What is the evidence that sound travels as a wave?b nm1806pgoi/ rcph v2

What is the evidence that sound is abrqtr upr)3hle( +4+ z form of energy?

Children sometimes play with a homemade p-.lt uq+zav:qf(00*pr snnz“telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into :-us(apn0qpqr0f +lv.t* n zz one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expew 0c h9pf0j042cftcz ujws.9jct the frequency or wavet 2.00 40cpcswhf wcz9jujjf9length to change?

What evidence can you give that the speed of sound in air does not depend 15(bpzqx) ady significantly on frequency? apq(zd5x)1yb

The voice of a person who has inhab*xn yg5i,(flx;gd: 5mze a( j/tbv.lled helium sounds very high-pitched. Why?

How will the air temperature in a room afe(7mws9;r pk rfect the pitch of organ pipes?

Explain how a tube might be use8mh na5 o 7,oadvrj3t-d as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muao7hdv -3 8rntja m,o5ffler.)

Why are the frets on a gui*3v y2+u - 2)yaz rd 3lvl/ebbjz6yiiztar (Fig. 12–30) spaced closer together as you move up the fingerbobz+z-b ed/az22*) 33 ylvviuyjr yli6ard toward the bridge?

A noisy truck approachessl5kinr*dorp +7x6 v.rb 3x 0o you from behind a building. Initially you hear it but cannot see it. When it emerg.6rl+3i sorpkdb 5ov xnr0* x7es and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to sxv*v: l(k5 wd“interference in space,” whereas beats can be said to be due w(x*v: d5lskvto “interference in time.” Explain.

In Fig. 12–16, if the freqy 7m4i0 cscmpbyl, 2f*uency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togeyb0pf* cy,7mm2cl si4 ther?

Traditional methods of protecting the hearing of people who woao,9sp r: b8qfrk 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 toa :s,ofpq89br 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–* i+3 tq5.4 (jbalrtwdbhp ds031. 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 the two component frequencies farther apart? Explai5 wrb(t+0t*dbl shja i.4q p3dn.
(12-31)
(12-18)

Is there a Doppler shift if the source and o,.akeu it o va/:2opik8:hq1k bserver move in the same direction, with the same velocity?v /.u: 1ko 2qh:ikkitpa8ao,e Explain.

If a wind is blowing, will this alter the frequency of the soundlaxqg2n;ckea +fd..q+u k y9:)) yjwm heard by a person at rest with respect to the source? Is the wavelength or velocity ch k9qm+))d.ljan k ey gca w2.+xuy:f;qanged?

Figure 12–32 shows various positions of a child in motion on a swing. A 1-qc,.m nr 9rycp;lxvmonitor is blowing a whistle in front . lnrx yc 9,rpc1-;vqmof 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 lake by listening for the echo of yg + v60mcfgpcp/sm6+ her shout reflected bygmfcp0msc 6+yg6+v/ p a cliff at the far end of 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 of89 bi qdx 71gnc8 tuf0rz/f*uv his ship 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 s1qu/x guf90z*d n88ci 7rtbvf eawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtu2*z u24sg4axj tav2jxm ( 3oshs in air 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 kn**xtm r;sx l vnr9-:just above 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 bmvx9l *trnxkn :r ;*-sackfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top kxz r8 17nk+riof a cliff. The splash it makes when striking the water below is heard 3.5 s later. z1rr78 i kn+kxHow high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stri xmj1l/ss k4 nnn.j;5mke the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other inxmnmjsj;s l/ 4n 51.nk 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 y;c)nnl(egweiz3x)x1p ef 91 error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30fznw9)x enp1 );(x ely13eigc $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the fmdo1cp;0 n8tpain 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 a502rf(kdez(gx5ni y h sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prod3 b .,)qhnzdupwz9z -v2f f/hjuce a sound level of 95 dB when fired simultaneously at a wjn 9bfu pvzz 3zh.,/hf-qd)2certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four wr(18p o pe)nfmyx.eki2 n+qs/ u (f2sequally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if x+f n((2romk ypp/n s ew.2)qi f1u8sethe captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dBfa;4vabh s0a 6, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 54; 6 bsvh0afaa8 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powaz s o1ccv g-i)v0z(b/er output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over0vz1s ba( io)cgc/-v z 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 area i)tovq wfan 3:sjp+w:ajv ,p1. s $5 \times10^{ -5} m^2$ (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 more modest amplifier B focl0 :ui* c*kis rated at 40 W. (a) Estimate the sound level in decibels you would expect at a iocl0fkc* :u* 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 register/f4u9i +izg + dssrr(ied 130 dB when placed 2.8 m in front of a loudspeaker on the stage(/rfi+ 94gdu rs +isiz.
(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 differ g2k taft)kmd3xk*au,0p8n* rence in sound level of 2.0 dB. What is the ratio of the amplitudes of tnkpma 8t k*0 d)3*arkxgtuf2, wo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor willc1k( )2 gzzrdiy* yk-c the intensity increase? Increizzy(2-y1k k d)g crc*ase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tss;ten o :*/dnzw l4x*wice the frequency of the other. Wha/wn z*;to:se4sx* dl nt is the ratio of their intensities?   

