What is the evidence that sound travels as a wa y8f sxzp6,o1qs0.twpve?

What is the evidence that s9hb 2 mqv-lw r67p3bi8un v7bxound is a form of energy?

Children sometimes pl8- saz 5qd8m5zf( ejajay with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sous-8qdjzjm 8fz5 5 aea(nd 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 wcghbxsy j-)f21a3 3oiu 8yz q+ater, do you expect the frequency or wavelength to changeyx)3jsio q3b-a2ugc + 8 yfhz1?

What evidence can yo+n kl5mif pw7 5nwfnjq9 p9,-ito6c8ru give that the speed of sound in air does not depend significantl w6 5i 9o 985nt7+ijcfm-k,fpqwp nlrny on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whyb szmjd9 vwyko8- 9q.dp7.ja3?

How will the air temperature in a2 (af; fmkgb2 fn7dx05q7smg d room affect the pitch of organ pipes?

Explain how a tube might be used as a 28j bxu2yutp jv b(v;4filter to reduce the amplitude of sounds in various frequency ranges. (An example is a2 j tb;8u(bjv ypuv42x car muffler.)

Why are the frets on a guitar (Fig. 12–30) spac*q/ 6(*lqrflveu xxl 3ed closer together as you move up the fingerboard toward the br( 6/ql*l3*fvxlr x equidge?

A noisy truck approaches you from behind aj5.t :hx8w8 7lxvqfj9n xj.yd building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brightx 87.9 : dfjtqx jxy5l8.hwjnver” — 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 “interference in space,” whereas beats cj :pz16 o6stcnan be said to be due to “interference in time.”c tz:jp1 66nos Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, w3jkn5;4k6eatgqy lgj;2(gb g ould the points D and C (where destructive and constructive interference occur) (g2t5y jnkgbqkgl a; e 6jg3;4move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wi glgzc9e16gm+jk04gh th 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 nokg46gh gem 19l+cz0jg t block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can v iwk f4exhvq(yw8g4) ::jw:f 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 a (gef8kvifvwh ::x wq4)jw4y:part? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directionrei on ,2;oae- 6t(clm, with the same velocity? Expmt,e ;larn( o2 ec6i-olain.

If a wind is blowing, will this alter the frequency of the sound heard by a ut3gl x uq- oj)shxp)1wu+/.b0(mm koperson at rest with respect to the source? Is the wavelength or velomo0bsl-u +.w)1m 3hup k)xxqtu(/ jogcity changed?

Figure 12–32 shows various positions of a c/la 8ve(ghoqv .(3w.2 eko mq.jr mc5child in motion on a swing. A monitor is blowing a whe5l . /c.mqa23r8wjqvo.omc(hkge v(istle 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 your reasoning.

