(d.+5l-oof2wb2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency sm:5qv/vxwbmt.,sp + i1 2 jogcq, cb(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? Are1vq /b,p(m: civm5o c +sx gs,wb2.tqj 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 the same single frequuggc5dkx, 7ns lr (j22ency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the fr gkxl22cn(j, s7ug5 drequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz an5n( kua td+ce2d receives them returned from an object moving directly away from it at(kd t +2aunc5e 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) -fhfsbtd/;da 4r a6l an ultrasonic sound wave with frequency 30.0 kHz. Whrb ;sd -l f6d4faha)t/at frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopple+b zt;p 3akx/su ii.8ur experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in th 3/+.usu8xtipzka b; ie railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. i6w/ ,ta7ntzmbgwz i7r+ /b(w Suppose the device emits sound at 3.5 MHz, and the speed of7nwa7m,/wt zwzg ib/(ri +tb6 sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavb6b83uz ro817oq6 ) hknwqv htzeg/+z es 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 sou2cgx6mt6 sl e0nd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, atx626s c glm0te 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 83u2vf86 zbcwvww m8ccaaa/c zkxj/42-6er x 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 speed of sound is 310 m/s (a))uyy nvxm)pdy -g52r** tu s8b What is the angle the shockd* rg5vuybt)p) y8n -y s2u*xm 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 thek)vwb66i j4qm thin atmosphere of a planet where the speed of sound is only abo6bw6 )kmi vq4jut 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 the shock w*k rqv uz.m0c0kc 9241zdgg+fxk e 0hwave angle it producrg9.1 *fkvckge 0qd2x 0k 4+uzmzc0h wes
(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 myyil*e wee1+jza 6+bu0y v:ly.. *nq$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead an yv;g4d+1nj feu xg*wd7gh,m+d see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12– y+ v;7jgu 1,dexngwgmh f4*d+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 dnwqhse bv49e1/ id9 z6ownward froib hvn96 /w4s ee91dzqm 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 fresh water)?    s

  Approximately how many octaves are the9gt le5(3wbwrnv4 er+9yo ;ek 5cbh3ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It conq4dx-h 2yskl6 sists of many plastic pipes of 62xhs - ky4ldqvarious lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold ofs0wdx 5 mv/d*p0ptiwx:x e1 v8st3ef8 human hearing (0 dB). What will be the sound level of 1000 such mosquv/v xw3esdmp0se x ix :twtf81 *08d5pitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 1pa8sx dxb6;y-6e yvl87-dB sound are heard simultaneou1l e;d p66ybxvy-s8xasly?    dB

  The sound level 12.0 m from a loudspeaker, pl qv, -,p7 mziwstc;e*laced in the open, is 105 dB. What is the acoustic power output (W) of the speake,m c-lt7i,svze*; q pwr, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hm u aok,m6en:z0 ihzqy kj;lt pz1/(,3z. The power output drops by 10 dB at 15 kHz. Wp(:uzkley kznoj,31t / q ,z 6mi;mha0hat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ear8ixt jgnb*tdo y 7p.m)dldgzv 0a-4- *s. Assume that the sound level of a jet airplane engine, at a distance of 30 m,d 8ypazldx.0ng bvd)g -o- *ij7 t4*mt 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 sy 7y63w*;3o x9uidabb j8klnodstems, 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 frebn4; )fcl(hxc quency 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 point3(* lw qbi(7wv5ko yuks with a fundamental frequency of 440 Hz and a ( * li(vuqkbko53ww7 ymass 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 vibrvt ;:pmpl/ho( ation 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. What is the frequency ;(:vt/ mh plopof the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 -z84n 1 jfo dwie,/wh/ms.vrag 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 third harmonic in the -oj,.nra4iwdzw/e mv1h f/8stube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one gd x(j7wz(d.oi jua55b/oxy+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 cominmmm 4ghmzf*59 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 find9*mgmm5z 4f hms 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 s4b :;sfz 8qsip4tfi2e5f ezr 9tationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other trrz5e8siq;4pt z:bf4 fi2e9 fsain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle nr 5o bpo1r/hnox; 2u7as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How f5u nbpoho/x27nr ro1;ast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of 4zwkj6f; tm0xcars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppojz0;fm4 k6txw se 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 together, produce a beat frequency of 11 /*9odnrq t0f2ualyh 4.(zyjxHz. The shorter one is 2.40 m long. How long is the other4yjx(n/2z0 h r9fdytol u a.*q?    m

Two loudspeakers are at opposite ends of a railroaw2 k4h(my 5zbw wk*4rx bf)xe.d car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by tfbxmw4xk4wy5b ekz*rh. 2) w(he 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 norm c+ er2m6ye(emally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed alonem 2(m 6+yerecg 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 flying toward the ba4*im ; tk;zd/it sa2cx n7i2gat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequenax2ki; 72stt;g/dic * iamz4ncy of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound puo g ;ql2fv*2pblses 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*p2v o; lg2qbf the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sek 8w4wi,3kyyqnd signals from one Alpine village to another. Since lower frequency sounds are,w4qiy3kw k y8 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 12–3.) Model as an open tube.

  Room acoustics for stereo lisz5eanmhnrw4bts63o wj +1 a:iy2 9ty -qy9n 8ktening can be compromised by the presence of standing waves, which can ca1q yea8 tr3o+jy 962bw sy-ht mnw 5zinnka94:use acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves wrn,f4 2n4ubi a long, slender aluminu4r,ni nf4 u2wbm 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. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency ofgbu0n0aqv+9t 8xyz q6 abbq0a+tx8y6v g 9qunz0out 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. A d8v3ov/ l,ssafe2ztwj4 n/+xe y+t y-n observer on the ground hears the sonic boom 1.5 min a/ sny+2v/swyf+4 d -tt 3,j8aeov lxezfter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1swochg q w,-o;(,se /j5 $^{\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