What is the evidence that sound travels as a wa x zc*xg1lxabd,u d mk+93( m/+yo6ckwve?

What is the evidence that sound is a f p:9g7j, fgj2ttzj6 weorm of energy?

Children sometimes play with a homemade “telephone” by attaching5c btm*9k (2cpwzobd2 a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12zbp *9tm w kc(odc52b2–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you exbge4xn;(4il yj8s s7 i 839klqx9uh 4vmyldt. pect the frequency or wavelength dxl 4hjily7 u;eq g84vyim .s38b sk949l(tnx to change?

What evidence can you give that the speed of sound in air does not depifo vl vi8.rnbao z5033(r mr,end significantly on frequvrnvb(r.ii ra33f5 ,omz0 8o lency?

The voice of a person who has inhs0rvfaa,8x p7 eype+ (aled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitchf .8vp-bqq n5m of organ pipes?

Explain how a tube might be used as a filter to reduce tydv v8e: c96znx0c-dhhe amplitude of sounds in various frequency ranges. (An example ise: 6h0cvz9cdny v x-d8 a car muffler.)

Why are the frets on a guitxrz u 3-hezkghwd 1t19kww+w :7n2o *war (Fig. 12–30) spaced closer together as you move up thewz w ogdu912kn:t- 3hx1zrw7w+ *ehwk fingerboard toward the bridge?

A noisy truck approaches you from beh .ddqcc84nj9ct,8i( xs/bkr le( r.e cind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of trtxc(k(srncq.9e8/ ddej .cil c 8b4,he high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said ti2 c kdd1(: 0v)rihrkob;j1f po be due to “interference in space,” whereas beats can be said to b ;h jfci2iv 0dk1krp:r1)bdo( e due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poiadh(g* njq7q )nts D and C (where destructive and constructive interference occur) moveqja q*) (hng7d farther apart or closer together?

Traditional methods of protectingqkwn z08 un6ubo33j0qo8c;d ucy(: pl the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn 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 y0po :q6w;boq8 ncl d3u8jc(uz0nk 3u sound levels reaching the ears?

Consider the two waves shown ins,a(2 qwi:rre ps) ;ht Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are (sw :2eis) q;hrpt ra,the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the szr,berh / 0s/same direction, w/0ehsrz / ,rsbith the same velocity? Explain.

If a wind is blowing, will this alter the frequen7yx+xup 9o7-dqikhz np 3m08/wscm m.cy of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity c 7qo3xm7pm0 .mc8d9zi-/knxuphsyw+ hanged?

Figure 12–32 shows various positions of a child in motion on a swing. A monito 0+xiqzein27o) yu-air is b)0iy 7ozii q-+u2eanx lowing 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 lakekbrbsr69v *q:p4o+ de by listening for the echo of 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 69 dk4evbbs+rqpo*:r the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bebyrni5zt b f/)m 97op lk( (boyo82:eylow the waterline. He hears the echo of the sound reflected from the ocean floor direco/zb5( k)o pi mbnb8y9rt y 2:7(fyelotly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airsh(xp it.b)dpcwe 3*+ 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 of tuna on a foggy da o9 nup9xt+ z*ehit7f8y. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a*98xn9t7ih pze+ut o f) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash i):(ski(a-/:soc cxxf m siz i+t makes when striking the water below is heard 3.5 s later. How high is the( im) /zo:- s(fcsix :ks+xiac cliff?    m

