What is the evidence that sound travelsbpdbp1jg5rc u ;l gfa/3ig 1.; as a wave?

What is the evidence that sound is a form of energ35(ppar uxs)fyd xk3 ;y?

Children sometimes play with a homemade “telephone” by c q 4cqcw- q;bok1: iei2(y3fkfl+0eoattaching 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 ccil3 c c21kfq0+weo4qiefoybq; (k-:learly how the sound wave travels from one cup to the other.

When a sound wave passes frl e /n0m-zcj68 repn:rom air into water, do you expect the frequency or wavelength to ch rp/nne rczme:-l608jange?

What evidence can you gbw,arlo86 ty3ive that the speed of sound in air does not depend significantly on w,btlaoyr863 frequency?

The voice of a person who has (+t 9xj8gp6n-gt/ a u*)wtrbv(iv br dinhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes?k,xa 8j:ahug5

Explain how a tube might be used as a filx+/ux y) ;xwxrter to reduce the amplitude of sounds in vaw+;x )/xr xuyxrious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mit5,5woq + aqvove up the fingerboard toward the v,iqw 5q5o+ta bridge?

A noisy truck approaches you from behindxeb zg(ci9qr+(/h 8: vmpwe+p a building. Initially you hear it but cannot see it. When it emerges and you do see it, itqvpexr ehm+9bi:g / 8 w(+(czps sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sai) r bfway) qpvj9/*2fbff+,wdd to be due to “interference in space,” whereas beats can be said to be due to “interferencq *fw+wrv/ d ay,f2j9b)f)pb fe in time.” Explain.

In Fig. 12–16, if the frequency of the speakers 5 qayy5xyf 1p5abty1t3i9hm7 were lowered, would the points D and C (where destructive and constructive interference occur) move farther5a qyit9mpyf1a7ty1xb 5 3 h5y apart or closer together?

Traditional methods of protecting the heari:b2 gdyt oq67ing 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, then feeds it to the headphones in addiq:ybi2gdo t76tion 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 thoughtbm9r2/oszazphx 0mk) /8i jpe 9)vyy: of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the wavm/9j9xepy)0 kz )2a8/mpizob rsvy:h es, (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 moj7*l6 oq9 rpuave in the same direction, with the same velocity? E76* lqrp j9uaoxplain.

If a wind is blowing, will this alter .rcrd+k7a+gq2z r -r-vx1eqe the frequency of the sound heard by a person at rest witc7e + +gdr-2rr -x.k1qarzv qeh respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child iaqfvq((onp*- 0ws 2de n motion on a swing. A monitor is blowing a whistle in front of the child on the (*(pqenq a2v-w sf0odground. 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 for the echo of h 0kk901rr 63zkcm tp rcfhr3+uer shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the l6kp3 00+ukfrr1cmkcr 9 t3zhrength of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hisj )nm doecgqj:*wq9 ik0b0(z7 ship just below the waterline. He hears the echoc jin0q 0 (eo7)zg:jkdwq*9bm 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 with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airpke0cdp.gd ws1k,,5 l at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just abovexw8o xaci+nxkx :3 .9u a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapsesaoxx.uwc38 nk9 :x xi+ 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 makes when st9s9o3 )- b uytrp+zvmsriking the water below is heard 3.5 s later. How high is the cliffs-3pv+my uo9zt )9rbs?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pave2ia9:/q wxl aament. 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. How far away d xliawa:q /a29id the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mkn+7*sy.+ggtjw ox.i ile of distance by the “5-second rule” for estimating the distance from a lightning strsgig7towx k.y * j++n.ike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at tm, e,sick.5ya icju4 9 t75u:1vf xumyhe 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 oy9nn+nlf+ur. .rtm / of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at8 tnfouljyy0g9* rj5jty* z8zz*;q u9 a certain place, what will be*0rj jnlujyz8o g5q* 9t* zy8uzy9f; t the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance fy2lh,p d8 ;pvr*-v0, zf yfwwerom an airplane with four equally noisy jet engines is experiencing a sound level bordering on pepl0 hpfd,w*,z f2vyy 8r-v;wain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have jc4ck /vvq:o;txv y21a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensity cv2cxq:4 1;votvjk/ies of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ogz1w 9sayn ,d6utput of sound from a person speaking in normal conversation. Use Table 12–21as6 z9wn, gyd. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is hsad 3c3u csm-*)2laz*wv ky8$5 \times10^{ -5} m^2$ (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 mz(rq*n ct,cpq6jn 6z4ore modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeakez( n66q cjn*p4,zqcrtr 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 placed 2.8 m in front owu4f*n;wt 8 fbf a loudsuwt8fbf;*n 4wpeaker 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 deteif- h7:y uwyemy*3v1ect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of t 7iweuy ef*-3y:v1ym hwo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavrzb 6zn,)e rj8e is tripled, (a) by what factor will the intensity i,jn re6zz)br8ncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, c.5- ;pbkv,y6wukq zv3;csx )prfo2 g but one has twice the frequency of the other. W p5r ;ykq wfbu6k;sxv.-,gvz )23op cchat is the ratio of their intensities?   

