What is the evidence that jr-5 wv e98 xo9x:ihnjsound travels as a wave?

What is the evidence that sound is aom91 au*-hdq6 ,fmuhq form of energy?

Children sometimes play with a homemade “telephone” by attaching a string tog q sllpw-3g3+ the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain cleglgl+qw33- s parly how the sound wave travels from one cup to the other.

When a sound wave pas8oukn;6ayd pj .zl+9eses from air into water, do you expect the frequency or wavelength to chan9+j;oz. ue 6knply8da ge?

What evidence can you give that the speed of sound in aplu q(i/e0q uk* (ju,mir does not depend signifi0j(u* q/e, im(plkq uucantly on frequency?

The voice of a person who has inhaled helium zj2j pm j:*v+8xpnq5esounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipesjtj 2knk)o-wo cy +*s/?

Explain how a tube might be used as a filter toml+ e *umox1 s)g.,mdq reduce the amplitude of sounds in various frequency ranges. (An example ix1s e*+d,ogumm l)q.ms a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yo0,msvx:t)2ecd n,zxnjp l 2ssuz24-. 3hln a cu move up the fingerboard towazeml,navt2uj c d-40c. spznsx, s2l2x)nh 3:rd the bridge?

A noisy truck approaches you from behix iqaxp4dr7*u0 /7md6lk5h)ckq5 sf y nd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — yuq h x/05l kpsa65 q7cr7 kdydm*i)xf4ou 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 in space,” whereas8:6*hyp0 niqqi9uz j a ,+ r-i0ciunih beats can be said to be due to “interference in time.” Expla 8,c-ia0 u rq96ihhi iqu: +pzyij*nn0in.

In Fig. 12–16, if the frequency of the :w8gpcl4d bj9uf5hdq59 h 3 iaspeakers were lowered, would the points D and C (where destructive a84 5u j wdfag9bci59qlhh :dp3nd constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of plpq7 -u2s3aaj 9qpnfprnh1 c pe 6oi4h/:81yveople who work in areas with very high noise levels have consisted yirn 2 1s lahe-/ovpp1qc unq6a 39p:jfph8 74mainly 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 the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave ykb y 2ac*4iy.can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? 2a4i. *kbcyyy Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dqw zswq8 hji/m5zn 5(1zxqm twaj;:3(irection, with the s(tq5w8nah/ jmwjz1 ;5zxq3w:( qiz smame velocity? Explain.

If a wind is blowing, will this alter the ,ooqzth+*+ns k ze,o rau9b6 6 paj2v6frequency of the sound heard by a person at rest with respect too 6aj+zrpe,966au+h2k o q,v*nob sz t the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. frajf7k,1z3t 3z dec9A monitor is blowing a whistle in front of the child on the ground. At which position, A through3t1d,z 9jfke z3r7a cf 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.6 vlekin*cna9p: bz0 her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. kzcna bnel *i6:.90 vp$\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He 5*1nlb 2dp/jaj+dgiy9a.xvi hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly wi j1iia .y 5j+d2bxl *vp9dang/th depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air 2 zp 2pdp0yuf8ayf8 az+*2dcf at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school on zsk.vp3s cn/h9pi5.f tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elap3/pshz. k9nnpcivs. 5 ses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. g)1os6qegr /7ra: inkThe splash it makes when striking the water below is heard 3.5 sr17snigr:/g q e6kao) later. How high is the cliff?    m

