What is the evidence that sound travels as a wavk9s49 fsb uro4n7cf ah4e6k(be?

What is the evidence that sound is a form of0qpxda :dn.uhx9 m+5m4+dki p energy?

Children sometimes play with a homs1kp o tua).-pemade “telephone” by attaching a string to the.okpapu st )-1 bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air intol*xbe/n. kx0 i water, do you expect the frequency or wavex/ inx e*.0klblength to change?

What evidence can you give th2 y (erxhu-5r-f4sp 1 dovbx0iat the speed of sound in air does not depend significantly on frequencyei5u r(2x10r p4hoxyb dv- f-s?

The voice of a person who has inh(se 22ts.tz64 zvlk9cyav t5xaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgwb0jk2*p 8w yz1uw4vman pipes?

Explain how a tube might be used as a filter to redu sp wg6*;hemu+ce the amplitude of sounds in various frequency ranges. (An example isupe* sm;g hw+6 a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaceddfv: ,2e9xsq b closer together as you move up the fingerboard toward the bri9,b v q:d2sfexdge?

A noisy truck approaches you frolnz7mb 8bi /3om 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-frequency noise. Explain. [Hint: See Section 11–15 on di3 7 olmnzi/8bbffraction.]

Standing waves can be said to be due to “interference in space,” whereas n t+;:c;+.3 jyzg:xkouoie hrbeats can be said to be due to “intg3;+j n c::oikoxzh e;+r .utyerference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the y:)cxzyz pik6l .s ;t:points D and C (where destructive and constructive interference occur) move farther apart or closerzsi.) yxyzc:kp6;tl : together?

Traditional methods of protecting the hearing of people whvr;2kl tt -jp6o work in areas with very high noise levels have consisted matrjl6vpt;- 2 kinly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves sjx zo pg69(:a )n*tryi)btw)gs*4bu 5s keli*hown in 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 wotpg insbwl*t*) zs)j9 ) yx(5ebig6k4u:* r aaves, (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 move in the same directioq ,h;+b9adf:yp x-utxun0/h an, with a,yth :xp/ub9-d;fu+0ah x nqthe same velocity? Explain.

If a wind is blowing, will this alter the frequency of th(y0 vuh,p sobm q0/.lve sound heard by a person at rest with respect to the source? Is the wavelength or velocity / y (h qm.vsuvb0l,p0ochanged?

Figure 12–32 shows various positions of a child in mdki egn ,*9 yyt 3sfyj+t89ah,otion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the souef*9+tdt,kyg 3s8,i9 h ayyn jnd of the whistle? Explain your reasoning.

  A hiker determines t :dkz)u c3i3l.bt(dto he length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hear)lbo t .3duizkcd3t:(s the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his s2.dutn vqv ti:4-o i7jhip just below the waterline. He hears the echo of the sound reflected from the ocean floor directly beloji.dvo42qt7nvt ui :- w 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthh.1mo9 y fnop5*(pib ds 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 just above a school of tuna on a foggy day.v-,vjy- b0aae Without warning, an engine back-j vaba0- ,vyefire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it make1yb7b.0h -kmz,nilv ws when striking the water below is heard 3.5 s later. How high is the cliffz7yvn. l ikb0w1h -m,b?    m

  A person, with his ear to the ground, sees a huge stone strike the concrvdnarv fy9- 6x 92o8tlete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apartfa8vl-2 ovyn drxt969. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second ruigbwns(0( p kh /3bx3o)(mjsele” for estimating the distance from e njhg 33o(pm(/w(b sk0xsib)a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 0 heq s79ev-yo120 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 soundh-n6)6*gm69kr gfop t9m lakd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lev x9dwrwxd/frkad2 0,0 c9 ioyo*o02syel of 95 dB when fired simultaneously at a certain0axr os0/yr fwd xi0do2k*ow9cd2,9y place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certais9p8 mrs8y9 gfn distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 12y99mf8gpr8 ss0 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 saidc7ju0vg4r k +r(v: x e*l9nplp5:zzir to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is jzk n7gr+ (*zp9le:x4 r5vu0ipcrl:v95 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 om;zreqk 27vq8 w l)v7mf sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sph27) rqzkwm;m evvl87qere 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 w*phe l .pw.s7uhose 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, while the more modest ampliflwmqy zc67 s96owrk+o:4sr 4uier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker col96 r qk47su 4y+ww6os r:mzconnected 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 placedkopo/m:3z2f r 2.8 m in front of a loudspeaker on the stage. rfmop zo3k2/ :
(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 typ:ctdl i6pm852h ih4 gfenbc69a( ;qe dically detect a difference in sound level of 2.0 dB. What is the ratio of the ampl6pd:h4c 69it em qadcg5i; fbn8l(2eh itudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound waixtvh, .caw6d2p2nxlu.1 x( cve is tripled, (a) by what factor will the intensity increase? I1 t2. 2ccidvx. n6xh, xpwula(ncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplituded 11*p wbr. vt4xa4exss, but one has twice the frequency of the other. What is the ratio of s 4x41 er .t1pdvxabw*their intensities?   