  A hiker determines the length of a lake by listening ki b8az09zg3 m7no pb qb-(q6vfor the echo of her shout reflected by a cliff at the far end of the lake. S3m9zq0 nkpgboz6v8( ia7b-bqhe hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears t4 65+s w3v zuhryc7sqwhe 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 zc7ysu5 +w s4r3hwqv6significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aq qe4ha ry2i +o5wscm/ 8mpsann-q: 85ir 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 tunbd*q n 8-ui-fia:6m:7o rnr wgid::coa 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 backfir*qau :-f:b-n7gi8 :o:ncriodd6miw re is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the tom1 aj6h:25r4ug i1v8bkdguc s mo+ .rlp of a cliff. The splash it makes when striking the water below is heard 3.5 s later. Howldb6j akg 5 28v 4+ishro mc1:ugr.1mu high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr htrd8tgyajzt45) 8- oete pavement. A moment later two sounds are heard from the impact: adhyoz8t ) r5t 8jg4t-one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erryyr b+f:j::fa/lk - eior made over one mile of distance by the “5-second rule” for estimatinf+f k ey-ly:/i:baj: rg the distance from 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 pa w urabx ))us;*-qp 0tl1qnku8in level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whosupk.d74l/ q acl+ kfr5e intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of2d5zl3 h-jwrp 95 dB when fired simultaneously at a certain place, what will be the sound level if ondjpl- 3r5 wz2hly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nois /s)mc;ywnw :eibw29n* uolc6y jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this personwbcm /9lye : wn;sow)u*i6c2 n experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for 9 2cydjipz p+:a CD player it is 95 dB. What is the ratio of intensities of the signal anpci2j9y +:z dpd the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powewrz 5 gg*vrom-0xapc4( eau8q t :nagm; eq(+8r output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphert:roem (-v 4gz0 a8g+xe58 cqnaap*;umgrw(q e 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 st mojx.76jl5 *va/afbc rikes 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 )s/ier4;1xef adz zbiq. ss,;more modest amplifier B is rated at 40 W. (a) Estimate t;;zi 4ei ,qza1.fes)rsbsdx /he 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 pk 5; j7kurs 7xx(hk 3)f8bjdwplaced 2.8 m in front of a loudspeaker on the stag;rhkx7u5 bkj87x j)s( dwkf3p e.
(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 typicall fjd ixb*xlji.w 0 j-/xog)* j/o8)alwy detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whi ba)/ol*lxw wgjjjj )0o x*8f/.-idxose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (gke.tjm lw* -1a) by what factor will the intensity increase? Increase by a factlm1 *gje.t kw-or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equa fqzkr17mw-0 , rwzr;p1q l.dyl displacement amplitudes, but one has twice the frequency of the othrmw-0f 1q zzy1qr 7 .wpdr,kl;er. What is the ratio of their intensities?   

  What would be the sound level (in dB)l efs.wa;j9;(+ dp1c*b5rj8 exmir mt of a sound wave in air that corresponds to a displacel+*i5(sw. ;1xpdm ;8aecfr mbj9 jetr ment amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soundop2r l.3bd 8k60l(s/s9pyb gx c,o)xft tmp0s level to seem as loud as a 100-Hz tone that has a 50-dB souy9p06p.mrx(0 , g/s3o2p k8 flsx)blcbd tstond level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detec9tifdc; mgcr+ d2f +exm-+*fwt when the sound level is 3g+9 wid- +*tcexfm+mrfc;2 df0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the/4hadm06;- c.km urlg qvaw9n ratio of highest to lowest intensity at 4 ;-a/u9 d mhq0l.mvgr6acnkw
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fun1/,ix4tu2k-* xix2g cx vwer cdamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stringc1xc-kexu 2vgit4 xi* ,/ xwr2 be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fi6esbgmd sd*vu-10+m yrst three audible ovvbue1d0*ms+-ds y6mg ertones 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 top of an( c25 ;1czn6co 8 dtj7khgblvb empty soda bottle that is 18 cm deep, if you assuo6k8ngb7z5( b2dv hlt1 ccjc ;med 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 ptxs*u n8s)r1u1ycyp t)wk n5:ipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes )u)nk tc1ysy* 5w1p:nx s8 urtrequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its 2u -qftfrft dza o/231third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its oritf 2r/fzotq31fd2 au- ginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned tojsd/mut0cc ,c 7c6(gc play E above middle C (330 cd7 cs/cc6 utc0,(g jmHz).
(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 orgae5hmigc.v4 * f9flso9n pipe that emits middle C (262 Hz) when the s9l.e4vo5 igcff9m *htemperature 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 20 eb50(-b8mp oo afa-ot $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flu8id 7xc- ap6 svr:ps( 1gwopd/;wos0f te in Example 12–10 should the hole be that must be uncovered to play D aps(w dio17cgdswv o: ap/s;p r8f60-x bove 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 a u bqospkj78vfmm5)gcq*-./a t 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) S.pjamofkvu7c- )8m5*q g qbs /how 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 is open at both ends. It reson*vi x(a3mwq5 bfbd+*tz b1 t/ep: 6menates at two successive harmonics of frequ*b/m3+i x: p5fw(qtme6tad*ezn b1bvencies 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 1y r9(kb6jyku h, )hb64jg)d ljcel+y$^{\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 for a 2.14-m-long oy+y,zo(m .x0 i2ackoc rgan piyc+o(k2c.,azxmioy 0pe 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 ik4p3 y*j2ypzlbc0:z v s 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 information in the j 2yp c4 0*kzbpzyv:l3graph 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 adjustj;mi4;exh ne*(;xgb o4urg1z cj1, p w two strings, one of which is sounding 440 Hz. How far off in frequency is the othe(j,xnr 4go 4bp1x * j wzi;euchm;;1egr string? ±    Hz

