What is the evidence that sound travels as a wave? :tj l .+f.79tzuzlpwq

What is the evidence that s*cun gs+gv cee1kmg/oi: ;xm zfd n9/ .oap85*ound is a form of energy?

Children sometimes play with a homemade “telephongx)hvl / wwaa2: jt/z: dbz7s6e” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig.sl //gj:6 :x2ahtd7wv zabzw ) 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 or wavpp :ynyu(/.es e(ppu y.es:/ny length to change?

What evidence can you give that the speed of sound in air does ned,5,+zp nj ml0lq z 8n.1vs1n3pa ishot depend significanzsls8v,, l5 n zpp+ h.e31dj0anm1niqtly on frequency?

The voice of a person who has inhaled helium sounds very )vv 5ybnk5h sad i6)3lhigh-pitched. Why?

How will the air temperatyw,6+ ,.pxs2 lc)ez aq :ptmboure in a room affect the pitch of organ pipes?

Explain how a tube might be used as9ffr2c z 1b5cp a filter to reduce the amplitude of sounds in various frequency ranges. 59 rzcf2c1fbp(An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog(i.9nzx)v/( bna: s ws8 kfmtiether as you move up the fingerboard towiv.bt/a:() nzfsi msnk8 wx(9ard the bridge?

A noisy truck approacheqq 2u3zj4uo c2s you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequencyu2czou j42qq3 noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherh1nrvshfvrjo287. (k mhu-+neas beats c jv1h7+nkfs . uhro(vm-2hn8ran be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of tnypudr-.ddee u 7a2,/ he speakers were lowered, would the points D and C (where destrednpa/2. rd,-uey7 du uctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing ofu4( vwmt9yvuy0n y6(c 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 i4c 9yu6nyvywm( 0(tv ut 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 be thought of as 7arvfq) w94 gqma*+o)mn df2o a superposition of two sound waves with sligg+mwrq)qo 9nm4 ad*v)7a2f of htly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source anymdgs( lt 3 ,qrp(67cjd observer move in the same direction, with the same veg,((p tsc7j q rmd6l3ylocity? Explain.

If a wind is blowing, will this alter the frequenc)at:fr- 0r-6ycbk i:n.tlqxpe, ahd7 y of the sound heard by a person at rest with respect to the source? Is the wavelengt.rkneidq,x7)6 - ahy:lbr - atpt:f 0ch or velocity changed?

Figure 12–32 shows various positions of a child in motion on p kxs8, wkpo1lqs8,,t a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will thet18,lwpk s x8ksq,,op child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lafwbt;bd2( 70*. y eop8czjblfke by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2 0j8wopbbd( e t2z;cy7ff*bl..0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears then+g;d7 j :kzpu4oos4 uyitb3q0c s6o(ky(w+v 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 sigot s+kgiopzkb3n4(yydu +j 67v(: 4wu0s; coqnificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at, zxyk ns3w :5bzggd olyo/: *ts-w -u4(jsit- 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 ab ban hc:8ik1n- ngo4sp.mx -1eove a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is hekn-npm181 :xc-ghn e io4s ba.ard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when xc pc64v/e4. bhg9eypstriking the water below is heard 3.5 s later. How high is e yvp9exb.c /6pchg44the cliff?    m