  What would be the sound l 7deg bo7fwp n,3fy.5cevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules y7ne.fpo5wg 7f c3 ,dbof 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that hvu,*3fdk w :z l70hikhas a 50-dB sound w,d:hu*fzk7 l3v 0ikhlevel? (See Fig. 12–6.)    dB

What are the lowest and highesg(mnimh). s5 g ho cnsc1y*d*3t frequencies that an ear can detect when the sound level is 30 dhgn*chgm *5i.s s (n1my cd3)oB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range o3byec,ln gky hz96 :d2f sound levels. What is the ratio of highest to lowest intensity at z32ykg9cedh6:y n lb,
(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 frequwum um3kdm *io(g 1o*)ency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g.)(mo * dk*u oimu31mgw Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are be8g 8e3vjfn9the fundamental and first three audible overtones if the pipe i8 3e9g f8vejbns
(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 wouloh :sr3 lbecs4mi -e5m)x9xa7 d you expect from blowing across the top of an empty sodi7 )mrc x 3:9a helox-45mbessa 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 w592ofhws** rchfh51 chrty ;pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes req y;5rf *2rsht5howh*f w hc9c1uired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frp*oqt2p0k 5 qwequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origpt5qq 0wo*p k2inal length?   Hz

  An unfingered guitar string is 0.73 m lo*) bpm+5fd up(/l3 r5qbzcahang and is tuned to play E above middle C (3 d5hp/clam)(fup az 3rb+q*5b30 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 tok; lh* *;lsxahat emits middle C (262 Hz) when the teml*la*;x oh;k sperature 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;pzh 4 ,g1vop 6w mrtv.oc.tt2 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the c)2e* a n 42qfw5wzwnshole be that must be uncovered to*w cw 22senaq5)4wfnz 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 pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, buj u ;)-v 22npexsuxx;yq2 qo7st not at any other frequencies in between. (a) Show why this is an open or a closed pipeyu; qj 7qxs ns2 ;o)x2eu2pvx-. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at tw hp1 us6qi) c+)wts3smo successive harmt)pi631qc + wmh)suss onics 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 j(2q*y1fj zht /k,mpj*cix 1k$^{\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 w5h ;5rxqk* lkkithin the audible range for a 2.14-m-long organ pipekq;lk h 5xkr*5 at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside a.lz2;- yopa9 i tecpr q,8uh;:l1cct knd is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves i-1ce:, l;czpytqc;h 9l p8.2 raki tuon the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strin)clg4 e8+gtvl /xl k3jgs, one of which is sounding 440 Hz. How far off in frequency is gl+4lt 3v/gcl e) k8xjthe other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andlel gdk ;/r/f4ff38g+mwi xu/ $C^＃$ (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)61 cxqboo:co f;-d+bg operates 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 operatoo fxcc-1g b d+6;bq:oing frequency of brand X.    kHz