  What would be the sound level (in dB) of sy1r+9 j 7lerja sound wave in air that corresponds to a displacement amplitude of vibrating ejjl9 rr1s+y7air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soundq4ke m.gm v)/k level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See F).kq gk mvem/4ig. 12–6.)    dB

What are the lowest and highest frequencies that an ab; 3z9 k*l/ngx2 / jqs0 pwp)sregi*dear can detect when the sound level is 30 dB? (See Fl*bjq ;nxips/r0)ag dez2* p /sg9w 3kig. 12–6.)

  Your auditory system can accommg1v:r 85r ztzeppgmxrs o)o 9s:hfbb0m 9h+06odate a huge range of sound levels. What is the ratio of highest to lowest intensity atxs1e b0f:ozp 9pt6z8 hggv rmr09sm ob5hr):+
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The-r1hq4rb:gt )(buhzqr) 9q bo length of the vibrating portion i 9bhu)1btrr -qh4 zqbr(og:q)s 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental andt7 h7y6e qrmb-ddc,q 3 first three audible overtones if thetc -mrd 3hey7q,6qdb7 pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across thc/ m; oud).adde top of an empty sodddu.d m/;co )aa 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 pipes spanning the ranw / ozlji,h ukxbpk/f;k ;.*i8ge of human hearing (20 Hz to 20 kHz), what woi; i k,//oul8hkw;x *bkzjfp. uld be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as rx/ed )u wh-sz/ly*,pi55aen its third harmonic. What will be its fundamen y/liz)ne s,wp-e/5au hr d5x*tal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p,bawjrmzmb-t 4h 5-1sd - 4cuslay E above middle C (330 Hz).14 -mw-5r u bbm-a4zh,ss tdcj
(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 Hzrhr m26c.bdi c2-/cg rc.je0 z9 q6nzg) when the temperatu.9/.2n cmgz-r gqj02r6zercd hcc6ibre 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 zmrpzb0p. kt je-.g u*x6u) ;v20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fl4srq kc0*ui tcp:41t u/wfv-kute in Example 12–10 should the hole be that must be uncovered to play D above middle C at/sc4-4puviqwc: r*tkfuk 10 t 294 Hz?    m

