What is the evidence that sound travels as a r9yfcz23ud7 7usu/ymwave?

What is the evidence that igqn+e4 ah*raia k6 b02;4fu lsound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string lr 0/edk9dpfun.z3y4to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sou0ku zpld fye.49/ n3rdnd 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 exwj*(t m /ls+-bdlk749 bcakbspect the frequency or wavelength t4btla/csm ksjd -b+l9( w7* bko change?

What evidence can you give that the speed of sound in air does n1h eo,ztks :z8ot depend significantly on freqoz,1kh8 t: zseuency?

The voice of a person wbrkq.e/ 0ww4loh/ ho0ho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room m kv*-tiqnd8,x8s+ n maffect the pitch of organ pipes?

Explain how a tube might be5 +f2b4vylb cz used as a filter to reduce the amplitude of sounds in varz4 bf2cvbly5+ious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mo2m m h(.4tj6 ixa;efjave up them4h( jai6faxmte2.j; fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but wk;4 i4v-. *65.xpib9n.vql sjomalo -w ixxf 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. [xvxw.sv54wbxl q.4*;6 .n ki -o lmj o9-piaifHint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spt1 qp/d *oiymd-td0ia9 c0x5sace,” whereas beats can b1ap0cdt ox*/5 q9d0ityds m -ie said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakw4 re p a-ije28ppjoo t**w80kers were lowered, would the points D and C (where destructive and constructive interference occur) move far8epwe2 ooji t- p84w*pa0*krj ther apart or closer together?

Traditional methods of protecting the hearing of people whoulajswe+xn+d/ yc))1 work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically,+ )n ec juxwd1sya/+)l 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 ind:2bny vr p)2g 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 theb:2y) drnpvg2 waves, (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 directdvgv/mj57i:l;k 6 rz*c( lyw qion, with the same velocity? Explain( ;cw mr/:vz* qk75ljgivly6d .

If a wind is blowing, wqmn/ sim;n 3p8 axdr8,ill this alter the frequency of the sound heard by a person at rest with res/mn8rpqx83 sna;d m,ipect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitoko c3 eiikxig*i34,d6 r 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 sound of the whistle? Explain your3c,* 6kkiio34xieig d reasoning.

  A hiker determines the length of a lake i/s h40 5cdzumvv89bsjo 9/ tdby listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the m 4vciov/shz85j9bds/ d9t0uecho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the6 d7q+ spegu1 ;+hankr 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 1560 m/s (Table 12–1) and does not vary significantly with depth. 7ugrpshae1+dn;6+q k   $ \times10^{ 3}$m

  (a) Calculate the wazjzo h6-ham2 5f: n6s9j6i gpqvelengths 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 jk6.uxe /:(sazcnf2 k sust above a school of tuna on a foggy day. Without warning, an engifsna(kk:2xs e 6u/.zcne backfire 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 makes when stqahif/iek c .0e*9gg zvv8j9 q).uq4zriking the water below is heard 3.5 s later*h k .80 qq agcvqeg)/u.feiijzvz 949. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stcer++pw g:k 8 ab7f1vkone strike the concrete 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 apart. How far away did the :+k8ra1v p+bcegf7kw impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the ( flr2tum3a1c“5-second rule” for estimating the distance from a lightning strike if the temperature(ucram1tlf 23 is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sounadw zl4th(3p-lbr1m4d at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leve81woe f9(pbjs l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producegqmn,0e fj 34d( olj 25i4f rqm5yytw4 a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intj3 i5o2yj4t4l r5q,wqf m 40fymgnde(ensities, not dB’s.]    dB

  A person standing a certain distancc j8v,ssl -8ic8pu vc zha7/0 bvph(1de from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain sh1il7c sv, dvbj8c c8a8p-vh/0 ushp (zut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said;dpvgnxdz4 c(*d pny.g5qr+z:3 slma 9i 5,ib to have a signal-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 background noise for each device? 58g ( 4;id3: i.ly nrz5 xp95*mq,csgadn+dvpbz dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound :n .e gyzt2w0ifrom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniforml2 :zewt0 yi.gny over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikp;grgjx e -9.eoar3 ,ces an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest cya5 /o:4icjln5s*dh amplifier B is rated at 40 W. (a) Estimat4c:oih/ ad*5s jln5 cye the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 mcryr, bozta i+px7)at-3 2zs, in front of a loudspeaker on the stagr, istra zxb-7a,t)3 c2 zoy+pe.
(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 differcpl+i6vi *m- qence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels - +qv6lipm *cidiffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what facto*,paa6 e: axjvr will the intensity increase? Increasx6p,e: aa*vja e 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 twice the fremv 2 rthhmxgfh4-.q sb520 a/vquevsrq fxvb2mh0 4m h 2.g-h5at/ncy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thatf0 yx 0,v16d nwwwgx*mwmn p15 corresponds to a displacement amplitudep0xwym , dw15 6x0nmv1wgn*fw 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 1u)2dtm n 2 vcii9ah*j200-Hz tone that has a 50-dB sound level?2ma)v2jdtc2 *i9unhi (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sou4.05c0d txk4yaytkwac,6tv j t er);d nd level is 30 dB? (See Fig. 12–ay ctk,twxya0j; 4 .0)r5dtcvek64td6.)

