What is the evidence th7o lg-bzj,a a3at sound travels as a wave?

What is the evidence that sound is a form ofoq n )jw5w/y9oohv e1or yjd05 0*jn.l energy?

Children sometimes play w1li yj6-g hpfmwk/ g-2ith a homemade “telephone” by attaching a string to the bottoms of two paper cups. Whenf p -gh61il/g-myw2j k the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes f 5zacaoo7:y+ 3; t7dx aph,pfvrom air into water, do you expect the frequency or waveco: +x 3pa5opa ;tyfd,h7az 7vlength to change?

What evidence can you give that t:e5om6/xq* lw w zon4the speed of sound in air does not depend significant:tn64xw/m*w l5o zqe oly on frequency?

The voice of a person who he xi;g) czkz)s85(a8kjc z3w mas inhaled helium sounds very high-pitched. Why?

How will the air temperati,zu 0umrg:ac8 fhs (5ure in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplixkdto5 0n-vy 1tude of sounds in various frequency ranges. (An exaxko0nt-yd 1 v5mple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together r 6 q vm/v **qqyvnl6jh(60jhias you move up the fingerboard towardvqvyvh (r66 jnj** 6/ 0qhmqli the bridge?

A noisy truck approaches you from behind a building. I:rb n(,*. vkj w; uljuz/iypt9nitially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Exj(wivt;.r uz b*:/pj 9n,yulkplain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to* 4gq pc/bgo,/q)mg ey “interference in space,” whereas beats can be said to be due to “interference in timgy4)og/e /q b, cpm*qge.” Explain.

In Fig. 12–16, if the frequency of the speake0 ohuqv8;jh(bw teas*e(61 x mrs were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart o;hmeo hx a 6(8wjus1tb*qev0(r closer together?

Traditional methods of protecting the hearing e(ul3o:c3 (l;lool sot) r6w il/ vqf7of people who 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 worne /oq6:oors ;w7l ut)l(fov3 l3i(ll c that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought qmgxdj h/ u/l+a5 o:1wof 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 them /j+o1qd5lx:/gwua h two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directi2-x--x 6 netu7i5 opxg-ct vrvon, wixotrx-ig 2cnv- e6-px t uv57-th the same velocity? Explain.

If a wind is blowing, will this alter the frequej-,,3fl3u3yhn*w k ckrb cj iov(t2)pncy of the sound heard by a person at rest with ,pjory n3tfui2c-, k3c h bvjl3)w*k(respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chdc4hy ;kdypv2ax7 b;u 3dv4,xild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which posda7;,bd2 cdx u3 vpk 4yv4yhx;ition, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout r0 z,t7czr yre+eflected by a clif +0 etrzy7rcz,f at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just y55kqec 6.rogf8 pbj6below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the sg j6ykpe5f q r.o8bc65peed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthdq: 7shvxw wmlzb*934s 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;)jf7bhh+yk8o )nf i:amrs,z is drifting just above a school of tuna on a foggy day. Without warning, an engine backf ),8bihf jsyfo:mnka+ zrh)7 ;ire 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 makaz*sgtl 2po9s)(xr y+es when striking the water below is heard 3.5 s later. How hit+sx r(y*sglz o9a2) pgh is the cliff?    m

  A person, with his ear to the groundtkre8 umg8c 2., sees a huge stone 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.t ckrgm2 8u8.e How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mc re qazdh,;3l/zkibq0zwu)ke+ f *;6ile of distance by the “5-second rule” for estimating the distuqk)* abzqc0iz+e w;/ ; fk,drl36he zance 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 pain level of 120+lot1gf zxk 4rdoz);zq, 0;oe; ywu0 q 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 soundo*lh8t 7+; azyk n ap korw-g(2oac/5m whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce as5 , )e z,g3 wdv:dgrgsg9: fwrzo3v2s sound level of 95 dB when fired simultaneously at a certain place, whrfwd3s,es::g5gs,d z gzgr v)vo2 w93at will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certaiq5 t uafm/lyl99 .f7/vjhqwl/n distance 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 shut down all but one engine? [Hint: Add intt /fhljfq7.ql awmluv99 y//5 ensities, not dB’s.]    dB

