What is the evidence that sound t5onjjh 1 all,:ravels as a wave?

What is the evidence that nsff:set6( 2h sound is a form of energy?

Children sometimes play with 1dwj970 zfmjb a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speakdwm z0f9 7jj1bs 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 from air into wateruiwqg gwx(e e63tg ex 0mps +*lh5r1ca:1re2:, do you expect the frequency or wavelength to e3cl2 1wpmtggrea5ux 1:*0+( 6q:xh rgwse iechange?

What evidence can you give that the speed of sound inrfm )u)ay wkg4g47 oc0 air does not depend significantly ay4ggou w 4c0m)7fk r)on frequency?

The voice of a person who has inhaled helium sounds very high-piti*n; -kcx (z+ rqnfh+ eq,;xnached. Why?

How will the air temperature in a room affect the pitch of organpqfd tmxj w/ lyft.8y25my65+h a-6wd pipes?

Explain how a tube might be used as a filter to re :c 5wo:6ivck2xo j1iurf9q .nduce the amplitude of sounds in various frequency ranges. (An example i:o cjfwk.96:1cox q 5riu2ivns a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced c+uw- hfo 0unk;ws h2y9loser together as you move up the fingerboard toward the bus-9ufk0o2y+ n wh wh;ridge?

A noisy truck approaches you from behind a building. Initially yo5sjuhg;a 8phh7+zw/f u hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more ;p7a hzj5h+uf wg s/h8of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference inhci+ 9kxr23qd -i3q5n dy dso+ space,” whereas beats can be said to be due to “int s-+92in+dkoi5qrdx3q yd 3h cerference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweredmz:h8p,rp j9w, would the points D and C (where destructive and constructive interference occur) move fartr:9 zm8jp, phwher apart or closer together?

Traditional methods of protecting the hearing oxyxsv pr)))18tj tzy+f 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, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound lev z1yxypst)v8r+)tx )jels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of agew77-i 4omykg( rzknk)8+wcs a superposition of two sound waves with slightly different frequencies, g-wk)7o ei w4c7m 8+(ygnkzkras 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 obser7,,ca7ouwad z /s(ip0c3xzfcver move in the same direction, with the same velocity? Explain 0icwfsuapacd ,7c 3z,/ox7( z.

If a wind is blowing, will this alter w2vhv:mx5 s gpdd6)*r the frequency of the sound heard by a person at h2*xgd5d s)wvpr m6:vrest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a seg8r/yf k :,kowing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the8gokyk ,r/e:f 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 shout8s5 e olu wbym,4qv;+egr4bh+ reflected by a cliff at the far end of the lake. She hears the echo 2.0 s uobv85+rs e,gywm qheb 44+ ;lafter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. c2emf9yy.;fy He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly wiyf9; fymyc e2.th depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air az35yp6(x leda t 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 tuna on v36:x q/p 2g bc6gu5*oayrtyea foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire isg 35x v:t *pbuga6roc2yeqy6/ heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whe ql6wal( 9wz;je3)objn striking the water below is heard 3.5 seb jzww ola6q(l j);93 later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge st 82fm y ag y6fyuyc:e5o2kj+:gone strike the concrete pavement. A moment later two sounds are ha yyg28y6ff: oce m+5ku jgy2:eard 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 the “5-secoe myey 9q0m vvxe0sh7ss 2 l;z)a1l8n7nd rule” for est vm0x;2 1s98h7v n lelsaezyems7q0)yimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensityj5.kqxcjal 7v0hr vtd 6*n4i. of 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.rcrt9g eipi( s/e5 j3 whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelvn*6s v)s+bcd11 q jfo of 95 dB when fired simultaneously at a certain place, what will be the sound lsb) dv+qc1jfos6n* 1vevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an087ecwqr/znz izru9/5 ;exe4jvg6 x f 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 intensities, not dB’s.] we cj9 e/85r 6zigzz;x7 xufn4r/v0q e   dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereaso 33/z1)lc, hhvtxsbt8h8wul for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise tsv3h8wl)t13 zlo/hc8uhb, x for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output on, 2jmrpvk 3x5 ,:lndtf sound from a person speaking in normal conversation. Use Table 12–2. Assu ltj ,d:5nr3pv 2,xnmkme 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 anddl lumo6bd j. a wvyvy-;,i wk,*o)8irq9-8h eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modesthrsyf2c: *)h+c hv0jni4r -h8hso/rin*an :d amplifier B is rashv+ :a- rsn*jhyir4n20o h/cn :d8h)fhric* ted at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when pl-q bm0vv,yia(-yvm56qfgn-o 8 n ;;(pmadq lxaced 2.8 m in front of a loudspeaker on the staind -lyf,g8m(mxa;6v (p vamq-on0 -qv 5q yb;ge.
(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 s6qzba o.)(m 2 wj3ehteound level of 2.0 dB. What is the ratio of the am e32 oj)a(tbhz.mwe6qplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) bfx /b5igw,6s uy what factor will the intensity increase? Increase by a b65 f/g,xsuiwfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacehvae 7p(y,dhi-v -x3 ement amplitudes, but one has twice the frequency of the other. What is the ratio of their intpa, -(h divy-x3h 7eevensities?   