  A person, with his ear to the ground, sees a huge rh7pi,cr+o 8*e vjp rq*fe1 o;i54zspstone strike the concrete pavement. A moment late7qoh ,eiprc+je8 4z*f rvpp;*5irso 1 r two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over oni/ etoi 9zs+yi+q c -41ebg6ene mile of distance by the “5-second rule” for estimating the distance f/in61eieito4zqby9 s++e-cgrom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity3d2 ;; ovbdjcs- a1r00oo*g.ag z6y ornx:lpi of a 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 of a sound whose intensity i ah +/m9)k0p/ oothh5wpury8vs $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simult;i )ji-9n 8j/qfepw tjaneously at a certain place, what will be the sound lev fj-iq ;w9jptjn 8e/i)el if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain disj,ym9f zk8sm.h c./ik tance from an airplane with four equally noisy jet engines is experiencing a soun fzc s..h kj,mki8/my9d level 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 said to have a signal-0akt n /xn3zgsdy*8j ,to-noise ratio of 58 dB, whereas for a CD play0 8n,x s/k3yg*njadzt er it is 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 from a person speaking in normal c/a2h8 jpezru( u18l hdu(hm) uonversation. 8zhjpmd8/r)(huu1ah2uu el( Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose areaa:*qr br.4/1v4knyrchtss3t is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the morts-64ovjb z 8dtns*1j e modest amplifier B is rated at 40 W. (a) Estimate the sound lesdzv 1t*so8bjj4-6 tnvel 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 placed 2.8 m if3 rd ) ry)fena6v50vzn front of a loudspeaker on ther 6ev5 3v razyn)d)0ff 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 -0c7ac - fbdqr f .k(dj,j*pvqy4yk3kin sound level of 2.0 dB. What is the rat0c - bkvq3yydf *(dp,kjr4c-q f7.akj io of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triple/ fm /y2m*,c (gjpfxyhd, (a) by what factor will the intensity increase? Increase by a f( ym*/fgx pmfjch2y ,/actor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twbjyq 2cw2v ,2zice the frequency of the other. What is the ratio of their intenvcq zj2w, y22bsities?   

  What would be the sound level (in dB) of a sound wave in air ruon el-un6t y6f8:wx vj7 1c)that corresponds to a displacement amplitude of vibrating air molecnv:6)o7n-f1u 8try u6jwexcl ules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz to+-kxm3 vb)8xscar 0izne that has a 50-dB sound leve k8sc z+x0r3)vx aibm-l? (See Fig. 12–6.)    dB

What are the lowest and ms-)wieomi - )r v:ae*highest frequencies that an ear can detect when the sound level is 30 dB? (See )smro:e m )-e-i w*aviFig. 12–6.)

  Your auditory system clup;hxda06 3/m;g jyn an accommodate a huge range of sound levels. What is the ratio of highudyp;3mxgalh0 / ; n6jest 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 nm qzygs.*c4jhm4j1(has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. gj 4j .(cn4h msymz1q*Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibl2ziz)q r/ie0ju4gw2le overtones if the pipe is e 2ulzgzw20 iij/r4q )
(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 expec8c j6ro1 xx/okt from blowing across the top of an empty sookxj8ro/x16 cda bottle that 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 pipefx ;m rrw ,ws9l7:r1vis spanning the range of human hearing (20 Hz to 20 kHz), what would be the, :f rilxs1w9w 7vmrr; range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequ3m *slw88 hczlency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of itl3lch* w8m8zss original length?   Hz

  An unfingered guitar string is 0.73 m lp6 r 6xla /i9wlrk+(gfong and is tuned to play E above middle C (33l6+9wr(apir lf gk/x 60 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whenm 1e4hdllvem2rf7(36;wap k 2 ac-w xh the temperature is xc( l23v1hlwh w d7e-pkmr; aam4e26f21 $^{\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 yn+e zx nvzr ubi7,c8n60aheok1 5k0/20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mout4dr8 -9oodnko,5tf kd hpiece of the flute in Example 12–10 should the hole be that must be udr8,5o 9odknf4k o dt-ncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pip ikwxq iabk0p3qr cp p/w+70-9*yrd8m2 -torve can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. 9pvy/ - i0qrrk d-o r0 c2k3tabxpm*+wqw78pi(a) Show why 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 1fv:iol;u 42v e) :fbmp.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whav ;bfl)e2f :4vmpo:i ut 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 qof69 up:bn,3 rrnh.5- amgnt$^{\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 tha8yxg1 w ngi6*p;6tx xe audible range for a 2.14-m-long organ pipe; 61x6 iytxg8 *panxwg 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 ope du- d,3irqsa;n to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the informatid r ;i3qd-us,aon 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 va8zrrws) .)xvb):r ytrying to adjust two strings, one r8)vw ys vbxr.):za r)of which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)j6fqyp vu9a r8w.4eu/ 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) operates 4v0qnv .teap5 at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of 0.5vta neqv4p brand X.    kHz