  A cassette player is said to have a signal-t/b-ov 1sqg ni./y pxf9sd4j3ao-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 n yapvs.j / 9q-fdio xg/s134bnoise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakingxu wuk)c7:k:lckw e2- in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mo): x 2clkwckeu-:wk7uuth. $\approx$    $ \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 whow1yse0 rg.wz *exl p0+se 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 amplifier B is oie 56+x 1zqitrated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker co6e xt +ozi15qinnected 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 pi wl/ .vti4h/oesa8*flaced 2.8 m in front of a loudspe/ wf.o/ehl*a4 sit iv8aker on the stage.
(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 differenc9so 76 ;t;fzvfzh3mhre in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this am;f6;fmvzzt7h3 o hsr9 ount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) b 902ov2vp dktfy what factor will the intensity increase? Incrvd o2kt20vp f9ease 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 frex2hfnj-u j rmd k5uu2g7 id9+;quency of the othen-9kh7f;jd umd5xu2uirj2 + g r. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air tham9 nrcac24fvrv w3/ k7t corresponds to a displacement amplitudf r/9kvvanwmc42c 3r7e of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lc/6s*hvv5b8vpd uu w6y2js5 xoud as a 100-Hz tone that has a 50-dhus/sjx dvy8ucb652vp v5 6*wB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when thiqa, 8ay88 k4kyj3x emt1t5n wrz4pp1e sound level 5 py8m1nej8aa ty43 8,1xiq ktw4krpzis 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge3 a zteo)ww 32omj;9lewymo;sq 09,eh range of sound levels. What is the ratio of highest to lowest intensity at;wo;y3soem q a9e,l) 9 who3ew0zmj t2
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440-d 5pjgk;hmyg: - q3g3du oiz6 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must duj:y-6m- kq z 5dgohpigg3 ;3the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamentboi0yut ,kj7:4 /zzgjh 3qq: fal and first three audible overtones if the pibj7qkiu: 3/htjz4z0fgo,qy :pe 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 bl uage /l3de;x2owing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a close/d2gx;aeel3u d tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ uor8)s64he 7q +bwnigwith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requireon) su8gwir6hbe4+7 q d? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third l:cofy- a+cy;ga;r; wharmonic. What will be its fundamental frequency ifgr ;;a f- ;lyacocwy:+ it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar s9k.n t7cz(nxcnc)jf- tring is 0.73 m long and is tuned to play E above middle C (330 Hz).xc( cn 9.n7k)-tzcfjn
(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 (21ib (d);z/f7 cdjad;m4njfx t62 Hz) when the temperature is 2d1n4f7 xjbf/i(tcdja;); mdz1 $^{\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 yoyicl7f+aj6r alut 9qfb- : )p. ay/+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 hole be thvyw( 6).8ctcxqk ni. n/5eg uiat must be uncovered to play D above middle C at(ci cxy.k/nve) 8iq.65n wtug 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 pipes1e d, guk zz9e*tzvpf,lyj./ 4us;:n can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other freqly 4pk;unsze,f :,ed9*g t vz s1u.zj/uencies 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 resoni6zu/ q9e/ojv/bl *erates at two successive harmonics of frequencies 275 Hz andb/o 6q* jvr/le ue/zi9 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 -bk*-z:a urdo$^{\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 qmv2 am49akb9b sl6/cv6xch ) 2.14-m-long organ 9b2xmc6a4b m/) vl9chks a 6vqpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the ou;-q j 4ldhv2tk m1*c)p jh9ygetside 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 igetd1jjlh94*ympv2 ;c)q kh - nformation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 7ul 58h5bandr2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How l57 8d5hanrbu far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C 9,j-jvyr i m.n(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 pbn2(k.a 0wu-s jv/hy*b6oco. z 3j xwkHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played s.j n * 6k02bjo(z y/av 3ocuxhsb.-wpweparately, 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 whe0v2p l0b-um zm)y g6hz6nd1l in sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequenm0my-i 0l21l 6hn d6)gp bvzuzcy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hf7i(v 1xzonu8 z. The tension in one string is then decreased by 2.0%. Whatv n7uxi8 o1(fz 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 twp6*k90eyj*ro avr u 4po identical flutes each try to play middle C (262 Hz), but one is at 5.0°C 0a*4oj 6k9ppruy e r*vand the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forkiy g3t)i0r(c os, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded toge)o (rcity03ig ther?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A persojv8avtb*7 s(gwhfcr2t*q (4 ln stands 3.00 m from one speaker and 3.50 (t7 rah*ls2vv( fjgct48*qb w 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 atyp+,x68fqc +di9 jnnx3 qj/ ot 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vi3n6tp+ y9ijx 8+,fo/x dqcqj nbrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How mvvt 2bu l :m4*opl.:)s8 e,uwe pq-sgyany beats per second will be heard? (Assume *v.e4p os2v :-:ltqe lmwuy8pb,)ug sT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when ylgiw6qo z g8.p9s12ei qyq nz2)lzxu *u-a4: at reszu6-)z 18ywazxl qig q g.iopu24e:*n29lyqst. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency 1fg qec4bzsd:34s o2vioe 8c ci)uy,( do you detect if a fire engine whose siren emits31ciucs4 )gve( f,d42o8zbosy :cqe i at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift i ;++ k xz2 s;dfqhkoj3d,n(jewra g76wn frequency if a 2000-Hz source is moving toward you at 15 m/s vero7aze+d6;x3nk kj,sq h( j;wd g+2wrfsus you moving toward 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 equip7gap+ 0hd:,q ghzk l/lfl x;,aped with the same single frequency horn. When one 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 Hz. What is the frequency tg+hd0, x/lk a,:zlq;7alg pfhhe horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them rc h qnb4k48oin ;6rc*geturned from an object moving44kc8qr 6nhi *nb;cog directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a w9rnv0iu w*7bsall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fr*w 0nis7urbv9 equency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving ;qaa *30bohd pflat 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 *h3 padqaob;0beat 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 q 1uzf8jt grrc/at5v.l41wve z2mt.5 to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, andgzr4.l55 zrtt2tvf ucqe w11j mv/a.8 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 ultrasonic waves of a (jwre u)x: d:kii,n:k5ae (ufrequency $2.25 \times10^{ 6}$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 i -f4* :jivfe ew7;e:rmzb.mhof frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, a.-r mf:jibez vm4 :ew;e* ifh7t 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 onyt bn qn2bu-j3 23z,ee 1.evor 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 Mac so)pb9n-6m7yvmb u2th 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with thnvs pbm7o-96t2ub )mye direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed 8s.5)iee.i9azf cykj of sound is only about 35 m/isezf.i)8k9j e5ay.cs
(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. Determin8ire eqdxvln3+dbl81)u8 v f)e the shock wave angle it produ lfeb1+3d)n ev)lu d8q8r8vixces
(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 jrohddswe+49vx39k ,5 z//7du b mft* zkrhx+$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan*)embw6 ) *57gb knmqoj8kolse exactly 1.5 km above the ground flying faster than the speed of sound. By the m5bwbo7jglk *mqs*)n )ke6 8otime you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends ;i of h/rq+;qz2:nle v)pp 5yc20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the np2z)eoqp l +;rcyqi;hf:v / 5maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how manyr5 qk7f4+rsle)ce zn+ octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calm6wx tz3pacg hk,:.u 0led a sewer pipe symphony. It consists of many plastic pipes of variokz :03 gcp hwmxt.au6,us lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 mpg3zz9kk 5/1lmtak:q h)hu.r hy;b0f from a person makes a sound close to the threshold of human heariny3/pu bm:tl;q k) ha f1g5z9h0zrh.kkg (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soundld88r,y0d/7tuzio4u 2s jijt are heard simulta 2zdosi0yu,u /td4t7irl88j jneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,nxfbrik .n34 4, oq2se is 105 dB. What is the acoustic power output (W) of the speaker, assuminr,sn obx 4qnk43.if2 eg it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drop.o qrjnon60frb8/rk j/. 1 g8sv3r/-icdi orts by 10 dB at 15 kHz. What is the powet jj rfd1rnq/s /8o 0onri8-3vc6oki.b. /rr gr output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their e0l sbus t9y1q6ars. Assume that the sound level 1q9uytl0s6 bsof 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 communic b e00104y p.cfmm:rvwm 8zn ceh))bemations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned topxn:kt n i5i-) a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a funda5i iqvk pjya.;z 0*h, s0ghnx-mental frequency of 440 Hz and a mass5*is0.yhznk g;a-hxij ,p q0 v 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 verticalp9t11ukdqw *+y*c2 c khzjt5o 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 again at 0.395 m. What is the frequency of the qyod ckz1p*+ 5tck1tu9wh* j2 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is openi4e6dlzw :znj 0*+nnh at one end and 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 w: zdhiz*enj4n n+6l0 tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate a(garnc5/ zh y6mj6iw7 s 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 *g8ntw( blh42(z kqlh the 500–1000-Hz range coming from two sources. The sound is loudest ath ( n2(*q48bgk hwztll points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz wyivr 2)qr. 7w0ndlg10my6k y yhistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when thei0 y6q yr.n)m lk0gdy1yvr w72 other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trai,/c47edze 3rfn,xwe pn whistle as it approaches you is 538 Hz. After it passes you, its frequency e7/3wf d4ep,,xnczer is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can esmudub/o41 n; tv../dkdyh-p t:fl g 0btimate the speed of cars just by listening to the difference in pi/ .b-khl d4ud /;ng.vtodt:m0u f1pybtch 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?    m/s