  What would be the sound level (in dBn erja(3 wdin9c-8 fp,1 a 1h)qlrmcy/) of a sound wave in air that corresponds to a displacement amplit /1f aypd e-hm(c,1c qw9 jlinr3rna8)ude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a pq8hje9lkf*u8y*r8)5 uy zmyvlu .6 t100-Hz tone that has a 50-dB sound level? (See Fi) 8u ye8 j* uhvzkpll9.r6u8qf tm*5yyg. 12–6.)    dB

What are the lowest and highest frequencies that an ear canb ze5sk tx,p-e77 f(au detect when the sound level is 30 dB? (See Fig. 1pzs-5, tfkaeue7b x7( 2–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the l+ 1c,rve-)xgkz jm ol5 .:b9c ssb4 lnajl)e.ratio of highest to lowest int.) an, bj1r5l.ssgclvj c +l-ox9b)kz4:meleensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a viol dngp m7 nq+l;-i9fr9xin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be9p m-7f +qrlng ;9indx placed?    N

  An organ pipe is 112 cm long. What are the funda b8 ge(xe+;e mtl9r0opmental and first three audible overtones if t ;e0pe+x(btr lo 9gme8he pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of an-mmo l.g - x38lyz4xcnpe dt4+ empty soda bottle that is 18 cm deep, if you assd 8tx -.lpyz 4en +g4cm-xml3oumed 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 spanning the klr.8vpc*ek 3ce ,sf6rmf6qbas)f*6 range of human hearing (20 Hz to 20 kHz), what would be the range of f c)*vre6p3rl6eq*k,.k f8scbf ms6athe 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 hag (u awd1b3 q7ji+ji7rrmonic. What will be its fundamental frequency if it is fingered at a length of onlrg37(q7+ua bji wjid 1y 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is t b( y /u-qr2azp(b:dnsuned to play E above middle C (3( y-qr bdbupn2a/:(sz30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits midvg7 sloj l/61;e18rrms 9iuffclpp7 7dle C (262 Hz) when the temperature isos119l77pur s 7f;jv 8lrelfi c/pgm6 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 uh kjq 086fyb:1 1q)4gaakvsm$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampk+nfte x-6;;ej*qh3x. hyd vnle 12–10 should the hole be that must be uncoverednd6;-he3vjn q*tex h+; kxfy. 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 Hz, 440 Hz, a+lfbv ;p o+ ;k+f86 g cuv/wx;k4xiwsmnd 616 Hz, but not at any x;k4+xs ; ub8pv+/ mc wolvkgwff6;i+ other frequencies 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 resonates tiigg7oz i-nt9cb7;a sxi78)at two successive hag ) g8 oi7xib7 t;aiciz-7tns9rmonics 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 -eq qqq(5nl0(l s*s z8j,w3f pbwz9 kf$^{\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 r ypnig6 tqa28.ange for a 2.14-m-long organ ppq8 ty6 .ga2inipe 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 toug0hn qx5-wq1 ;nx dxdfn69n. the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the r9n -dq6fxqxxhnd0 n.1;5ungw elationship 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 ky alyl( y0m7pgj+5j, s when trying to adjust two strings, one of which is sounding 440 Hz.7 yp m,lj(a+y0gk lj5y How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middl:p0dy0 f ko5s71lf ly)z5fcice 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 h. e70mgppv)skHz, while another (brand X) operates at an unknown frequency. If nei m.e0p7hsv) gpther 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 producpho28j5 /l vx8jr 5xuues 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 352 rpxjhu588lx ou5v j/5-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hznx v;yz ycdq7 xve4+,9v rl80r6g3i(dsopo d/. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two qy80x6+/9g (oeo pizvrnds, v;drl3 cvdyx4 7strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flujkb7hjd-7 w3e).c r 6qwbmj6ntes each try to play middle C (262 Hz), butwhj.e mb3 d7)k66ncq-wb7j jr one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freq9go j tfr9(wbabx3svgph,:, 9uency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is hef(h o s,9rgjgv:93 p xb9bwat,ard. 