  A guitar string produces 4 beats/s when sounded with nwh ak2jtm.616 :fepi4pxuf , a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hikj4hnfet, u.w 6p mf26a1xp:z tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hr4vi -o:m )cw9h9)wszli asv-r*a 2dmz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are plavl)r9 zds: o*cwi-rv9-a sim 2)4wmhayed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to p51;f:l j. f/wgr nedbylay middle C (262 Hz), but one is at 5.0°C and the other at 25.dng; r5ffj /bw :e.1ly0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B wxm m: m uxev98l jt90ilnm.4/.7knjthas a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. Whenn9lv4tx9wm lu .ni8e7 x /t.jkm:j0mm B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.i.eu6r-f 1awtl /yc:+/adxzf 80 m apart. A person stands 3.00 m from one speaker and 3.50 m fromuaffc w.l t:r 1a-y zdi6e+x// 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 be00t.y4) wm yesebdez1 vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of twm 0te)0ydzy1e4 s.behe 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 2em7cj p,- pcdy4g:p hseh(0 -izj)emand 2.76 m in air. How many beats per second will bc d ,jmee(cji - : mp4pg07-hepszhy2)e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engi91l ve1vca7w7az 9bw ;4uss btne’s siren is 1550 Hz when at rest. What frequency do you detvz9el abs 4tu abv7s19w71w;cect 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 freqz tutv2/5/pxx rzjpsm 67hqi0: pqn8(uency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3xtnp /5j(v7r / ps2xhqpi :0q zzmu86t2 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 yx;tb++)a h l ljvn7)uaou at 15 m/s versus you moving toward it at 15 m/s Are the two frequenc v bl++a)h;au)txl7njies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the sax/ s9q.e78 0 wxi1p(qu8ztx kfa 5axjame 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 x5fx0 kzt8aas(78u9i1axeq pwj / .q xhorns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultras 2xqui60grkoye 6+my6onic sound waves at 50.0 kHz and receives them returnu0x6rgym 2 o i6q6y+keed from an 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 iw5n o *u2n2wyqt flies, the bat emits an ultrasonic sound wave with fre n5q2 wyu*o2nwquency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat js-wafz6ppvb4*9p9ztrain car at a frequency of 75 Hz, and a second identical tuba played the same tone while4s *fa6vpw9j -pb9 pzz 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 twky 8yf*t e.b1llq/ zt a1jjk189 jh,xo measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expectjxb8*h twz1y1 j/8l,e 9yqkl1 t fka.jed 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 ulb bk0,ls0ncd7 trasonic 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 the wind velocity is 12.fukif dy,q0rr l9 86gi)+xl *b)kg kg m/s from the north, what frequency will observers hear who are located,br08fkx ggg+) k .lfq ,yr)l*9d6 iuki at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spejp4:/ t wbm/l9xswr/ned 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 3 7j8ouz5,,f h-gnd fdk10 m/s (a) What is the angnd fj f7dk5h,og,z8u- le 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 hifjie y1qwgdx3 +b,*3 c0l jy0a1) yta planet where the speed of sound isdayb j31,i1hx q *jiyl0 f03eg+ty)w c only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine t *3s*o6cvm y )yw ;)swtsf;lqphe shock wave anglemtso l3*)6w yspywfvc* q;)s; it produces
(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 jhqio-fn;1 pk00ei*k$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the groun 2k 9h /15sevmttq bwqzi 0it:-hbq6v5d flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled -bv stq:iktze2h5wt0 qm69/1q5vh ib 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 w 6z0tgqn qq8zbf:0a2-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for w z 00g8anqt2:wz6qbqf hich it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the huma*uv t8i2 e*2yxvpgtg3n audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphon6uy6 6 b ghs-ypeqq8o1y. It consists of many plastic pipes of various lengths, whicqy1oq 66bs-8u6h gpeyh 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 fro5s/ myx x nx*i*o8:gm 7jvban:m a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 : **ax o:bgy5nm8mvxji7xn/s such mosquitoes?    dB