  A person, with his ear ;- f07 i8ovran+yi0i2mmz+tyqloxcp , 5.pevto the 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 r vmam t +iz, pfe .yxp-i7oi0v;8 nqyc+50o2lconcrete, 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 --wai-d 8nbcloefm3/of distance by the “5-second rule” for esib-e-fan-wcm3odl /8timating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s-vjnb-na ;hxcirey-0xb; fi/ a; m*0 dound 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 of a soun fpl3a5a+an+kd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produ19z.s* x ll1eye p)l*5 wxvmnwce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exvl1*e9 s) yxww 51plnx m*.zelploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance e pib4r(ix3 z(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 all but one engi x(i(ieb3p r4zne? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-n. 10 lzy5va*k- prtl arcol(3poise ratio of 58 dB, whereas for a CD player it i5 k(c azaop*p1yvr- lr0l3.tl s 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound f:t.b4gt yh2 wc 4no*8 it:bxfgrom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cet.* c4 :8wtbgxb:not2 4fiyh gntered 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 st.ku9b0 pmb1rsm *lsz gd;5-tirikes 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 nha). ko / qtm0i6)/c:cykqeuat 250 W, while the more modest amplifier B is rated at 40 W. (a) aium:q)konc0qk6ch/ t./y e) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when t;g o;-xvsecg; mhlyw1 l:i// placed 2.8 m in front of a loudspeaker on the x 1l/:;se ;ochyi wtg;vg m-/lstage.
(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 typicahc3wju86e7cwhwc qrb1fiibf p+v );4n: f .f6 lly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds3 ewi6f. nwchb:1 c ;fr)qb jp+7wh cfivf468u whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavz07: qeqj .sfxe is tripled, (a) by what factor will the intensity increxqf.j s07qez :ase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equalmj*w6(vv2 zdqk3bzaa. lp8 g jwt5e.4 displacement amplitudes, but one has twice the frequency of tvjket(2 mwj6.aq p zl4vab3g d.5z8 w*he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave y4 (oy7.zyv+llhp) sf in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mo)yzy+l4l7h .fpvsy( m at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100- 3hgbq33smc k6lk)zh5Hz tone that has a 50-dB sound levelskkmc)z 3qgb6h hl533? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thatt 1gjh9m9 ta.kwa1 7ny an ear can detect when the sound y7hw11j a ma9 ttgkn.9level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge racbu m(mfob3ej 2/1cv1nge of sound levels. What is the ratio of higheso1vfb/ ujmb1 c32cme (t 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 Hzcfn t7n7-;jl p. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension musc7f7n pn-l;t jt the string be placed?    N