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 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 personjwn:2k81 bvy+fz7 oz3j+ysx t stands 3.00 m from one speaker and 3.50 m frofy os:v+tzknx87 3jbywj +z21m 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 Hznavwq1wh.5c tcd3 /o-, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be thevnaq how31wct- c5.d/ 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 beats pe9smvvgou6f3 ()mq 8 lrr second will be heard? (Assume Trs 8omvv u9m( f6lq)3g = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sir 9ylij0p yp,.5pf ;aayen is 1550 Hz when at rest. What frequeajf p5p;0i,ly. 9yy pancy 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 do you detect if a fire engine whose si)smlnh 3.u p+ fuq(ex)ren emits at 1550 Hzqs)+h npx(e)l3 fm.u u moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencyux32rhvx lutlqyqkl: 2q+1kjd42q6kc, / f k( if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at l kq4+q f j,u/kl:32yqk2q 26ltkh1cvu(rxxd15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single freqi2dnxr8m-zui(gv i(7 uency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver a2(dxn ui(-7gi8 rvim zt 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 alcv/i t07xrdy;i 9y 96/ fvrfbnd receives them returned from an object moving directly away from it at 25 m/s What is the received sound /9v7yc6y ix/; dbiflvf9 trr0frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a n+jb*9 :lslxyjylxi(q 0 io41speed of 5 m/s As it flies, the bat emits an ultrasonb0 il: in9y(x4 sl+ojy1lq* xjic sound 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 experiments, a tuba was played on a moving 8 *n *t zv*nufkt.w*yxflat 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 w*fy*ktv nz8u*x*t .n 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 measu dik*3bddzd/mmz+;w 0re blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s Whz*d k+ m0;z/3 ddwimbdat 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 zck(r;q:jiwo7bo 78mb-(n fw 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 of frequency 570 Hz. When the wind veloc. xa(1 y, 0tbbwuyvv4xity is 12 m/s frv4,y xt.(b0avux w1y bom the north, what frequency 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 if its speed at y- +qyt sv3q;a20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the s9y.-ovr joz r wnhfdza0+* z,3peed of sound is 310 m/s (a) What is the angle th z ja+z*w , rnf-d.o0y9vrh3zoe 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 thin atjmds,re m* /67fpvmq6va og+-mosphere of a planet where the speed of sound is only about 3p ,vor *m6qs- jva+/6gdmf e7m5 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 theslzf,7e w9j. b ocean. Determine the shock wave angle it producess ,zl9 w.7fbje
(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 n38 7nra- wgza$/theta$ 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 qda+f3;; ez dwl8w sjtgbz1to8540xjthe ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance ofgz;jewxj q 83db flo 1z;+swa05tdt84 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 20,f(wpxr y h)i7(d kl7i)9*w qsi000-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 x iys q9i 7 ((w*pir)7fldwk)hthe minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audshnbp (u2s: vt e:o e.wqhdz689q;h-dbz: i4 dible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of many: bj m6cqua p5lxy,;,c plastic pipes of various lengths, which are open on both ends.m,u5axq 6:;, yc ljbpc
(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 lz,q1yzc,slw8 fmc3 )k) *naqxzr1 5 wm from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? nws l 15r,1zqzy8l*3kmq fzx)) ,cacw    dB

