What is the evidence that f:eo ts p3, s,ut :m1q /o:cuu:-oqvyrsound travels as a wave?

What is the evidence that sound is a form of energy?z7 dtop2m4 g.u

Children sometimes play with a homemad mcuy wp06(f 8juqs9v0e “telephone” 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. 12–29). Expl0 6q0 sf89ujyv m(upwcain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you exper 7br2 +pqpjn7c i+vh+ct the frequency or wavelength to chan 7r+rv2pjbpnq+c ih7+ ge?

What evidence can you give that the speed of sound in air do2caj :mkiyq,suohtx ;3k. c4+:iqrv+ es not depend significantly on frequency?4qjs:+ymhx3+. aokc:rkvqc2 ui ; it ,

The voice of a person who has inhaled helium souv/ji2ilpu)+,nw p q/onc2- g1lchty-nds very high-pitched. Why?

How will the air temperature in a room affect thzueouqf40 uocn(93. 9z)l nz ue pitch of organ pipes?

Explain how a tube might be used as a filter to rex257l:4 l4wqg)vxubb (ejwrnduce the amplitude of sounds in 5 4 )(w72qeuwb gv: xrj4lbxnlvarious frequency ranges. (An example is a car muffler.)

Why are the frets on a /zoma/fj5;b-x.//otok 0 a gcmf qitj./b9 vtguitar (Fig. 12–30) spaced closer together as you move up the fingerboarjm9bai. b5/o;to-v/t.gt 0/fmo x/zja/ fc q kd toward the bridge?

A noisy truck approaches you from behind a building. Initiallyi6 oj(cdwzv.j.wv:f . 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-frequency noise. Explain. [Hint: See Section 11–1zdi. 6w. jvf:(w.cvoj5 on diffraction.]

Standing waves can be saidcy7.ajx76bta px ; jv -cett ;h1s(.es to be due to “interference in space,” whereas beats can be said to be due to “interference in t6a(7cspte 1 b;ca .7ey-v.jxjs; hxttime.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowerj 2v(da k8/8(xr a exg*th6dgg 9yhjz-ed, would the points D and C (where destructive and constructive interference occur) move farther apart or closer tog8hy986 er(xxd2takjga -dzg(h */jvgether?

Traditional methods of protecting the hearing of people who u*j 4 htwqsvzgoe1/;;9ajt*u work in areas with very high noise levels have consisted mainly of efforts to blsoeuv j;4* w;z9uthq/g1a*j tock 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 0ac2pwo7lvlznm:8v c 2ty+n1in 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, p c1 lalz278w 0 nmvcn:v2toy+(a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer m/h sj0sobei.l c,p mmo/9f41uove in the same direction, with the same velbjosl /cfeu1 ip40s,9/ o.m hmocity? Explain.

If a wind is blowing, will this alter the frequency3:p bm1bmd( (qfvil4+, nnyse of the sound heard by a persoe,(nb m nl3v:y+(d4i f b1mpsqn at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various po)(7e:c tl/qzbvyl gy)7jp(1, unl wupsitions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A throuugwb7 pl()vc71t(ly/ ),:lpuey zqjn gh 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 listenie*ijh z6q7w,wng for the echo of her shout reflected by a cliff at the far end ofwqjh ezw*,i67 the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship3vb- birh x3v9 just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560v -3rb39i vhbx m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 lp(3 *ygu7vrt $^{\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 sr5 ej(5 r l*ila1z34w sediz(a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the3 15s(le*id4zsjl 5zai r( ewr backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clif6dg0h mxak7k 2f. The splash it makes when striking the water below khg x7 ak2m60dis heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge sttfwfp i,4,v223ppu:l h* l qylone strike the concrete pavement. A moment later two sounwfplli2fh 3,2ppl,yu: *tv 4qds 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 one mile of distance by tynsx7/2ruclab;w,,swv g l c7 )-je1t he “5-second rule” for estimating the distance from a lightnb;7 2uccsg - j,1,ysllxwe wa)vtnr7 /ing strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pai5n rhq,7 (m.cc 1( ;vpjv4vsws7 fbimdn 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 sou/31b yj 2lwrlund whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously ,w ;srx1hqqs /at a certain place, what will be the sound level if only os1q hsr;,w/qxne is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equallyszvb.r0 xha 0f (z2l3y 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 engine? [Hint: Add intensitie3z0bxvfa ( zrys0l.h2s, not dB’s.]    dB

  A cassette player is said to have a signal-sf;2ybl 4qx j(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 backgr(2jqfb x;lsy 4ound noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pers nyqs f zq)hgg987*5 3qdacaf6on speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over aacfqg)yah365 *9sfq qgn8d z7 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()m-ifwgvwrlt1) , m h 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 at 250 W, wk t2 + bmg s 8r4rvvq2bw :)b2s-kzftpx0dpd6-hile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would exrvm 0sg 2b: z8+dpkb2kr4 td2-qwsvb-pxf 6)tpect 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, azocvm(s * e:dn -31nmk dB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the st3kmn( no*:e 1md z-csvage.
(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 differeny5fk ;-k )4p )8qz5s zbig,,qgclkejpce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint:j,ezy qc5k 5kl pqs4fi -zb),k ;g)8gp See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the ifao.ef riqh9. . 1tzl6ntensity increase? Increase by a factor of ehf1.r fzi o .6lat9q.   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacementa* j+phfr ev/* amplitudes, but one has twice the frequency of the other. What is the ratio of their intensit*fhav*r+ /pej ies?   