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

  A particular organ pipe can resonav wr7 .j3 r1kh(1qychate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thihh( a kr7jyvr1.3wcq1s 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 v2cyf jd.l1qk7f qm994rbme8 1.80 m long is open at both ends. It resonates at two successive harmonics of frequ 8yr.mv l b qqmce9f174fd2j9kencies 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 +o ) 1j lkt k):hcxrktz1n-n0z$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range forp+g u )by(:rqn a 2.14-m-long organ :gn)uq( y p+rbpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approp0ses ej*p ryx9xp54 *ximately 2.5 cm long. It is open 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 informatiop0e*4 *9jrex5ps pys xn 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 wanv)*m :vf8ux hen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the n*uv vmxa):f8other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) f90y,-qnmv swand $C^＃$ (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 at 3 9:iznizlwhgr 9z1g4 an zr9zl g3wig41 in9h:zunknown 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 brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tu3l4fg4*/ et: x uwcaalning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibratio*w:c/g3fal 4 x4ual tenal frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one63w s.,stvjn,ilbs ;l9 w aml6ka +a2r string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.] asl6tval+lka9sr6i sjww;, .2bn m 3,   Hz

  How many beats will be heard if two identical flutes ea) n(yejhv1ju+ ey-(o34umfy8ax x2n nch try to play middle C (262 Hz), but one is at 5.0°C and the ot8)evuyxfnn3+nomah( 2 xy-u( jy 4je1her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, zih tll-td(,37,ctqpgjtz 35A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded 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 ar, zq(h t5jtpclt- t,3 iz3ldg7e 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 3.00-2n rh( ablmh,0x l:is m from one speaker and 3.50 m frl0hrh2 mb,:xlan-i s(om the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hzdff/y u +3l1jjk.w.gp, but a piano tuner hears three beats every 2.0 s when thef1j+. g/dpuw k yljf3.y are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.733d twee,d 6aw7vg xxsyyg* hk80t3e4.gy (r c6 m in air. How many beats per second will be heard? (Assume y4tdx8y*kw3cdhrtey v( 0 g.gs3ex,w73 gae6T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when zm+,ebyd)cmh 6wa ),71ijthdat rest. What frequency do you detect if you move with a sb1 hid+my,)a m etcjz7h 6,)dwpeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still.qgo . zw:3y uz20g3xu7syy4:i(iwauq What frequency do you detect if a fire engine whose siren emits a(zxy4.3u 3u youzsa:q 0ggwq 27yiwi:t 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source 4pdies9mo) j /is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are ie/ sj d)po4m9the 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 the same single frequency horn. ik9qz0k,+xi3 tmd95f d ti9bz When one is at rest and the other is moving toward the first at 15 m/s the drive,tqiti59 09z3fbdk k+imx d z9r 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 0 8iinsmdf:cr18ls x6and receives them returned from an o8:f 1n0l 8smcirxisd6bject 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 gkhj4 wcl-g 3+h qp+ali( 0it,p6y dc+it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequencyh ka jc c 6i,hwip4lqgtgd+(-0py3++ l does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba mx6 nw40f9go xwas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railwx 40gm f6o9nxway 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 ultraso ph3uejjanhut)z--)/zu ., ozund waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound i zz,e-p.uh j /u-tz)) 3nuaojhn human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavmp91q3m04gxrgn v ,gmes 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 ofzrg p1p(r)w8q frequency 570 Hz. When the wind velocity is 12 m/s from the nor(wr) 8qrp1pgzth, 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 moving on laj4jew nvcz9o 5-:vpv*v-h wh- nd if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/sr l7)qlap9i+k (a) What is the ak +ipl)qr 9l7angle 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 d tcf:8m.qr/ vp0w ry/of a planet where the speed of sound is only about 3: t0 /q/dycmvr8fw p.r5 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 ocew8 ey;/m+ ai k1besme5y 8)pxian. Determine the shock wave angle it producem8ia)mb1e/8kwi +y5 ;e exsp ys
(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 q3jh;wqeb giilix8 gbs/;i,g- 0w(:g$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overi/6vvm2 . (m+sskyromhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time s+ysmi/ov6vm( 2kmr . 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 sonar device that sends 20,000-Hz sound pulses downwa h7mfij7+;qc6kb w( bnrd from the botb;fb+q nwj i7chk7m6 (tom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in +x0b ka;prq nt,8iqo: the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists2v vg.0 p)rxw8xi tu o639dldh of many plastic pipes of various lengthugotp rw98vxhdxi. v2306d )ls, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresh b44u/*wcvoe+zk hvd+pf ;r9fold of human hearing (0 dB). What will be the sound level of 1000 such mose ucdb/ kpf ;+zo*v4v w4+9rhfquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hesepz b70 4vkv3ard simultaneouev4s k 0p3z7bvsly?    dB