  A person, with his ear to the groun,8qoh9a0:a4 m cudazo, k f5vau2k9cfd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in d,c9:voa,0 haf4m5 9okcfuqu2 ak8za the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secobs+m wowz6+i)nd rule” for estimating the distance from a lightning strike if s)z+6wim+bow the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level offuw(+:,d 9x;i q9;pa qbitaon 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensi -mhhv4.wym0ucjz/ / t9 *+uspdyp2tuty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sm.kx co4ob3tl 2 3u.zpound level of 95 dB when fired simultaneously at a certain place, what will be the sound lekoo4 ptm2x. 3.3 zlucbvel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an v7r54ats1u byy 5euw9 n/ yej7qkz;o-airplane with four equally noisy jet engines is experiencing a sound levelyn7oz-sk; / uujy795e ey5q tvba4w 1r bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is og azd2+bxs2l1az94gq1sae 5r .5y y esaid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devige sys5ga2azdl529b14oqerz a+ 1 yx. ce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normalmo/dd0e6 :a zq-q z(b,ls m.nl conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered od6l0-l mb,:da zonz./sm qq(e n 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 eardrum5q)r 1 k2t - lyboc3w;vgg2woz 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 Agb/-*ppir )md8zro ofh x(a4, is rated 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 m p),fhzd-o4xp g rao rmbi*/(8from 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 registur.mkt3 )isv6g sf8 ,yered 130 dB when placed 2.8 m in front of a loudspeai t8urfs .3v),6mgyksker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2mq nrmchj g6 ov 8-f*u:*a33gd.0 dB. What is the ratio of the amplitudes of two sounds wd6*3mr g:mc8- qo jguv *3hafnhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wha;y)rhaopt q rd- oe,1of6;jh)t factor will the intensity increase? Increase by a factory), tje;fd rho hr)1aq6 op-;o of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frequuj/do vr-ve9+)cc *qf.jj7x dency of the other. Wj)/ojxc*.rvj7ud ve df+c-9 qhat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that -;yqutyh93.bmaj3 ri corresponds to a displacement amplitude j-itymqa;ury3b9 3h. of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have b, f my3qhr7h*0fu*psv(il)s what sound level to seem as loud as a 100-Hz tone that has a 50-dB sbs ,7s0hf vy3*)u rlpq*h(mifound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detecte2l pk+hd*m-e when the sound leveh*eke 2d+mp-l l is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate biko pdr ghkc,-(y0i3 2b+9nka huge range of sound levels. What is the ratio of highest to i d(0chgbyk n-p9r2kob+ , i3klowest 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 440nzms(j vrt)) t7j it7,3.iefcm,i 8n u Hz. The length of the i .r(m3,u7n ))fmitvsjte,c 8it j7zn vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the 5dhzdfxls . t ;,h uix 96hm(ac9ti/4pfundamental and first three audible overt/mh4.lxf dx cut;z5 h t6(p ,d9h9isaiones 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 blowing across tz;m)gxn znr :g7j ,z9zhe top of an empty soda bottle that is 18 7;g ngjm,zx 9:)nzrzz 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 t:gj 0cux k+g0)bv3k rup8 wc ge/li7.she range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of lgb +v: guxr.pik )/ec gkj3u078c ws0pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as .oqdjdvz d 16v0g v2/rits third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60 d6zjd. /v dr01v2vqgo% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p is.yhxt8. +6y mhx1qllay E above middle C y 6i. lqt8hsmyx.+h x1(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 m(ffjh,syu x5r ih). h:iddle C (262 Hz) when tu) 5 h,rh:sf (yhifxj.he temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune auf2o 2d1u 4kykp ba35vt 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 12–10b:j n5uezz k3: should the hole be that must be uncovered to play D above middle C zb3:jn zk:u5eat 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 i7h7:a0aolw.ww: d ykresonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wwh.7 7:awyk0d: iwalo hy this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It renpcfzeeyx,0+o; :kl t)n5h6 v sonates at two successive harmonics )6cnthf eve x:5n;o0k,p zl+yof 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 bg 4rpgl1c ;.h$^{\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-(uz3lp ;7ipk nlong organ pipp ki zlu73;np(e 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 outside anyj2f8 ebt( iva(m s5,ad is closed at the other end by the eardrum. Estimate the freqm ,j(b5(8tsyea2fia vuencies (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 whqqns , 1:b c0nndn1nj*en trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? nn,1jd ns1 cbnqn*0: q±    Hz

  What is the beat freq z4pddrmq5. 4sd/hr,auency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operate (77q/nsus1nyaxj daev-l76ks 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 ( a/s-uaesqnk j vd76 nl17y7xof brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a )*-r inm/rv(sfgrez-350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationa r szm(e)-nv/-r*if rgl frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to .q8apqo s4mrs4p.l dq8 -nm3rthe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will.8maq8lso- 4psqq m3prdn .4r 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 j(3p:;;b)ox3ayhbae 5 igvz qflutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0ogqp;aa) y3hbzxjb:;3ei (v5 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, anjpayd 7p(rr v-1hxf1a9d0x/ od C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded x1xdh a9 pv-r0ao (y17pfdrj/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 swp57m a,k. 1wqru5nvyy 5k u.person stands 3.00 m from one speaker and 3.50 m f ,ukqnpra575m1 5.ywwsyuv k.rom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a, yfz5qg) 9dwv0vxpaq,sd6j) piano tuner hears three beats every 2.0 s when y5j,,g)q9zax )ddf0qv vsw p 6they are played together. (a) If one is vibrating at 132 Hz, 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 of wavelengths 2.64 m and 2.7znojc :+z9(o) zzwx :*j v(gci6 m in air. How many beats per second will be heardczwjj)v :: g+c izo(z*(z9x on? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire ejs-f)ug,j1g vngine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a sp-,ugg)1 s jfjveed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engi ))xs(jev xogtmee(78ne whose siren emits 8sx)7( gx)mvjee(oetat 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you/h( iv mar3d8g at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are vma(8h 3/gr idthey 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 pe8xrw7* eou*xwm(,j the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the drive* e7xo,*wwxr p(uje8 mr 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 kHztntirh42.ai - and receives them returned from an object moving directly away fin.-h2rta4i t rom it at 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 2gi) ) acqqh2gq 0pvu6an ultrasonic sound wave with frequency 30.0 kHz. Wqa 2h0)p)6 gc2qu givqhat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played rct9h; jw24rd 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 approached 2d wth94r;jcrthe station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bl2-hnos--zu) d9len kc ood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is-- c2-ulosezn dhnk9) 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 uc6 of0st9b + p hp*9g/etu4mulsing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits uzy;th+ged 8t(*no +csound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at r(ent8z*c ty ;hdug o++est,
(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 f 7txt , 9k17(5u97algyvhnpehr1q qtspeed 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 spee+b5rmr w +hxr)/fw7 ted of sound is 310 m/s (a) What is the a r) t+r 7wr5mweh+/fbxngle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of aakc1g(+;meap planet where the speed of sound is only about 35 m ;a1a+p(g mcke/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 850ne py ehv c)4k1n)1lp50 m/s strikes the ocean. Determine the shock wave angle it eknl45y ch 1v)n1)pepproduces
(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 hb+i f x 0bo7f4xdh7y3$/theta$ 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 sh.+w;nfq1wn vwdj v j: g3 shal:;4m/1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, 4q:w :fh w;j1s v / svdm.n3gnw;+hlajthe plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses dowg hy4u;0li5cwnward from the bott ;0w 4i5yglhcuom 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 octa t eifazat*c b6(ib,( qqr4t24ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called wsw4q(a km/ u t50pd5ba sewer pipe symphony. It consists of many plastic pipe /4pbqk(d wt5usa 5mw0s of various 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 rn* pwbn7i;,5q ; bzxqto the threshold of human hearing (0 dB). W p zbwqb;*7x;i,nnrq5hat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound levelhd g wl) :qhpf78b1ud:/5cunk when an 82-dB sound and an 87-dB sound are heard simultan plchwn7k1/d )d:q:5bu8fgh u eously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dzs szs( 9lx6tn);,l.mdruo* iB. What is the acoustic power output (W) of the speaker, assuming it radiateszd t. z9)li nxs;lr6(muos s,* equally in all directions?    W