  What would be the sound level (in dB) of a sound wave in air that corresponds tobwr :)vlb34xsz: jk4u a diklv4)bzs4u r:x 3bjw: splacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-H2/kte jg00x rzz tone that has a 50-dB sound lev 0t0kj/ gxzer2el? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an e8l jr4sh-0mfks ao d2(ar can detect when the sound level is 30 -2amrj08f dohs k4 ls(dB? (See Fig. 12–6.)

  Your auditory system can accte8he 93r;l2z(q8 d jvefd zb-ommodate a huge range of sound levels. What is the ratio of highest to lowest iee9- 8dhqelzj3zrfd 8 ;bt2( vntensity 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 frequencyi+7dmmv1,gs0 s 6mfav.r tv0v of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. i6sa0 .r 07v1vf+dgmmv,mtvs Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamente ,z,s*ud2a p enbttiet5wz1qi3+-i 1al and first three audible overtoe 5 sz wn,iz,ptiu ea3tt1bq* 1i2+-denes 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 wovffn3 pz;p*z9x s*ig, uld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you fvgs;xz* n*zp,p 93f iassumed 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 spanni qso90s,o4yylng the range of humaysql9s 04ooy,n hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hasvt9f u fui7t/3 a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a l t9v3iuufft7/ ength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mev7 skmb 6v)b3iddle C (330 H7svbvekb)m6 3z).
(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 os1.qqjhadb ku-1 w 2o5rgan pipe that emits middle C (262 Hz) when thk oa1 j.sdwh 5qb21-que 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 at auuea+t8h05b5vk o+x20 $^{\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 thay cd68)g( f77kqi r*)hrrejglt must be uncovered to play D above middle C at 294 7ed h k6yc)l*)rrqjr( 8 7gigfHz?    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, and 8+qk af8 v2jgp616 Hz, but not at any other frequencies in between. (a) Show w2jaf+vq p88gk 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 t yb;)*re l.vttwe /6sends. It resonates at two successive hae;btr *lw/sv t6t)y e.rmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 l(5f;i 7m- v gwae,3w)wvge zp$^{\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 audib*-c.ntci s x3jle range for a 2.14-m-long organ pipe at 2t -c*n ix3csj.0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. j y7a;gqb*mvs2d v+5c It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audib57;my2+j* abdq svvg cle 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 oneh o xty+1+huj4 beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off iu+x y+1h hjto4n frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 cutao + c m39;lutk/p3Hz) 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) operaeu qs80 z-q(kutes at an unknown frequenc q0q(ukeu-sz 8y. 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 brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3503e i 678gclcqd-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explai6 8g 7ceicqdl3n your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensio)-ijqr+egu+vblr*v+k 2 oi; f n in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togetheij i qlkvr+r; o++ )bf2ge-v*ur? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try 83 j,/v kn/na wuxri)qto play middle C (262 Hz),, 8qn au)v /knxiw/3jr but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hag2q/-ck 4 c4x 2e4*. fywlmq8wizhdmms a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the bea-ehw8yqw2x 2mfk l/c4 4q cgi*.mmd4zt frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one spe--wu(w ff 8frziyei:,xu z /a fly2f u99;p;fdaker and 3.50 m from the othe xiipywfua:/ -u9d;8f,-(f z9ffr;weuzfl2y r.
(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 pianvnb8 q8q/-im e kf.:hso tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be theqve 8fhkm8i/:sb. n-q 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 2.76 m in air. How atiz,*f a7s*emany beats per* ea7 fizt,*sa second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s +b 7jf+nwa v4fsiren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 3aj vff+ 74w+nb0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stildjjs4;g 6wd*:ygc km*l. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at :gk4dmjw j* *y6;cg sda speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shif g xt+,o89lgfrz- o.ziad3u/yt in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15oyuoli 8r fg,3a /z.d-+ gt9zx m/s Are the two frequencies 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 3 hwzhquh;sqt)* 3mm*the same single frequency horn. When one is at rest and the other is moving toward the firsq3hmw*m hs3z;) uq*htt 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 = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and h w/tw2nw(go5x lhj)nbnq+1 5receives them returned from an object mont(h +wnj )gqoh5bx52 wnw l/1ving 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 flies, the bat emits an y.4ixvgc9p0n ultrasonic sound wy94i ng0xcpv .ave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was platihfmz9 zbco (aa+ :.0yed 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 traini:a c. ozb9za+(hmt0 f car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. S z7tvh1 (.* )mkoeygdr( 8xbofuppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to8rfhtvz 1mekb .7d(* oo)x g(y 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 ultraso1q tvb8// ddk e0,c*gh8lukiig. n2qwnic 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 emuja* zv6 .le/sits sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observeae*s zlu/6j.vrs 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 object8e,i9w 3 7r qyskb.nal moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 whc1 ae0d0qxakn4 sc4j;*bc7eq l5pd 1yere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the dired pb4qn sec7cea qd*5x0 4a11;yljc 0kction 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 w* mf :5ge40nwfshn9u vc3v 8ythin atmosphere of a planet where the speed of sound is onl:5w8 fsv 3gcn uh04yew 9mn*vfy 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 9 ,an jbo8a/zf8500 m/s strikes the ocean. Determine the shock wave angle it bfa,a/j9nzo 8produces
(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 z (a xea- im,z)lyxdr( dv;*y9$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pl+tk+quf)1upfvs m 8,n74 uqdlane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the+7mq k1f +vuftu 8 d)4s,qplnu 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 sohgrn3,5jwj/ g/rxjh //,uyetl iilv; 9 ht1s6 nar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum tx//giijrnlj w9;3hhjh6 se/ tl tv51uy, / g,rime between pulses (in fresh water)?    s