  What is the beat frequmy (d a6azkt,+ency if middle 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, wyrog 7bf:6n kmjxgfx)8z+ b5i fas3*6 hile another (brand X) operates at an unknownf8 oangjx* 7 )b:f6isb6 gr5kx+myzf3 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 tuning fork an t;0zbgzy 9p38k5e* dwhf nh8aq)ba,zd 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain );95 wzbtp hdh k*0 qe,zga38fyzanb8your reasoning.    Hz

  Two violin strings are tuned to the 2:2v bgx+o dhjsame frequency, 294 Hz. The tension in one sd2ogj2v x:hb+ tring 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.]    Hz

  How many beats will be heard if two identical flutes each try *32sqi l,dyxxto play middle C (262 Hz), but one is at 5.0°C and the other at 2xdsy x 2i,lq*35.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B/raup yt22:c s, 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 aretu 2y/:2ras cp 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 standsr ur,dvk0 x-u; 3.00 m from one speaker and 3.50 m from trx k-v u,d0ur;he 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 supposy66av )d hor/wed 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 vibrating at 132 Hz, what must be the frequency of thah d6/ wy)6ovre 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 bex c5azr4p ok)2ats per second will be heard? (As )cr ap2zxk4o5sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15g2 24s5wo+jtb3p6 f;;gcntg k7 l krlk50 Hz when at rest. What frequency do you detect ptgjl b t7 4ckln+gf3k6 kog5;2 ;w2srif you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. W.wgoofb,v;y pkcx;17 hat frequency do you detect if a fire engine whose siren emits at 1550 Hz movesok1.xb7;p,fv ywgoc; 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 tow +v:jtg dr :jjw;pwd,-ard you at 15 m/s versus you moving towarddjwwd +j,:tr:pvg-;j it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the f5vq u52-uw/upy t8zf same single frequency horn. When one is at rest and the ot2 -y5q/8vtfu5zu fwu pher 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 ultrasonicnpml35xo4 ,d, 7mf wux sound waves at 50.0 kHz and receives them returned from an object moving directl4xw 5 x,um fm3lp,n7doy 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 flibqpaf ;; pdgw/h /ltc+-k2) i4 nog4mues, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. m agu+/;lip44to) hqg;pd- b/fnkc w2What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plah+s,j0u vg 12ik *s:zmv jnh(oyed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station.u(kso 0:i +g*j1svn mjz2hhv, 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 g5fke n n++o6twaves 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 arteries at 2 cm/s directly away from t f65engn+o+t khe sound source?   Hz

  The Doppler effect using ultrasonic waves of fre:l j)ry6 pdl2s c*y0pwquency $2.25 \times10^{ 6}$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 embzr, yp7jmkqoc19 3p) its sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hrqp 19 o jz3k,c)7mypbear 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 moeqjy5m4 r*s0 z1q*dzuving 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 is8:kgs; ham7 73i,k;sfwsdzg s 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mo 7z,: as;8k7siks;3 sf gdmwhgtion?    $^{\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 th8.30 uo lsopoxcu ;ka9e thin atmosphere of a planet where the speed of sound is only .8auokl3x 09cpuos;oabout 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 the svs--4oc vud+e hock wave angle it producev 4-e+ cdvosu-s
(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 lh b 6 pa2pscg+, ,5(teig9mbdrak26 p$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheadi 6p7jrs9a8zj and 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 distance of 2.0 km. See Fig. 12a98jrpi 7s jz6–34. 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)id;kwz94cs rp , gko5 sonar device that sends 20,000-Hz sound pulses downward from theg9skrwkzo4pc5 )id, ; bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audiblksmyq 84mlue qdxk18/ *1 c1gae range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonsh1v)bs.o xu4 y. It consists of many plastic pipes of various lengths, which are open ss4obvx .1 uh)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 threshold of ho4798xl r kh 0ex.jktb*ze i)iuman hearing (0 dB). What will be the sound level of 1000 su78kxe*jii0tzbe.o ) kxrlh 9 4ch mosquitoes?    dB