  A guitar string produces 4 beats/s( +olpc1bhwi4co 8 ebrq, nesc,4 ,9fd when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibre4h ,l , fb io1pcc8erqbc(ds+ow,9 4national frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in ons fh5i-,jt o5u+ od*b6ax4xro e string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hin ros6 uhb,f+tdj45-*oxxao 5it: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicvn+8,*uo rww7 k+yrckal flutes each try to play middle C (262 Hz), but one is at 5.0+n * rk8,uokwrc7y+wv°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fokm ds8/i)lvl: rks, A, 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 whenkls 8mi/)vld: 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 smpx7 *kj6nl l+peaker and 3.50 m from the kp7l jl6n* +xmother.
(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 suppop(* chf7lnpwi l k4h5h i*59wnsed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrhh5nc *4 i5p w(lnkpilh7*9fwating 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 2.76 m in air. How many beats wgr;b;p-0 bd2g m xtm:per second will be heard? (Assume Tmrt;: 2bmgdb wp;0- gx = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginn8q;0 9adw q oc4tj8rb nv51uie’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a ; 9niao41rcw 0vun8t 8bjqd5qspeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Whnk1t h3e:z)apwr v ow7ia66, vw:hp;vat frequency do you detect if a fire engine whose siren emits at 1550 Hz mop6teo 36h,:n1vvwi ;w h)zaap7rwk:v ves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at va,)z5gtgcj of:3 y,x 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the 3y, zago:cvxg),jf5 t 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 singlemwbmw4rt )h4e illv/ r.7 5s9t frequency horn. When one is atm v4/iw r9tl sb7t. rmel54)wh rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rg6bqclr jcj + 2,6*peaeceives them returned from an object moving directly away from it at 25 m/s What6 jgal rp+b26 ejqc,c* 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 ultrm)t4s, by4y giz0:iep asonic sound wave with frequency 30.0 kHz. What f :)i,m 4ze0st4y gbpyirequency 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 t oc n-w)mgo3i;rain car at a frequency of 75 Hz, and a second identical tuba pla;-nomg 3 )ocwiyed the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ult*g2nwum*03zxqf,-cf pa , lfvrasound waves to 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 expected beat frequency if blood is flowing in large leg m,u 0 *fnpc v -zfwfgl2qa*,3xarteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency y7zixw q5nqouv 5p5 s/ .zp 1,:9zqexo$2.25 \times10^{ 6}$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 vp-m 1wo9b3sm y/s/ tgielocity is 12 m/s from the north, what freques3 g/91 obp m-m/tyiswncy 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 land if its zw;u(0 8ufefpfg.u e-boy(*lot/ qd3speed 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 the6avc rmzt7 q56 speed of sound is 310 m/s (a) What is the angle the shock wave vaqz r765cm6tmakes 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 a planet where the speenqfvk;kf jqukp;8ozv ;5t;;*d of sound is kvq;*;f8nju;z;t; 5povqkf konly 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. Dx6h0s l9y cic b g.j;vw),gtu*-;sskoqp 3wl 2etermine the shock wave angle it;vibs;sogsj lkqhy9*l c 3 p62u,0ww-c.t) xg 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 pljgsboj5 gt 47v+:p*f+ 1win$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead ol 0f :qh0:yhsxql 1.jand see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal dilh qxqsf:l.0 1 h0:yjostance 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 dw 6rfz wdv2d9rjb(+ v2w;9gl levice 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 designedwvgz9226+; vw9l r f(bwdlr dj to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the h-2 ze;viks- eguman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displaygf +juu39q)mq called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whijm9u+u3)qgf qch 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 sourhm3t8dw2w0e nd close to the threshold of human hearing (0 dB). W8te 20w 3hrwdmhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sowy9 a3qi;00:akpemzjuev 1h4(n mg k9und level when an 82-dB sound and an 87-dB sound are heard simultaneouslazm; h9i19uk em0:ynkaq0pv(ejg 3 4wy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 a1+v2fst4bct dB. What is the acoustic power output (W) of the speaker, assc tbav st41f+2uming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W o: gzb:okxcp c*5p 6r4rutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output c:zpo 6:cpr kb5xg* 4rin watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their-/ enifzm-eh f8)2ixzd ja28e 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 e2 e ai-/f z 2m)xe-88djnhfizhas 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 communicatio h7nk ; ckdms hww7ls.br c0a6;(kws.0ns 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 freque1; 8z+lxfy3wsrnjg 9n8o d2dwncy 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 fundamewm n5q*,dwlt7/hzqw +ntal frequency of 440 Hz and a mass per unit lendmwh 5 wtlqzq *w7/+,ngth 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 y5x1wp qwbk-px8z(9svibration 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 thwqywz xp 18 xk(-bps95e tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is ,d7g 1d5n6 itaw8r3th cm co6bnear a tube that is open at one end and 3 bgdc1dm,86ttownac i56r7 h also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one qiqr nfa615 v.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 coming from two sourc.w cwp8(diqx+ es. The sound is loudest at points equidistant from the two sources. To determinc(xdi qww8+.p e 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 whistla5 pv5kuu , ,uy3ryew/es. One train is stationary. The conductor on the station va5k,pwy5uyu 3e/u r,ary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 53cp a+* zckkobe-ty1228 Hz. After it passe122kkc* +ay-pbtocz es you, 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 the2u1:d ui rlheq 0g-io+ difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a cer-0u1gdl 2he:qioiur + tain 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, proi/ jtprt3ptn0n*b + sxl/p2c,duce a beat frequency of 11 Hz. The shortec0 sp/2i tx/*tnp+nl p3 trbj,r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mo8.fjho 2xnoqa uv4 g39ves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after4jfh2 gaqno 3v9x o8.u they have passed him, at C?

  If the velocity of blood flow in j2x6-qk lfi 3xv(bj5*hkr /qwthe aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assw3jiv5f26xb k(-/hx ql j*q rkume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mothnfpd 6:r3hk.3bp2j)(qn 5weg-j*eb opfv +s n at speed 6.5 m/s while the moth is flying toward the bat at shq3p+eswbg52f)p* j o dp :b3ern-f. (6v jknnpeed 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 highx-):(t nt gbvs 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 (:st vgx )b-tnchirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine v -59bsl.,mri*c rgc pbillage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to cr-l9m 5 rrbsb ci*c,p.geate deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can 9m.l72scgw2 znv u(j4vzv:i tbe compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressurv9zmg7w:ncts(uzv v . jl 2i24e 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 demonstratg3iaj3g r(q0w fi- :mnion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little pa0q-wg ijf3i :mn 3g(rractice, 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 0 otmp,r 4or+hthreshold of hearing for the human ear at a frequency of about 1000 Hz ispr0r4oot +,mh $I_0$ = $1 \times10^{12 } W / m^2$ 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 soikhtv) pn,23+d82le 1j ie dzwnic boom 1.5 min after thih+z ,2 13wtepdjnldv8k )e i2e plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 +-*x gql0jdkc $^{\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