What is the evidence that sound travels as a wavcp-b 19d uka/bgws,p: e?

What is the evidence that sound is a form of ene(ny .i6ttfgq 3w +vi;jrgy?

Children sometimes pll960t t(inphoay 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 sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave trave itt nl(9h06pols from one cup to the other.

When a sound wave passes from air into water, do you expect the f.isy:(*q.yv ng sefv :requency or wavelength to change?s (: eyngsqi.vv:*.f y

What evidence can you give that the speed of sound in air does noc)-hd3: u j( wopmbm gme2ved4n2tv56l2bn h4 t depend significantly o:(4 ehmen 24t lv3ud2 jdw56npb g) hom-2mcvbn frequency?

The voice of a person who has inhaled helium sounds veryx jkzbxsbb3 4yh5,k* . high-pitched. Why?

How will the air tempi3l7 z9oawp5 qerature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ayo/uu/ q.fu.j0jps x3mplitude of sounds in various frequency ranges. (An examplj uyo/.qs0/ufux 3j p.e is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov vd.+id;i )i5m1bq fitwsg71ve up the fingerbo.+ bsmq51 ;7w vi1d)gtvdf iiiard toward the bridge?

A noisy truck approaches you from behind a building.i qh)zi)8d 5yg;hemm* Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the h )*imhiym8q;z) 5gdhe igh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacw9r 4;oxjs/ks7jx jn65b7h nn e,” whereas beats can be sa / 49wsnj57njk6;o7 bxxnsrjhid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequencld ;b6 3yzw hns9yx1-u6js8no y of the speakers were lowered, would the points D and C (where destructive and constructive interxn hd6 you3lwsy8s 6b1 ;9j-znference occur) move farther apart or closer together?

Traditional methods i7 hxfj a/3q kkk4i5v8of protecting the hearing of 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 worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, the7xq 4vk85/ jifikha3 kn 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 bp h mzp25f4rl0e thought of as a superposition of two sound waves with slightly different frequencies, arl0 5p4m2zphf s 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 move invg / u,,hb:p qrqx3 8lrjcs, 6:d rn3yj+sy+vb the same direction, wit6:jbrjhlv8sry/nsgvq x, , q,r:p +3db cy+u3h the same velocity? Explain.

If a wind is blowing, will4 oneh5jsk--,sho78t a(q5qezh crm 4 this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity ch-o-eacs4zs7m, er hth5(5hnkq 8qo 4janged?

Figure 12–32 shows various positions of a child in motion onlu 1:g0o p.sbmdestp5xv*,5 pl ulr.b3fs2(r a swing. A monitor is blowing a whbfp 5r*sltemb1,p2.3. gsurdo: luv0(s5 xpl 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 fo5q( hv3a ro4zsh8,thczm65a l6i+ qw pr the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate th,qm3h 6piq65 lz8srw+zo 4hah5t(a vce length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears 3 -gtmi-qe 1s5h : pu;k3oclybthe 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 u s3egbo:cy p;-m 1-kt3ilqh512–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a)-wtl6m l 4ls)mi g( 0glq8ztot 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 tufn /eapdom9 (8e6 5jxo,4-paf yc4eabna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses befor4 pfe-6 84j f (xaoeb,p/9dyaae5o mcne the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a il0yl5cekd3z -6hte)l ulf/3 cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the clie5lzdhit3f )l/keyulc6l0 3 -ff?    m

  A person, with his ear to the ground, sees a huge s agtzzhm/xk*, /e*7yutone strike the concrete pavement. A moment later two soun/k*a ,he zxt*y7m/ gzuds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by thag a:pv*(z 4sie “5-second rule” for estimating the distance from a lightning strike if the temperature is (4* iva(p gz:asa) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain c jcen;oye c4-w;)q+3uqop s1level 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 intensi ayvug+0( nh7gty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro.vy((hujeb g -duce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add-vjbg uye(h .( intensities, not dB’s.]    dB