  Your auditory system can accommodate a wfpdjjp *bjz-8 m :/.ehuge range of sound levels. What is the ratio of highest to lowest jmj bj8pp-:ez*.w/ d fintensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has dun * ;r0mt.cia fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of *0. r;umt ndic0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the*0o h;dltsj+t/,ftyi fundamental and first three audible overtojl/ t;yt+fs d* itho0,nes 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 would you expect from blowing across the toi+)yh6w7sxs.x2 ozvjp of an empty soda bottle thaz)w xjhv .s76yxos2i+t 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 pt+8hk 008e+mpfzr :x ot +hvr6t0s6onrp3 dkdipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes rek + 0k0+pt3o rv drdm6zx:o fttnh8rsph608e+quired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hal*eap- d3)lzamffjsv r(: ,; bs a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% ofsll):*a - f;3(adrb v zfepjm, its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle Cm hf, mi6wx/v) (mhi,) vmx/ f6w330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) dwgu8s 59pwhrkj;0m tqa) :48xtv l3swhen the temperatur:5du)tx38 a8 jskqh0;tvrw4 lwgpms9e 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*cqoy wqt( c;e/4gm3 zmr n7c, 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 Examwqv* /lfeh1o6 ple 12–10 should the hole be that must be uncovered to play D above m/w elvf61q*hoiddle 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, 4zis4jn/ 73 -2 ldcchqb40 Hz, and 616 Hz, but not at any other frequencies is2q4 ccz-/ihl7nbj3 d n between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long :dv uv+01qqwuis open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 3qv 1qdvwu +u:030 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 8dx)cduccei./uc5pf r,6ow2k 5e d (p $^{\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 ad 6gjog2a/2va)ycm6f + fi1yc*ws:spresent within the audible range for a 2.14-m-long organ pipe 2 gi/+aa6fwvja2 c61s)*cy: dgoy smfat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lonfn/59 b3baa6ha -d zxkg. It is open to the outside and is closed at the other /d 936-5fkbhabn xaaz 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 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 str uq ..(62 qsl( rddmav7ehizz-ings, one of which is sounding 440 Hz. How far off in frequencqzsd(.uh dvia7 q2rlm(-z e6. y is the other string? ±    Hz

  What is the beat frequency if middlq/izo*m cov-/aa:9 m ee C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (bt b-q h2:ld/sjrand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of hd:b2- l/stqj 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 u*kse w 3lk..bsounded with a 350-Hz tuning fork and 9 beats/s when sounded wit buekwl*sk3 ..h a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hzvop7hwhketx2ngw/4m3 d1 8(c . The tension in one string is then decreased by 2.0%. What wt4 dpewok h3 2hwgn /71(cvxm8ill be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idend8zmu i/0-kz, cq0 foj 0js5ystical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other 8jiz5dscq,u o00m/ zkfjy0s -at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, imk)l h(6/ypijiq f1z*n 0wx)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(6) )lfiywnx k p*/h01jmzi qi together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speel6 h d*u;qc4paker and 3. *u;q4edp6clh 50 m from 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 Hz, but02- bp h/xgpctsma8 dj)m/y*7b 3o1aiv+si p r a piano tuner hears thbgv)ax+oip2h70t i a1sp *8yjm r/mcsp3d/b-ree beats every 2.0 s when they 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 xm7 ou jnq9+-uwavelengths 2.64 m and 2.76 m in air. How many beats per second mx j+7-ouq9unwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at rek)e,nb3:u il gst. What frequency do you detect if you move with a speed of 3kn e,g)b3 li:u0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stillfo2 q 5r g*/hpasds34c. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 oc2ss4 fa3q*hgp/5rd m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movi5* huvssk6h)n n1m6n gng toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they clo6sn1)6n*u mhngshk v5se? $f'_{source\,movine}$    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. When on ;+jsh6k zpxw-lef(t/ e is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 wejk; /pts6f(zl +xh-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 receives them reta 7iz2frscb+5:qc4mhurned from an object moving di:f5ibc q+4r2ca h7smzrectly 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, theix2l ; jn-uflvmt:3/-smc4eo bat emits an ultrasonic sound wave with frequency 2u: lxmei ot3/fsn-c-j ;v4l m30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a7 0arb6n1w lq9 xxugcfn;-3m voa ,3mg c3f/ur moving flat train car 0av9 fxmcqbf;3/g6uguc rrao,- 3n3wn71mlxat 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 train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to x-byp5bz p*)zqgx*a pvo;2 7o measure blood-flow speeds. Suppose t 2v gb p7bxp*zz a;*qoypxo)-5he 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 arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraseg:cqe amv39ah1ur r9hr; i0)onic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound ofxxig:0/ (eh pc frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers (gcpx/0e :xhi 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 mp31h t;:da(w48c ssrindzvp *oving 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 where the speed of sound is 310 m/s (a xur a or6c bsoe,4g3 *bln,(m)aj/9rk) What is ,j,ko4 e carrr)a(x6g/b sbl o*n3m u9the angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the n.x, odlks981 ;mbnf;tpl)l mthin atmosphere of a planet where the speed of sound is o;l 1k bm.sfl8tnx,)p9dln; monly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine theanw9t 3)(mw sm shock wave angle it produc9n wws)m3mta( es
(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 8 etv-nnr- kb 0oj,)ye$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 8xa n*gahe3.r1.5 km above the ground flying faster than the speed of sound. By the time you hear the son rn 3ga.eax8*hic 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 sonarg7+j5t-)kqce y,jtyn2 a)d ir 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 it5jt,d n c+ kjta)eyirq y)2-g7 is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are the trjzk2 t1, *r:hsk-(fyavuy7 re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer m4w3 7rp(wxeh jn(q9f pipe symphony. It consists of many plastic pipes of various lengths, which are openpxq9(j 4n(3m hw7fw re 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 aq/27( i9ivpez-d x+oud br*vw sound close to the threshold of human hearing (0 dB). What will be thei7/x2(dq irv9vdewbo z+-p*u sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound :1 2wa(z0o6b us a3irefe4*cv vmfu; wand an 87-dB sound are hear fvu;z(ea1uc *mb0 3 w4fowvear2i:6s d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dBmcg,m-yl . w2t. What is the acoustic power output (W) of the speaker, assuming it radiates equally c2wtml,g y-.min all directions?    W