  An organ pipe is 112 cm long. Wh jgl3(hyx-.k cat are the fundamental and first three audible overtones ikl(hcgx-y. j 3f 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 yj+ r1ue/9e2fv tcrd;m ou expect from blowing across the top of an empty soda bottle tham eve/td ;c2j 9f1+rrut 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 ofha6t95p h(wims gh/n 5 human hearing (20 Hz to 20 kHz), what would be the range of the lengths of psg65/h5t (nh hmi9wp aipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What willuml-u/g+1 q ,pu+-lt6xigrtt be its fundamental frequency if it is fingered at a length of only 60% of its original len+-iul6uqxg/tm,tugp - tl 1+r gth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned t 25 q6.ixi+v.snglqdqo play E above middle C (330 Hz).iq 6.i.g+lx dn5v qsq2
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) wh)nyes4u5 i ucj);fc a4en the temperaturec j5 f)nuuasy)ci4 ;4e 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 2/75 kyhkc+ zbij el4d2)a+xvf 0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be tht og 02q;yftu2at must be uncovered to play D above middle C at 294 H2tqyugf20o; t z?    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, 440 Hz, .2g)d)i pfmts* 6f idagg+gf6and 616 Hz, but not at any other frequencies in between. (a) Show why tip f+. *g sfg)6g)fgd6mdi2a 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 xd;) 2qpgdkqd6. ao+m both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What isda 6pqdqx2dm+.go k );
(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 quv8ef+qh)0 agm(+ qohg ch*0 4vv9ii$^{\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 aq9-tks w *f/1grvvibx1zw ,ozo 8v2,jre present within the audible range for a 2.14-m-long organ pipjw1 21, wvv/of i-brg9o8qt* ,zsvkzx e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal islfo7l1.x kj0,kuuaairu4) 4h approximately 2.5 cm long. It is open to the outside and is closed at the other end h1a ukafokju04u r ixl7 4).l,by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust twr+ c t f4hikv3u,1sxb4b*+czbo strings, one of whicf 4v 4hr*u+1k3bi+ccb ,btzs xh is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if2*ftgowig8e 8up- pajy7o )/q 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 operatez1tw *pw9 h2fzs at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whinz* hzwpt 1f2w9e of frequency 5000 Hz 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-Hz tuning fork am 0 :z/3i9c+ fn/cmzajz in7nbnd 9 beats/s when sounded with a 355-Hz tuning fork. Wha: i cncnjfz3 97+nazbm//zi0mt is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned toy0 hsgkljh:3qpk76. d the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat freq g7. 0pq:j6shkdylk3 huency 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 pla5-i 11pw6una apz u/1m1kthmaw- p+afy middle C (262 Hz), but one is at 5.0°C and am1a +p f16uhia5 mpt 1--knaww1zpu/the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequencadwf ;b:0 : a( yho1n/)idupxun2s+c vy 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 H:ay2 /0i1: oxp(n;+sbu avcfd uhnwd)z. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from z8z jn x;ld9c4one speaker and 3.50 m fr ldzx;cj4z89 nom 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 ar jc3q0ux wdb +u+n57z o-xfa)oe supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are pl )-u q+3u z7ojox0n ba+dxwf5cayed 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 wavelen zkouu f(wrehq*:+rnpuy:40 9gths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = f:wuu:r 4+*y(zn0orep9uh qk 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren ayn.bzrqx*; kr 8*8ahis 1550 Hz when at rest. What frequency yza8.*x ;hrb r* anqk8do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freqh do kx e)6/y 3t:24de,ooghafuency do you detect if a fire engine whose siren emits at 1550 Hz moves at a spo2f/)h6t:eh4 o d gaxek ody,3eed 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 ,us cxki -w;cdx,g y12v4+s ramoving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they ivs;xu,d r -a2g+,1y k4wccx sclose? $f'_{source\,movine}$    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 q-7yplh2ag7ukf(at: the same single frequency 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 frequency the horns emit? Assume T akpqu:t27lah- ygf( 7= 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic so(daqd j paw5 f.e(.tv:832i yn*p ngtqund waves at 50.0 kHz and receives them returned from a 3p ntng:a 5jdvay(8i2q.wp tf*qed.(n object moving directly away from 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 flkg q9f 4:oiax m;3awf-ies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear io 4aw;g9q famfk3ix :-n the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played okh ykbgpkexak-pon)n9u * :7bl*,gne00qp .9 n a moving flat train car at 09y g,bqx p)ak 7.9 h*: ek*ebn-u0ngonk kplpa frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves ;d hsi z:2c4.czeywmfozux.,l.m 9 e:to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue isu c2;y,eoid4zf9z c slmz.hx::.e.mw 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 ultrasoniclsh4 x*le7*ge)gq7 sp waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When t8 gk8-cc jovc-g 6rpl-he wind velocity is 12 m/s from the north,o8ccr6-vk glc j-8-g p what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object movinq8 k1qry,h.a zg 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.hq0u+89q2555)xfa j xag lt rl3h su)z awvr6u3 where the speed of sound is 310 m/s (a) What is ur9jv )83h55l +ulas5 2qzu rxh60gatfa x)qw the angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmospher zu9y (s7z vb-d 2bayzbh/zr03e of a planet where the speed of sound is only 0 zya/73h(dzzvurby 2 9bsb -zabout 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 qau; w:j;d2; 2 uzbsixstrikes the ocean. Determine the shock wave angle it producesd; siu:auj;2xzbqw;2
(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 )f ytpd7e,*s le-wfwp :-li ;u$/theta$ 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 exactlyj9/1 bdw2nwjb 1.5 km above the ground flying faste 9bn1j2ww/ dbjr 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. 12–34. 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 sonarepwqx *9b27z+bxgt) fx )yza3 device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for wpbx yx qx)bt3we*a97+g2z z)fhich it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are ther.m z 2;k/,(4kc(ljyuiyfqi hwh/t qe -e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has h ( k1ngtxo3.spak nc6e+/7 kga display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both c ong3/gxks+.a67 k k(phn1 etends.
(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 clof;7, tm ;zzfmdse to the threshold of human hearing (0 dB). What will befzmm;d;,zf t7 the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and awoh227t8i0zd iqw/mp n 87-dB sound are heard simultaneouiz 2t 0m7wdo wih/8qp2sly?    dB

