What is the evidence that sound travels as a )zzzk75 .giaf-jktn cq+91a awave?

What is the evidence that p 5ad ;kb0ad8kwe7vpubt l;nkq/ )d3wb)kp96sound is a form of energy?

Children sometimes play wipsg m uy uf7sb1ils 4i4l496m2th 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 sound can be heard at the othiy2 414794 sum gfbsm6ispllu er cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air intofuy l6 f*qa54aojf(5d water, do you expect the frequency or wavelength to changufa(*f 5l fa dqjyo645e?

What evidence can you give that the speed of lk3 pkzc(/7kgiw;8 3aigcgk) sound in air does not depend significantly on frequekc i/k)8z3 k3ikl(gga ;g 7cwpncy?

The voice of a person who has inhaled heli +ch juy ocgpg* 7(*c.w:gw9poum sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch ob4abe)9y6 1t ju *p.z2r oyfzaf organ pipes?

Explain how a tube might be used as a filter to reduce the ly e/ak7f65hramplitude of sounds in various frequency ranges. (An example is a car6l/hr7efy a5 k muffler.)

Why are the frets on a dmxpk, 2xk+k.tnn .4oguitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge? 2tn.km.no+x kx,d4 pk

A noisy truck approaches 1k6ulup( +/k dfutkjv-y z) -f5wjmc8you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sok-f1)yfju5-8 pmlu+ k dvwzt(ku 6 cj/und is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas be3s94kt (xly lkww8d) jch -(unif9c3aats can be said nw8c ajl(wlxus fkyc h)33i(9d94 k-tto be due to “interference in time.” Explain.

In Fig. 12–16, if the frequenxlmu2u:dmy u(tn+l6egqa 68+e+3tfp5 dl d(xcy of the speakers were lowered, would the points D and C (where destructe :5y+ndf+23+dxme d6p gt(aum6llu tx qu(l8ive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work 95so l xd-h:i-kj4umg 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,xd hiuj4 os 5k:-gl-m9 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 be thought of as a suu 39a;wc.zboc l8m- jbperposition of two sound waves with slightly different frequencblc9jc; ba8 u-ow3. zmies, as in Fig. 12–18. In which of the 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 mo8mzsxc0) (r *q(hkou pve in the same direction, with the s 8cxkz u0*m(rqpo)(shame velocity? Explain.

If a wind is blowing, will this alter the frequency of hbxr2mm 3+5juthe sound heard by a person ub 2 xr+m3mj5hat rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positionz-p.g1cfssok 9nk 4xl 2)u b*vs of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle 2skcpg1fnolk xz-.u4 v)*bs9? Explain your reasoning.

  A hiker determines the length of a lake by listening for gze)y71hknas ,: wl4hthe echo of her shout reflected by a cliff at the far end of the lake. She hears t al wyzg4k)n17s,heh:he echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship 97r pbs (ffakj,j;h9a7 r*lzp just below the waterline. He hears the echo of the sound reflected from the ocean floor dira7pj(skfl f,pr7*r j9a hz9;b ectly 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.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 :n2e hlj;vo9uek7+rc $^{\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 oi ntx8 )f dx,1m.8issof tuna on a foggy day. Without warning, an en sftd88,xs i).mn xi1ogine 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 sd u(j t+k1mkr1j 4;si. osr/lnplash it makes when striking the water below is heard 3.5 s later. How high is the cli/(4l1ur;sk j ido+jkm n1ts.r ff?    m