  A person standing a certain distance from an airtt:.w0zjl1w a v7rc x n3a5k:5hlujv.plane 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 en:w c 5 hu3.5a k0w1ja:.7lljrtx vzvntgine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas fo,r hy etngp21/r a CD player it is 95 dB. What is the ratio of2 1g nyep,rth/ intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normalrmu qygu8x/5 a( u4hi4 conversation. Use Table 12–2. Assume the sound spreads roughly u45qyuig ha4xu8 r/(muniformly 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 eardrumo8 ,o*xct k(bi whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is ra zd -lzs-kqi5njg9e22 ted at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker cok l-2js5i 9eg-ndz2qz nnected 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 metfcv ad 1q8;ol:er registered 130 dB when placed 2.8 m in front of a loudspeaker on the stagec o:a;8dflq v1.
(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 so r: cqjmmp12,rorfb1j0+ee w 6und level of 2.0 dB. What is the ratio of the am2rwqo+r10 1f:prbem jm6 ec,j plitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soun7dr6d lu5l6i4h 3 +odstu.wjuh c3tu7d wave is tripled, (a) by what factor will the intensity increase? Increase by a fat676 d o5 + i3.ul 7uus4hjrcddwuthl3ctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twicep; .rkk lwx,c ,tv,an: the frequency of,,:vp,knl; kt.xwar c the other. What is the ratio of their intensities?   