  A stereo amplifier is ra 3ezgxk4 5hvvs .b- lng -pc,-rs9zy(xted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powy.-ezg (z9 scvvx4 br,h5s3l-p ngx-ker output in watts at 15 kHz?    dB

  Workers around jet aircraft typd7r9ibrs0o 2e ically wear protective devices over their ears. Assume o092ies 7 rrdbthat the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, tv9)xzemk544f. lziih he 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 t:va jtcna4-+ 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 longg: a5l0n:b ulr between fixed points with a fundamental frequency of 4rnbgal:05 :lu40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set inx0okv gbnh458ekibd18c) 27 na0yf bzto vibration 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 agaikb1gayehcn)v0bd5 z7 2 i80 onfk 84bxn at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of m3wku+f;msm l)e(+fp:/+mis e gr8 axo ass 2.10 g is near a tube that is open at one end and also 75 cikomgsxflmu:+(rs) /ae+38+e p wfm; m 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 reson1fi0 vk2z -ueuate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in 4q(pf) z(8 8lvkybbfx6m8c/ ex:him u the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, tq:fmhlb uc8m8b(pyez( vxxk f4)/8i 6 he 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 axwb0 n3q -jd8train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spew-8j b3qa0xdned of the moving train?   m/s

  The frequency of a steam train whistle as it approach ,,if70x xhgdjes you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assumd7, g, xx0fihje constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by qqjq: avg7wvk8me m:2;a(5yxlistening 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 (frequency halved) as it goes by on eqaa 7j82(v :;: mxg5qqwkvmythe straightaway. How fast is it going?    m/s

  Two open organ pipes, soundi41o* oylm gwhwr,1h(a6a wf o6ng together, produce a beat frequency of 11 Hz. The shorter one is 2.wryh(om flaw ooa 4,*6h16gw140 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rai*c 73 ixop9o,xrjb h9xlroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the oxhipbxx9r 7,3jco 9*speakers after they have passed him, at C?

  If the velocity of blooyy,wo f h/6rhedk/iihg+ .3e7d flow in the 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? Assum/ei dgwy/ , hh.fiohk6+rye3 7e 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 isxzq8.f0rpcnv*-cfi g wc ,m 2(a +ycg/ flying toward the bat at speed 5 m/s The bat emits a sound wavx0yfmn( +c-8w *frq2 ,ac/g cc.zipgv e of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it app q3gjfr9l2(.m xanjw0roaches 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 afn w0r3mqjg.l9j 2 x(the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to s / 3lbf cs*od-oma-ueo/(u d v.t,2ixrend 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 3i2- uc/sof .xtvbro- a*(d/uo ,l emdG flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presencrhgpzo cukc.osi 0d:6/)zh7 ogli v9o2x;).x e of standing waves, wogz0 ciu;hvo2r:x.9l 7 z)6.soiogdhk)p/c x hich 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, called “singing rods,” in8h-+yz ld*r nvocki;v1* o dp7volves a long, slender aluminum rod held in thekdvv ;r ho*c7yi*zn8l d+-1po hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing forpp;jt9oc2 q9p the human ear at a frequency of about 1000 Hz 9jt;pqpo92c p 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 grouy, coegngf2a 74)nm,v85 mjmond hears the sonic boom 1.5 min after thm5myf,7 g 8)2agnve4j ncmo,oe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 6g( sspdffl p0a-0/zc78jnr g15 $^{\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