  A person, with his ear to the ground, sees a huge sonlcg b-wd8f3 8wy5vs6ne: *xw5/bbi tone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the oth 3lc5s: ownxwfni/6*y5bbbvd wg8-e 8er in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one milezbom kv-tl 8+bft0n)( of distance by the “5-second rule” for estimating the distance from a lightning strimv(-) 8lb ztf+bton0kke if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ofm )obz)v j ljiek9(n:;n7o k+l a sound 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 level of a sound whose intens j7hdg lva0 ).mbp0jf, w7gurr d.2hh*ity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firm 6 .rvp;/lvooed simultaneously at a certain place, what will be the sound level if o v o;m.pl/r6ovnly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distn;vmya( ,y 5qxg7r(clance from an airplane with four equally noisy jet engines is experiencgvqxc (n;yy5 ,marl(7 ing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noishj(s;dxr 4*i kt ;o9ile 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 okl 4 d;t9si(xh;ij *rdevice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spe c14u 2tqedk0q04b,1rzuvs gcaking in normal conversavg10q 0bdku q1rc u 4z4es2c,ttion. Use Table 12–2. Assume the sound spreads roughly uniformly 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 strikes an eardrum whose arwpf *i5 t hsd)k74jv5hea 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 flj3q-3i7 90)a-b lpcrsl99 aahygs i, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspe9fybral l3ca7-ih a39l) q- isjgp0s9aker 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 whe1d1z5 0ph3mh onx5tdz(oy v*a n placed 2.8 m in front of a loudspeaker on the stage. hy3ma z0ph* v11t5o5ddzx no(
(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 difference in sound lev0fz lb29r tylwrx(4r8y * m c3.madqo1el of 2.0 dB. What is tr 9.(drqx 3by80l1a *fw romctlm zy24he ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound w (wulrn3u8fdw :1 gak(ave is tripled, (a) by what factor will the intensity increase? Increase by a factor:ld1g8w (nfk( wa3uru of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacelj9xbso v44g/glh0+ 4t hnct1ment amplitudes, but one has twice the frequency of the other. What i 1 g o/nth4gxj+htl9l bs0vc44s the ratio of their intensities?   

  What would be the sound level (in dB) of zjx6 oz7w-sp7wt*,t3zn,cg9 pv(ig ts5jcq /a sound wave in air that corresponds to a displacement amplitude of vibrating ai 6tn9,cjq ggswivzo *c / 7t ,3-5p(jwspx7ztzr molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz zqf(v(r;zso 7 tone that has a 5f vz(q (so7;zr0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest ri9mhf,80b 1weg a5ftand highest frequencies that an ear can detect when the sound level is 30 d5 gf,mte bw air81fh90B? (See Fig. 12–6.)

  Your auditory system can accommodate arxp + a,.kv/g+t(tomi huge range of sound levels. What is the ratio of highest to lowestkt x/+,pt(vmoi ra.+ g intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 44sksp 2p9g vy( 8tbvc+0axr7 j b94(rxa0 Hz. The length of the vibrating portion is 3x809rsvpsrx+j 7a(a pg2v4bct( ky9b 2 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What ai 0jf+0cs5ca sre the fundamental and first three audible overtones if the p5i+ ss0 jfac0cipe 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 acrosf;(z rlb)v 7gge )j4uzs the top of an empty soda bottle that is4ge)z7;frblj u( zg )v 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes hb, k*ddyclc6,q*ol2spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the length qclhd * *cl2d6b,yok,s of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wha39j/k pa z)0 +8igzhu0c wz1 3)csoeow-wduv lt will bez )zas/d-o31+zwoh3 kl c )u8wc9je u0wip0gv its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above m )rg5 fhz-ci)pbyvlg (,ak2y /ijoq+v( au.2xiddle C (330 Hby-v.2cjrio()/flap a v , i(zk2g+x )hu y5gqz).
(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 pipez *hefssbppt)6.o v (6 that emits middle C (262 Hz) when the t spv*h 6b)t.p(szfeo6 emperature 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 ef)daz ,09 xp5+l famuat 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 3n rz7tbn 8:,b yppr4nhole be that must be up,z7r8tnb4n:ry n3 pb ncovered to 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 r1m9p u9g( ,s (ppr fc j0/uha6l0/fxwqe+qnycesonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequen0w 9xm9a f0+e6jnc ypp hgl u1((/ ufqc,/psrqcies in 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 is open at both ends. It resow l4 7if x57termdu-.onates at two successive harmonlr4m-5uoiwtf 7 e .7xdics 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 lrfeu+1 7 x61hilk le;$^{\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 m el4a bl9ax(:;vli(ka 2.14-m-long organ pike abvml((;a4xl9i:l pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximate*1mclv qjl07; l7 d+qdda u-fwly 2.5 cm long. It is open to the outside and is closed at the other end by the e*llfjq;+d1c-a7 dq lu07dm vw ardrum. 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 adj l;m mc.f4ac;just two strings, one of which is sounding 440 Hz. How far off in frequencymc4l.;aj; fm c is the other string? ±    Hz