  What is the resultant sound l98u,m2uc qansewr- z) evel when an 82-dB sound and an 87-dB sound are heard simultaneousla2wu 8cs, e) mqnurz9-y?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i did*3jqh0t 6ss 105 dB. What is the acoustic power output (W) of the speaker, assumin*dj0hs3 q id6tg it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ou:qpnj* t-g-zv tput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What iz:jgvpt n*q- -s the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicii,eg (ol 6er+-zr4tvlrl ;/i ally wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jete iglit ;(l-liroe+v/r r, 4z6 airplane engine?    W

  In audio and communications systems, the gain +)t/hcdsooj6/:j b lq, $\beta$ 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 frequei z9w1dxmq sqj(ti056oufp* )ncy 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 fix+zshktm did)s2/ e3)ded points with a fundamental frequency3d)z) hides2stm+/ dk of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with cy vcq+x *g:q8wgc z/.uqc(p9 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 c* zvuq(p.9g w+c/8qxc cy: gqtuning fork when the distance from the 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 i lgxy2dy 5l f9rivu+ti65*x .hs near a tube that is open at one end ag iy52* 5h9+vt6 xl xyulrd.ifnd 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 observediryzn pbcm*/vz+l;qw ea200sy zp/:( 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 tone in the 500–1. vvgh./4 (arm-vb kfz7y9is c000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactlyh4v7c .9/a- sm.rfgbkiv(vzy 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 statij jvd+h/yi9 z va*/c7ronary. The conductor on the stationary train hears a 3.0-Hz beat frd7jih v9 v+yjc//*raz equency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it a9rku;n * 8fxkrah//( kg uah4bpproaches you is 538 Hz. After it passes you, its frequency is4 rgau9k8*/(rh; k ahf/ubnkx 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 justrw/q(ohjbvnm+s .0k,l2c w(c by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound +c, 2ws (hnvr.0bjlc(kwqom/ of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, so9) 5 u)*jkg9s.lrjy e3 giqsrnunding together, produce a beat frequency of 11 Hz. The shorter one is 2. r)jgnq .99essr*guk3 )y i5jl40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past ava9 rrh3ik;t / 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, ki9ar;hvr3 / t(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 aor2h5h-;t1g)qs.d d a0cltwpg bcgu92/k9 mnlo ta 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 from0hbca gw s-g2ml.tg 95khn )/;ddpq92tuclo 1 the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a morya, w5eozd maq5; - 9eezg67rth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave zqagr,er w-dm7;oz eey5965a reflects off the moth?    kHz

  A bat emits a series of hi9 hcb qwe*h54v q2+ndegh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns befhn4 b2q cdwv9ee*5+hq ore the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from onsrwtc7l q820hz +,/-e n , p3pqalhfxue Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frq3+qh,w20xz,l7spl c8enh-pft a/ urequency 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 c8an;zkguxi1b dxc6e4k* ; m ,i 3t)nwcompromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressurcx en81b6i x 3,;ndk i);m4zw*tkgcuae 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 “si f+mo;nm-y125nbvxwjnging rods,” involves a long, slender aluminum rod held in the hand near the rod’s mid1-oj2m w vfxynb ;5m+npoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a f(0(vhfvr dyt0 yv .q ej)+p-kkrequency of about r+th k)vkvfp0e dy.(y-j(v0q 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach ) dce-iecp29.x cnt 8( t/kope2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What kci )p tecepxdt-28co en/9 (.is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is u*x 9bi,m8rii 4gt7 zu/ w8c i /sbqlixc80d3e15 $^{\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