  What would be the sound level (ib gtzvk0t 4 .1lsoav)pa2bm 9+n dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules409za+ bpm1s avg kltvto.)2b of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soun fk),8a,rny6:, l m vbd6nlwlgd level to seem as loud as a 100-Hz tone that has a 50-dB sound le,wrdb,)l6a: vn,nfml6 g kly8vel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that-e id(i)yiv-m 3 93spypw o,bs an ear can detect when the sound level is 30 dB? (See Fioiid-y, ym33v9p ws-s i)bp( eg. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the r 3ctyozqyf2 q8q)h78zatio of highest to lowest intensity a7 t82fqyy qz)och8q z3t
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamentbi-bpl:6 9:ne7.pv sc 0ocrblhs(i e7al frequency of 440 Hz. The length of the vibrating portion ievbbbi7o h-pr6 0 csp.li 9:nc (sle:7s 32 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 are the fundamental and first three audi9gjn .45feq5 ouqxw- qble overtones if t we u 5oxq-9nq4f.jq5ghe 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 tohe mg+)k4gibyo :fdu,7c ) * 8m)sjxqdul o06np of an empty soda boh0u c)6nf4b dd 7)lug )8yeo gm,:x+*mjiokqsttle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipm n;5qvg, ztf+es spanning the range of human hearing (20 Hz to 20 kHz), wn;g zmt,5vqf+ hat would be the range of the lengths 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. Whaug ;*ox3ku d 8 p.ycu5*fikp*st will be its fund3pdkyou *u*uk 5g c8f; pxs*.iamental 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 abovqly98ca ry 8y7z0lv-f e middle C (3y7varc8y9 ql8fy- z0l30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an openc- 2e yd6w doa4pb3c ;v8jt i(m9rqd.w organ pipe that emits middle C (262 Hz) when y2 dmoc3. c6de(twr4va j 8ib-;9dpqwthe temperature 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 acak,-loei7n)6e 7jxek 6y.m ct 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpi1q b l0+3lo ena(mfk2oece of the flute in Example 12–10 should the hole be that must be uncover o2b+k (n1e3amfolq l0ed 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 resonate at 264 Hzc t. w:dpro),8agza -m, 440 Hz, and 616 Hz, but not at any other frequencies -pgc mz8:,d ar)o.awt 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 loc ly)qf /* 4 6nrk*rir78ufsvgng is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What flukf)/4ni*87 yr6vgqrsc * r 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 -shtx vo rr a1tj1.den97c. /n$^{\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 withs/zc2hbgw9 4 s6up(el8hy)8f6cz; r p oip8zwin the audible range for a 2.14-m-long organ pipe gw(r/ 8ushz6woz e8l 2;4)ppif ybh96c 8p zcsat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.tsqo y3:nkoz(, c9ufd h0r 61r5 cm long. It is 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 y (fotn6 z1o0 sr9c,rud:hq3k 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 whenqh)y+ .cs,mcknq zdz66(bfl0cu0qj 3 trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequjyucmkdq3qc. s+0bznz 60q(c f)hl 6,ency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Htqy ed)0t37 ggs -hk,tz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another e30t6lr 22(r s2zby.umimu8 mq*5zb yut7s qz(brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimme7t2 .iy* sq2uz6 blbm z52 u30rqzut(yr s8mate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35dkkdxps934 a.1 gow, z0-Hz tuning fork and 9 beats/s when sounded3.k xzp41kdg os 9d,wa with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to tzdd(o3 yi 4i 1zl-a,fz1ee4 pd fg+:gshe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [ 31gzp faei4 -: 4f(izg+yzd so,d1ledHint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eachvqo3sg,pxz :6 try to play middle C (262 Hz), but one is at 5.0°C and thoq p:,sxz36vge other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; x( m8 ./lwtcj4bb1 aoywhen 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 t/oby.b4jw(lac18 mxtogether?$f_A$ =    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 frd kgeqlha;o72*gvg u),4 t-qeom one speaker and 3.50 m fr* eu-g 2 4;t)g7dkvhqleog, aqom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hea 00pn7vr;lq.; ndhb crrrnd.n;; vbq r70hc0l ps 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 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:yn0f 1e yc-nocw8w: d m and 2.76 m in air. How many beats per second fd:o8cyw -cwne1: 0ynwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’6agj 0z1oei 9js siren is 1550 Hz when at rest. What frequency do you detecjg6z1o9 iaj e0t 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 do you detect if a fire engine whoseesq5 qv lv4s3/ siren emits at 5ssq/ vlvqe4 31550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency 1xb0 l iu*1 t:cgo+nrn-tvik3 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 fr0iv:rcnuk-totib1 *+ 1x3nl gequencies 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 same single frequency horn. When one is(d , *hgzxkwkv arp :-m7qiql)+sr56v at rms56: xwq,rz* q-ahvrd(pk) +7igk vlest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives thw2 /qom.d5waj9bn z)hem returned from an object moving directly away from it at 25 m/h2 wb9 ./j m)zwoan5dqs What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat,gu8dp1a ne51kzj vm9 emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflez8g5v m19 ud a1kn,pjected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played o3+,rim8dp j ub+cw4xe n 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 bea,dmu3x8 + iw+cbrpje4t frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow :epzkz7 slhqp q1vv6q,17 tx8speeds. 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 fvp67 se zvqkt1pqq8 h:l7zx,1requency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ux(1*pb)ww n dfltrasonic 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 of9qk/d*vj(vg nf h. ef n(wu4wp7)f3 sr frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequenjw( f.n3 rkn(*w9 7fvvp4d/uesfhg)qcy will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land iffxc-mlhfjc18zg*0d( 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 thelk /g glt*la+4odpr6 / speed of sound is 310 m/s (a) What is the anglkat p l/6groll+gd4 */e the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thip8hr9pl )*yyin atmosphere of a planet where the speed of sound is on*)phyy89pi l rly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oceawf5*x* bln5w3t n6(7cu yz uyhn. Determine the shock wave angle it produces(zw 5ubyc73f*wl 6t nnx uy*5h
(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 lm3o*duv5k f -s 6 ba 1-l reckxi34j5h)c8nkx$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhegzyw5b0zeeesa, 47d9wz0yi4 ad and see a plane exactly 1.5 km above the ground flying faster than the speewbzadz 0e49wy5esi0 g 4eyz7,d of sound. By the time 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 sobt1/ a:rvns 4inar device that sends 20,000-Hz sound pulses downward from the boatr1i/4sn v b:ttom 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 thepkrea0 1jp( okn71i c2re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. .5xkjz5q, *7q.ay*a itnibjk It consists of many plastic pipes .5*t5ki iqa.z, qbn k7jy*jaxof various 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 m from a person makes a sound close wly,l hny,6f,y 3vh2wto the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquivh2lhwf,36y,ny, yl wtoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB s,of d1l w:k .g/r0zmdg-evh:round are heard simultaneously- d,f.zm:lro10edvhkr /:g wg ?    dB