  Approximately how many octaves s,*xzis0 qgwg,et0e34ah-gf are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consistsf4* bsq 3xgcr9tea y *f(jz+-e of many plastic pipes of various lengths, which are open on both ends. 4* b- care3s(xjy*fz gqe+t f9
(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 7vdrr )o5 j.ozm from a person makes a sound close to the threshold of human hearing (0 dB). What will bd. 7jvrr) 5zooe the sound level of 1000 such mosquitoes?    dB

  What is the resultant soundllxz5ol2 ee7 lz,( -d r7boym, level when an 82-dB sound and an 87-dB sound are heard simultan(- d2zzy,,lolm77 o5e re lblxeously?    dB

  The sound level 12.0 m from a loudspeaker, p 3 y/6nh fjdk3h)sxzq+laced in the open, is 105 dB. What is the acoustic power )k/y3 s+j x 6zqdfn3hhoutput (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 powe*zyhwc 2o/iy8x; vse qa5. e+or output drops by 10 h/sya285 * e;w.i cq+o zoeyvxdB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraftevxv w41r5em : typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m m4 we5vrex:1v, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicap .sahuxzm1oq 6c*x /0tions 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 an(d4o a4pkt +rwt+i3k 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 cma17**; )(t ycot mwxbt1z jnvv long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of 7bax( ) 1tco tmzn*yvw1v*j t;$6.1 \times10^{-4 }$ 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 vx dmy,3qk3z/ vj 7-iusevwyb *8(c r0cibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.ci0ey37y8 j x*crzbuqdvv/w k (m,s3-395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mas;uoz hupf77 7ms 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundame upz7;h7u mof7ntal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fxevuato,y q9h8fkzan-/ q)1 (wr, 8tj xl3)xkull 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 j q +ttt(4iiu61 )wqfftone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from )iq+1fji4 tqf6(u wt tthe 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 sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. Tdo dc.3z 3/./uthu eiw;srej67 q+w nyhe conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. nw6st; i3e/w rducouj7d +.ez3yq /h .What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approacx f3gqni m tg*,81m)kyhes you is 538 Hz. After it passes you, its frequency is g3m8gt 1)imnkf*x,qy measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spee )a54pjrq3 qpgd of cars just by listening to the difference in pitch of the engine noise between approaching and reg3p4ja5q) rqpceding 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 freelk)w:cj( 4 8bz e1caqquency of 11 Hz. The shorter one is8(ebc1qlae)c:kjw z 4 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movesbv/:e0 is+ tot past a stationary observer at 10 m/s as/ :+0ie tobsvt 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) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normall2evd2p)n7hv(u cp w e,a-puk2y about 0.32 m/s what beat frequency would you expe,h-7kp2epna2dewp) 2(v vuucct if 5.50-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/)lmy y7.p)z+r-a /lm-rthn3 syx4 lxos while the moth is flying toward the baaoz ly-ll4n3xh.sr /pmy)7+ty- m r)xt 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 hig c,k qs/ln*5.( 6anuyeamzq+uh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chir 6ycl.um(n*e5 a/qu z+q,kas np is emitted?    m

The “alpenhorn” (Fig. 12 ghgnqa.o0in h(y3 +x:re*( qhf 6im7c–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 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 o*qghfm ri7 x0o h:ah+ nn(c63.( eiqygpen tube.

  Room acoustics for stereo l , fa:wju49ttgu52nas istening can be compromised by the presence of standing waves, whicht n:,u 52a9jw sf4agut can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, cqzd0bpr5k *49gx/ml 2 ca8twd oe 8lp(alled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked witdp l(eoz0*q9 dlmkc24ba pw r58x8g/th 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 thredqd j6m1)xb*e shold of hearing for the human ear at a frequency of about 1001 qx j6b)de*md0 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 grocqlo1m94xk4 4cyj2y 9bk9 cgr und hears the sonic boom 1.5 min after the plane passes directly overhead. What is 14kxc ym4qco4r92 jbcgy 99kl the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isvc u w-libukf+6l(jx,+: i.l f 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