  Two open organ pipes, sounding together, produce a bebz 8l- k8dfh ;oq41widat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thefhio-1 8kqw;d8 zd bl4 other?    m

Two loudspeakers are at opposite ends of a railroad c6v/g bujkk)9 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 s9b) 6kk cu/jvgpeakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally aboutyf.1 - e/lv v7x*vt/x x-fmvzh 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waveh /zyv-m/x1f f*7vx- vev.xtls were directed along the flow 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 at0ro/4rt+5czxuv 5 i01vgx(zdpz v p.i speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound p xz5ti(54cd1z/0u v+irovvpg.x r0zwave 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 ap; r( 6;edc8yhn2kk vtpproaches a moth. The pulses are approximatert8 ;;26dvnkp c(ekyhly 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one ag8:r/e 9fkd) kslwggp-6ze7Alpine village to another. Since lower frequency sounds are less susceptible tofg sg/g :k awp97z6ek-elr)d 8 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 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 7n4.f/h bpbte be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the hn/t.fb47bpe 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,” involves a long, slender alubj/;uss:bgp1 minum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little pract bpj ;s1gbsu:/ice, 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 frequ3.ahtg- y;sj yency of abou3ygj yst ;-a.ht 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 2.0. An observer on the ground hears the so xkus c mi6cy8(m1e1.gnic boom 1.5 min after the plane passes directlym.y(8cei1k su mc6xg1 overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat imelnb4*4:8kdq, y2c x3x di(cha.zz ds 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