  What is the beat frequency if mm7fxu4)uoc / kiddle 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, whilx*e rr:ej )h zy8gv:q(e another (brand X) operates at an unknown fre*r he8y r:jqz:)ex(vgquency. 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 fin-i e f.zf-3fc2x, kgork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your riie-x,z2 gf. kn3 f-fceasoning.    Hz

  Two violin strings are tuned to the same freqa4g7- aorsb- ze.;ty e0jsbs1uency, 294 Hz. The tension in one string is then decreased by 2.0%. What wr bsaoa;jz. 1-4-bgs 0e7st yeill 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 ident r9xf7amytiyw5gm,5ny fa 1)2ical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at w) fm5ga2ym7ny 95 1yiaxrt f,25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; g)q dmmh) 59ezqat)k,m p r-4rwhen A and B are sounded together, a beat frequency of 3 Hz is heard. When)) at-)mr9pqhz5 rg,kmdm4 qe B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C 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 speaker y; hf:8np n 4thf8,kh: kynah0and 3.50 m from thehnf k:0yhy8 ;n8 4ah,fk tpn:h 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, but a piano tuner hetvx )jliz7-31 p cf3yn7n gv;hk90rqgars three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be tny737l1hv09 tp3 gviz q-fkjn cg)x;r he 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 beatzy 56v zb98aaubeg6 7kia-q 3os per second will be heard? (Assume Tzgb z7u583 6kq-yaav ae6ib9o = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1wcj6d(p q ict-8ha)h0+5e jzx550 Hz when at rest. What frequency do you detect if you move with a speed of 3e8 (-diwc x)qa6c j+thj5p0hz0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still.u)ksa1j*tj )ii/ 5n 9eoi2 lfr What frequency do you detect if a fire engine whose siren e9jn)i/uias e1t )5r* fjikol2mits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifta u c cvcz*1pvkx/v98* in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencz c1vk pac9 /*vu8c*vxies 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 efd0xzd4-2czp 5w 3sb;rqoss1g9 /9awayrc; rquipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the dr -z1fgyd q2a3apzd ;94cx rwrso0 r/scb9 5sw;iver 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 receives them z-jb.lba qm.2returned from an object moving directly away from it at 25 m/s What is the receivem-. a.j bl2bqzd sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall doj+++ 9 k3vpnubvtb)at a speed of 5 m/s As it flies, the bat emits an ultrasonic s3 ++)d9vnt kbupjv+obound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experim7r60 28vgn7fplb i c2dl,+uylpes;usents, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was hearup+ piy;eln7gfcd0 62,2ss 7b rl8uv ld if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure *7d+ nxi,osdeblood-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 sexn7*,d o+id is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultralq)lht 3d82)d l jb,nmsonic 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 x-uqacvj(rk(244x yxof frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear u-acyqk42( (rj4xx v xwho 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 iuo -cupod.a7 2rw zq:;e)+sn mts 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 t4+bw wto (uo bl7u5k/yhe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion74 +kt5wu b(woyo/ulb?    $^{\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 spgrcz+e9 6l,mf eed of sound is only about 35 m/e c lm6,gfz+r9s
(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. :s /nfiiu j/;oDetermine the shock wave angle it produceuino /i/s;:jfs
(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 30ed g,why /wm-h2repa 2uv r0$/theta$ 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 1.5 km above the ground*6 9a gvo7wyhdlbp5; x flying faster than the speed of sound. By the time you heary*v7 ;6olw bdx9hpag5 the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that send9kvra 9- /v tj3s)mpjps 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pkmv-vtr9sj9)j / 3 appulses (in fresh water)?    s