  The sound level 12.0 m from a loudspeake03adp(7ljpf dm;65ofl me1 gsr, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assum5js31 f 7flao;dpd0 em(m6l pging it radiates equally in all directions?    W

  A stereo amplifier is rated at 15 u3+4xl0d9wbun 5avf e0 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whauv5bfd3u n0 x4+aw9elt is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prot 3b5rsz::o3o6ndz cm) rqyjt-ective 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 effect-zbt5: ycs o3jo63rmdqzrn:)ive 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 communicati)r)s ckk(sgb1ons 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 isif v9qnw;8g33twm c7l 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 points with a fundaqruz +l;yd a1 d26lx7bmental frequency of 440 Hu7yd 6l1l2; +qxzd braz 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 verticapzl* cz4rq .nike nig;7 ua7.3l 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 a l7;niz7c.u3kpin egr.4q*zresonate 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10f6dq9 tae0u2r,2e6 gpf kzyd2 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produa22zqk6ef6ed9 y,u2t f dgp0rce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reso -, pg4;b zwlx;.rtrxxromb2z+ - 3otpnate 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 tg1 x+w0p mo)wk+ qsnv+wo sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequm1)wv g + xs+wn0+qopkency 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 whistlese+8).sr j;gwt 0xari q. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other t+8q;s.ra 0 g) jxewritrain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approacheshc-6v,c t;w2-b6n c5agpb; fgt7zvmu you is 538 Hz. After it passes you, its frequency is measured;cb7 g gn,c vu6 -a6;hvwtmt5pf-zbc2 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 justh04 sqa(mf;r+y4vxiy 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 sar; fm4qy 0s(vyixh4 +traightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 mu1cg-4h n:yc Hz. The shorter one is 2.40 m long. 1m4 :guhnc- ycHow long is the other?    m

Two loudspeakers are q.lh0h,)uzdj tx ,po;jc7jv3at opposite ends of a railroad 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 heax0c7qujjv)h ;jd3h .ot,plz, rd 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 flow in the aorta is oi ap(e c2j+gwa);h0 nnormally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flowha n+ )pio0wjcega(;2 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 is flyi)oe3r5wmp.xjwt)5ti(1l x y gng toward the bat at speed 5 m/s1o 5g5.wrt)t i ( jp)ey3xlwxm The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Thex8*ei j h tw,le:7.;ji4vuzkf pulses are approximately 70.0 ms apart, and each is abtxjwh vi:l8,fzu.47;k e j* eiout 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 frombu +h639kel4 )hqygl c one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtoe6 4 cg)3hyuq+lh k9blne is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by t/0r r c o:hyms5n2hkq3he 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 fqcsk 32 rm0/5o:hy hnrrequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singingf2 rgklne00 .;3 nzv9g- ofokq rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stro;n 2q.n zo9gel00k3- rokgvffked 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 hloszc971 bqb 1r8p;h: 0 pvaxthe human ear at a frequency of abaox1p 1 s9blc7pr 0hh:8bq;zvout 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 atctjy hpgbhq;u0 aib/3(8fm35c0u k 5n Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes dijb5n/tgu0 b8kmu 0qp3; 3(fhc 5y ihacrectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is vb zey6 r.s1elgl;:-3s1xy hx15 $^{\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