  What is the resultanxf)ct x-ukq+ umjxaza5-4 :,w bt.3qnt sound level when an 82-dB sound and an 87-dB sound are heard simulan a4x+ -jq ztb 3):xmxkt,fq w-cu5.utaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dBw2tcz2d8o9.m 6 ylpyx. What is zt .2 c9lxymo2dp w68ythe acoustic power output (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 drops b :q/ m05)ou:u: cx0 hfyigbsmmy 10 dB at 15 kHz. Whatm0q bmh: xu 5: u)0g:/sfcimoy is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective dev+vtazt 3( w6 (9ulsodeices 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 disv(tso6a edwl3 +t (uz9tance of 30 m from a jet airplane engine?    W

  In audio and communicatioza+gyq*/lf8 cw8y j(t ns systems, 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 gc+jc gqo*wuxj yi*(0. q+rm+sf.xx /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 longh xz6;x laho23 between fixed points with a fundamental frezxh2h x6a;ol 3quency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fili1y )lrz0mx ,xled 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 tubz1xi xm)r0l,ye 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 am .4px8(cpr z94. qkytda;a3biirv k.t one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundammxi.(iz8a;3y .d4 cqk9.rabrp 4vtpkental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonm8s6pnd ;s69zx tjl.-0q qrfxate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range comings,fg (pdk jy;x/-9v(: 7tu rqbkqb-nq 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 qk(q-yx-qs : 79bbndvgru/k;pf (tj,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. esu:i kcr 9z+l:d/:k bk98zvwOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the others:u:z:zd+k8/k v99 ic elwr bk train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train wbk94 ngh1tfiozde c9f59j6 7 whistle as it approaches you is 538 Hz. After it passes youbfg 9647wznt kief d5j1 99ohc, its frequency 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 just by listening to the .m5lao 8e so+odifference in pitch of the engine noise between approaching and reced8l+ooo sme.5 aing 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 togethe7k rqhoe xh) tw5-(not((/xj-xav uy)r, produce a beat frequency of 11 Hz. The shorter one is 2.40 7to- xoxu(/ wjy(n 5axhqt- )k(e)rvhm long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statiyt w0-c9fhf9 8 (xnm2lel4iv konary 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 8 942 lflwmcvk0 iy9fhetxn(-the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beatw iss8a5qwg2,him o 79 frequency would you expect if 5.50-MHz ultrasound waves were direc qwhsg,o9a52 7imswi 8ted 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 5 u/(koybai my5rdxh+/s. ,bl8k- py vwhile the moth is flying toward the bat - (vla8.m5 pys b/,ryh/d o+u5kbxkyi 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 wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth4- i25ldzxua b8aro .v. The pulses are approximately 70.0 msb25 zlv audr -o4ax8.i 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)m 5 bcon3 bbymre93w8.ik9i.r 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 sounds. When played as a musical instrument, the alpenhorn must be blown mb399i5w. y3 .rco8 imkern bbin 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 presence of standi(; kc*irzesqqs:a7 n;ng waves, which can cause acoustic “dead spots” at the locations :iq*a7 ne sq;c(rkz;sof 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 rtxvw8;m z- 1fjods,” involves a long, slender aluminum rod held in the hawt - jzxmvf81;nd 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 o1*5 msnvk kzmckt(b4, f abotk5 sc,(bkm1 vk4n *zmut 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. An observer on the ground hears the sonic boot;cp9;b ay: 4d:vla:fsc8+ob s ghv z1m 1.5 min after the plane passes directlyp ch ov:s::v1ltgaz;bb; f98+s yd4ac overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb ehsc8m n /)dl ,,tx u;c7zr)sz2.cwavoat is 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