  The sound level 12.0 m from a loudspeaker,x 8nk0;(eog coji) +- bjmxzp9 placed in the open, is 105 dB. What is the acoustic power oueznkjxg ic8p xm 9)-0oob;j +(tput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drobkvq)5p51 h)q1poayx l0 ihu6 ps by 10 dB at 15 kHz. What is the power oa)pvx qqoh) 1u5 bi5kl6h10p yutput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear p0 g.7ho9 t ,-lxa eq.s0(qns pzp9ndzqrotective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplnsed(,po9 g .0za-7s qq.n xh0 t9qplzane engine?    W

  In audio and communications systems, t) y op5rmo.c2she 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 frequency 1ptrh2 o5f 7/eo$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental /o ;6fkein0 0h0uwpjyfrequency of 440 Hz and a maw/;0hpkf y06en iuoj0ss 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 filledcy5zp, gj lv(( with water (Fig. 12–35). The water level isp gy,ljv5(c(z allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at +( i74qqqbcoe one end and also 75 cm long. How much tension should be in the strinoq+7 qeqi b(4cg if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one*q+6 n+ )fa(hdcpv3vhxrn5xo 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-Hzmb+c7 + vx:vji0-w.-ivrh d;q whwcs+ 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 +qciv h-drj+sc wm+h;vx.w bw- i07:vother. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on theygixx- y ,0knifc+.9u stationary train hears a 3.0-Hz beat frequency when the othnx0 xu ,+g-.9ci iykfyer train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After i5ogvh(zq, 4rn t passes you, its frequency q 5hr 4zvo(gn,is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars juku0 t0dsc7pnch,mx6 ew w09p.st by listening to the difference in pitch of the engine noise between apprn67hepp0 cd9w .m0twsku ,x0 coaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Thv u 0zzo0eo 6rul;9cmj(x1 f4re shorter one is 2.40 m long. rx;lro j61u( oz0mv ufcz94e0 How long is the other?    m

Two loudspeakers are aeze 4g.0bovz m*a zd/(t 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 identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) hee0a 4v*zm/ob (.gzzed hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is nm n e/me8.(o;6l wkc;ybii+ba *iwv,sc d6z7yormally about 0.32 m/s what beat frequency would you expect if 5i d8vbi memiwa lycos( c7,n;kw y6+b6 .;e/z*.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towar6 f-xy6g0kh 9 z*skictd the bat at speed 5 m/s The bat emits a soundc06z9s*xg hytf6 k i-k 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 fre2bhl)5;el8ab c xhe:zquency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and ee: e2)azh xl5b;l8 cbhach 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.f kkcv .(ky*bu;r4d3h 12–38) was once 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 soundsdcbk; 43* ukykvhr f.(. 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 compromie/j lr;-ir+2byi+ n nused by the presence of standing waves, which can cause acoustic “dead spots” at the locn+;ri/+- ejn lbu2ir yations 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 “siaby2,5qk* ct((2 o gmtd papm-nging 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 “sing,” or emit a clear, loud, ringing sound. For a 90d pyt-*,(2a cgt5kba2m(pmq o -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 ofr3aw16 s0o1 n czl+qlg about 13 1oc rzql6ga+01nwls 000 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 hn0qua tbph+u /kk,bmc,wv(0 /ears the sonic boom 1.5 min after the plane passes directly overhead.0 / v(m+,akn hupcbtb/kq,w0 u What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 -0,h/f q i0pk/yjiupx$^{\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