  A stereo amplifier is rated at 154-qu 6fkod4;o; z,v tvy)t kir0 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 1k )-zftu v6v;4 to;,ro iqy4kd5 kHz?    dB

  Workers around jet aircraft typically wear protective devices over y/hx sj* :uv1arsa/d8,kd fp; their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet a/8hda:;*vrj1d ,y ss/f kxpauirplane engine?    W

  In audio and communications systepp- (5o dh+hs4k9ah hgms, 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 vioh zh, cnhj/q7nyz3 g,le,.w+flin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with rtm zz).fx f:;a fundamental frequency of 440 Hz and a mass per unit length of zrm:f. x;)ztf$6.1 \times10^{-4 }$ 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 vz5 fx0fxdsdffsa5zcnux 3x5b .)x+17ertical 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 distance1cxsx+d x bsd axf3uz05fz.5n )x f5f7 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 at o5qlt.+ n pbe-h0zegme8. jx*j ne end and also 75 cm long. How much teljet.xpg. e+h0z-*8jb ne5q m nsion should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observq 4442ig. dugy; jkbmked 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 506husj86/rp/-cbl/ e qiwrm d;0–1000-Hz range 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 0.34 m farther from one source than the other. What is the frequency of the sod ei6mh 8s6r-qu bj/pw/l; cr/und?   Hz

  Two trains emit 424-Hz whistles. One train is stationarypur7)j)q ix +b. The conductor on the stationary train hears a 3.0-Hz beat frequency when uix7q +rp)bj) 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 i1jflt(lt-d 1)x /s gyss 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train mov/j s-d)xgllft1 ts1(ying (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of ci3gb p-nz8(opars just by listening to the differencei p(zo-8np 3gb 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 going?    m/s

  Two open organ pipes, soun0x cxtai(wx ),ding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long 0i,)xa( xtxcw is the other?    m

Two loudspeakers are at opposite ends oti)rd3:c4yux rx u x5p9isd33w cs-7nf a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer wh5scsdixi-d)4 r3u3 t ypwcx9:3uxn7 ren (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 0.l 1dtab*y7ynloifjk 8- w i+(032 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume thak-1+d(j*bi8 y7oyl t ifwan l0t 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 tazn1*4g ilx1 dxca1y 85tdtj5 he bat at speed 5 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 x5x tj z*g1d8nla i14ty5ad1cwave reflects off the moth?    kHz

  A bat emits a series of hiu(fm251)g+;y nujh6rj wtj p qc2 -vvjgh frequency sound pulses as it approaches a moth. The pulses are appro5uj2 mwp g)-j(rvtvfc1j ;n +y62uhqj ximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once r7;voo7pbxghgj)2b 1 yit1 n/xn,; z fused to send signals from one Alpine village to another. Since lower frequency sounds are less suob;yx ,gjv7)z2 1fopth nb i7r 1gnx;/sceptible 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 listening can be compromised by the prese tb8uw gey i,,ac9.k8rnce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m widkw 8 ,a.8y,t9ie bcgure, 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,w5 vyeyz ,u;:l called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “vzleu;: ,wyy5sing,” 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 e58vd3 a 2bwxhhx5):n-pl b/xot(xrx z ar at a frequency of about )dp8 (b zwn/ xvrxxt2:xb a3-lx5h5ho1000 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. An observer on the ground hears the sonic boom:ck/s qv 4dicxu93(72ir(vyq:h iq szuwr4/n 1.5 min after the plane passes directly overhead. Wha ( :nr z(qqq4uu4/hrw /i2ds7iys:9 3ikcvvxc t is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is9.uv tbxe -f4s 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