  Approximately how many octaves are there *duf6t fwp 61w.yo6jrin the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a afg8auce 5wy,c gv6:,hg *5jxdisplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which gxc:e 5gjufah,w6a g5cv* 8,yare open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold o q/jz;auri,;nd/ 21uy xi) hmwf human hearing (0 dB). What will be the sound level of 1000 such mo 2h 1;/)mi qn/axyjw;r,uuizdsquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are2i*k)u m2t lst heard simulk*2lt is2)u mttaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. W ,o/5 w vqur. .edxfhi/x*hr2ask6,cghat is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions,q.26hsuc,efv gk. *x/5xhw/ dori ra?    W

  A stereo amplifier is rated att68sm6v2rl h (uem0qf 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kluv e8 s(ftm0h2r66 qmHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft tyvkw+tf-t- *d ,zz5) pm pz6 qxa)kkszof *eq.2pically 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 ave a .z z -q2q zsx**5wt),fkk)eoppvtd6-kfz+m rage 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 systf vx0a4wxz,q7x5 av6 oems, 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 violinz,i l7in ,bus- is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed poi6 cwuqx j5y 10 pmoxu/z:b:u*pnts with a fundamental frequency uux15x/zp:6mc q*y pw0bouj: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 npz 77fnb u+e8;ro5eyuk)f n: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 aga)uony5;r f7febk n+7u:z pn8ein 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 near a tube thakm m5 8agw2bzvek2s6.t is open at one end and also 75 cm long. How much tensi k22wzm asbk v.8m56geon 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 resona7m.bhvh05 oykxr :4swg mw3j+te 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 500–1000-Hz range coming from twg qqzf1 t89(;e;pm;uera d a 4(uo(v8za(rdpmo sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves abouqp(fgp;(4 eru9rq; z a( ddv1a(uzae ;m88mo tt 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 i-m9 l 2)i9pyd9eo x6pamrb en3s stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whrnxm d 329e)lpapyoei996-bm at is the speed of the moving train?   m/s

  The frequency of a steam train u s xer*.r4kgfzl p;/.whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How ;4u.zr lkg*x.srpef/fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of car60mtz ty3h xi8s just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going? 8 zh0tm6yi3xt    m/s

  Two open organ pipes, sounding together, epe))sk(uh e s7zd15j produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long kze)7hus(pe s1 d)e5jis the other?    m

Two loudspeakers are at opposite ends of a railroad car as it0v u3lwb4hbg( moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequenciu 3h4bwbv( 0lges of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood foa nu,y;rsb8t9cczo qnl 8-n7e0 -l9t low 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 flo 80bzercqas-8 9l- nlt,oco 7ynn9u t;w and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth j61lccwz,xm6t 0sj (m4fxw5pis flying toward the bat at speed 5 m/s The bat emits a sound16m ztc0 x(wjs4xwf65mp,cjl 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 high frequency sound b;6d rzf kp:f2akxiv*tw,:t85j nk8 kpulses as it approaches a moth. The pulses are ap fkzva,tn:85 f k tid6k2 *:wr;jp8bkxproximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Figj/ 8px1rz *obd 6x(eoc5xp me7. 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When plcpm6r1 b 5p/xdoxeze 7(jx8o*ayed 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 be compromised by thehtd f(xvl34i wgp6 x+*m5u +sz presence of standing waves, which 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 pv5 +xdz+w4(s3 l6tumf* ihgx room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calle 6x-:.zlypw1ylp5ytax mc:* d d “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 practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-lon axz 1plpx w-t:5cyy:6l.*dymg 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 (;/tof)a sf7 *8jh8nuef7rk bd u2yw pa frequency of about 1000 ; hbfr a/u*eydfj2f (t87o7 spu k)8wnHz 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 ground hears the sonic boomw25.csrzk zsy7 )m.hj 1.5 min after the plane passes directly overhead. What iss.w.2) z5jmh ckzyr7s the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbgp an 1jj; n(in.-vrx( vfvw9+oat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h