  What is the resultantav4 d:kzkr9o /p;j4cz sound level when an 82-dB sound and an 87-dB sound are heard roczpk; 4kjvz:9a/d4 simultaneously?    dB

  The sound level 12.0 m from a loudspeaker,t-yns6(0 vh6ahr zv9o placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radia6h6sy(rv tz-09n a hovtes equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thea h,h+rw.pyd,3nx7hsm,j,gag sp(8x power output drops by 10 dB p ja,dswsg h,xa3p(8.+rnxhh7y mg,, at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectiv;gvgj -+kucy7ed . fubmw jc);om0 x3mvg(q (:e devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, i);qe3ug ;gvmdgc cju:wk0-bx +.o( 7y(fjmmvs 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain,m,2 w,ns)yu *gjv(tv-xqdcr9 vlw t6- $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a f6 bcj(i; qiav)requency 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,p4 pz nvuaakfa6j*9-3:rr zf long between fixed points with a fundamental frequencyf nj6z3-r ur,a4vzk* appaf:9 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 vi- qidxe gsm5/. 0evkwrk 3u)l3bration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so,i5-ek0w) 3x3/ grs.evuqm kd l 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube tvh 12d* e cz q2z)iribe6g59lahat is open at one end and also 75 ei*qz5h9a2 2v gcd6bez1 r li)cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as o, 8 v7vc4fqpgt3 s 07txise*afne 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 fromfa,x7:4whe aa two sources. The sound is loudest at 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 so7eaf: 4w xha,aund?   Hz

  Two trains emit 424-Hz whistles. One trai 2 giegq070crrn is stationary. The conductor on the stationary t0c r riggq0e27rain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistlepz5mr) pw -f(jgn,4fw as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How (g4f )mz 5jwnrf-wpp, fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed p*n.1b x7qsu aehqyx4zr0, )mof cars 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. Howq1 )m yzxaxp.qh0* senru7b,4 fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Th l mn+bvu4smhwpb303 2e shorter one is 2.42um03hm s bn3+4lvwp b0 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a st x3wn-t dan+r4ationary 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 tdtx- 3n4rn a+whe 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 normally about 0.+khy xt5:e5rva/ja/u2+q uxihoy- .z 32 m/s what beat frequency would you expect if 5.50-MHz ultraj5x5it +a vre+khuaq.xzyo //yh: -u2 sound waves 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 ax. )4k)val finb8h 2 rk95igxv moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat agxnx)85fr al i vkk4 bi9vh.)2fter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. The gs. ea3//p(b42xookily pa ,.rthb1q pulses are approximately 70.0 ms apart, an1(a./e,4obyrbl. qip x32kph og as t/d 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 signa ,p q7pfw+j(7l ai;l1jub+xeo ls from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is aboelpj; uwblq1,i+77 pxo+ fj(a ut 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 b 3).u9:95ekijiocj)jgcblvj y the presence of standing waves, which can cause acoustic “dead spots” at the locations of the prec)3 lj:jijiju9ckb .59ev ) gossure 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, 3 wphqag nm+t4f t(/2 kifxs1*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 ma*2x/t+ n3fwt( piksgm f14qh ade 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 hearv98of (3utkw aing for the human ear at a frequency of about 109uk8 tafo w3v(00 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 2.0nf pcv95t.8p0nxkd l6. An observer on the ground hears the sonic boom 1.5 min after the plane passes dired ncn509fpx lv.6ptk8 ctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isuryn0fw k7d . ez8,p3/4rbpk t,vafi0 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