  The sound level 12.0 m from a b() szkt9b k6-6 lxypk5(adxdloudspeaker, placed in the open, is 105 dB. What is the acoustic p6 kl5 kt9(d-zxbk6ax)ps d(byower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W o2wggg 1m n:zyl;3 q4fxutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What if:g1 w;lm4y2zqxg3 ng s the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over the * 0nvk1pbt/neir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that /ktnpe0* bn 1vthe 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 communicatizntkm5e/ d .6v n/n6rgons 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 i;dz +-na6zcot c h9*r3k0pz dbs tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fbyw yj jrh;oe6y/y.)m+ih jr/bn+/u4 undamental frequency of 440 Hz and a mass per unit length yry4 /r/; bi6h+buy oe/j.y m hjjw)n+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/i1bxlpok*qw qcezyn o- lq3- 0y0m6/ 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 t qn-l byx6ozi1m cqle*3 /q-py ow0/k0o 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 is8zz89q,y)qn-xa pjl a 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 resoa8zl-nz jy 8q a,9pqx)nance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsdtt n0ph1dzsf6o1m,. rm e:5g erved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure eik ;s krz5ue6g7r2) z(6rjc dtone in the 500–1000-Hz range coming from two sources. The sound is loudeu5)kz7k drgji(2r6ese 6c r;z st at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is 0bk+rh 7 3au6h7pgdn gstationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appror76anb dhh pk+3u gg70aches. What is the speed of the moving train?   m/s

  The frequency of a stwnu2n+8s.jh p eam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast n ns wjp+.uh82was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate sjch5ne pt1),e8k0yk-lj y qz2v2yr+the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave jkcyty0er kh2 -yjesn8pz1+vl52),q (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.y9*oh aj7thxdt*:d2 e The shorter one is 2.40otya *:dh dh72*xetj9 m long. How long is the other?    m

Two loudspeakers are at sbt*r rp3yu*vf6ut6m;.) dc2hh l1rk opposite ends of a railroad car as it moves past a stationary o p)2ud rk.rt*bcu6s;hmhr3 6vf1y *ltbserver 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) 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 whaa6( 9;ybtgm;45 rvt*n xzyux ot beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bl59(4txryo;6mgxytv zu *;n abood 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 toward0/ckdlu.j z .pjakw4 byd7r,79kz.ml the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wha7.cwd7byd/l zj4mkk, ju9pa r.0.klzt 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 :+3 p;texvh i8sfwiqn 574k-w1kpxqx approaches a moth. The pulses are approx7 php e:wnq-1w8i+qxtix k5 vk43sf ;ximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to s74ynd85sx 6vrf c ziu;.d -cwnend 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 .yrdunf c-68;z54w x vnd s7cionly 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 listenigy1 xqi( jex9qw:b l -if3n5;zyb;kh5ng can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Conixykqe5xf-b 5bhi3j9zn y;w g(;ql:1sider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slen7y32nc(k bx0v fkz s4oder aluminum rod held in the hand near the rod’s midpoint. The rozf0(7oyx3vk c4 s nkb2d 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 thrjq3l0 x81 elizeshold of hearing for the human ear at a frequency of about j813zl0lxi eq1000 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 tzsg7t 0lcxi+bq/ 69bxhe ground hears the sonic boom 1.5 min after the c /s9ti+ z6blxqx 7gb0plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iz s4jk8,hu1ps s 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