  What would be the sound level (in dB) of m4nxsi-7i 3i ya sound wave in air that corresponds to a displacement am4i is3y 7ximn-plitude 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 *iw t1mp 77j(z,g cd q/zl-l.xne*sqt100-Hz tone that has a 50-dB sound level? (See Fig.x*j et1pwc z(nd ,lq- 7*/gt qmszl.7i 12–6.)    dB

What are the lowest and highest fr nis4ozl wp1thymwlx )10z+ (3equencies that an ear can detect when the sound level is 30 dB? (See Fig. wh1(oi+1lp3)xz4sy l0zn t wm12–6.)

  Your auditory system can accommodate a huge range of sound levels. poez+ 2/ m35rteg5zal What is the ratio of hig2mp/rl 5 zetg+o5ae 3zhest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. Tp+povm*p3xqff.0p 3 u he length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stfv*.u p 03q3fmx po+ppring be placed?    N

  An organ pipe is 112 cm long. What a-;+ mi rcw hkqovasy*lz(d.2 8re the fundamental and first three audible overtones z d(+8qm- .sawo*cilk;yv2rh if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect frb 1k4 t: h (yff(kfzxdz/k-s8aom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a cl y1 k:kd -ffb4ftsaz/((kzhx8osed 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 pipesetm:+ oi wp9u. spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the len9iwm+t.:oue p gths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fp g433ixoxc i)n67x txrequency of 540 Hz as its third harmonic. What will be its fundamental frpnoxgc 3tx3)x46i7 ix equency 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 pla4(+a 5f1i ijccd ac*l:,myfeoy E above middle C (330 Hz). e *1dm45jayiil co(c,a+f:cf
(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 orga3n b;:x.ohp,d c+/ehbas xw9zn pipe that emits middle C (262 Hz) when bes xno:hab.wdh z/p,9 ;3xc+the 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 at 2k5ohnd4u (+8.b2wnrbte w3- p /hsawu0 $^{\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–gvtu9:w k5f0dwmg g0* 10 should the hole be that must be uncovered to play D av90tgu mw5ggd* w0 :fkbove 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 c:sm0z yjxo0; 0ilc *-jtqypj:an resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this isxojij 0j zsltc0 p-; *m0yyq:: 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 at two sj54rc 1 i3vigw7z9l-p om9 fgnuccessive harmonics of frequencies 2projcg75 m zi4n1gv99-3wifl75 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 wk+w y:sn/sm)t lwz0w1v )av .$^{\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 r9t7ba zg; (i xv1;uxkuange for a 2.14-m-long organ pipe at 20 xzuxt(k9b; i g 7uv1;a$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2ie/f4ymp1v x4 .5 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 waves4fp4/x 1emi yv in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s w /q4,tp/l, exnvt*xachen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stri4 p,n/lx/xqa evt c*t,ng? ±    Hz

  What is the beat frequency if middle C (262 Hz) an:sv sh s2mz in .0g9v( dgxbz/95e3+q,lactphd $C^＃$ (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 (brand X) operate;d .eaf.oa0iarpw *.is at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs wh .dp..a*i oe 0w;faiaren they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded w5of 5wgtwm55;gu ovd5 ith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning5u5 f;wdgtw5gv55omo fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned toe1+pwn3bsweo.,s6b p -oa(cz the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequ s so1+-3pc wob,en(az6be w.pency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to playhfvk5 l1p ak2mu) 1n;l middle C (262 Hz), but one is at 5.0°C and tn) 5u2phmfka v;11llk he other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fgk;;fl j z:txo nynx9;/e05j f:vy3cuorks, 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 be;tjv0cyk 3z e/ xg9n5:xjn f;flu;oy:at frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one spgm4 o1pab y57u2km1y woa yfhkz72q1.eaker and 3.50 m from thaa zhwpfk4yukm2 2m1y11g b. y7q7o5oe 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 sq)juempp(4z1 ud8* akmgy)u.+rf k*q upposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.km(uq zump ))*+8qg du ayp*e4k.r 1fj0 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 mw/x0* 1c-5,uz pukq/kiukr kv and 2.76 m in air. How many beats per second wil* 0q ,wuz5/ur k- /kkx1ipckvul be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at rev bl p+dplr/hcv2xn8;e1g ,j,st. What frequency do you detect if you move with a speed of 30 mvn2gjprlh;bp edl,+ 18xv, c/ /s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engineqz/(bhn ;/jp g (f6wvy5wet9 a whose siren emits at 1550 Hz moves at a speed of 32 m/s /a (wq/9h(ytb5 ;venw z6fp gj
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towar0omz :rz;mr z:,bt*wid you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same?;mi:b 0rz r*:ozw,tzm 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 singnu.nfzu* kf )p4x7k) wle 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 freque *) nz4fuk7).uxwn fkpncy the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wdl) aur/5fqa ,3w jfdr9 0(w 5d. uompn3pd3kfaves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is tndrddqdw f upa 05 .wakf 3f()pul5j3/ ,ro39mhe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fco s7y (cwerncoc)d*cm 316;r1 d .gsylies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in tn6y3y o(mcgs w ;c.r1scd1*o c ec)r7dhe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experi,uwcoudajw .+ 7)x):bjz-p6e why t* l vy*x)qments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the stw6.yxljxw qt zbvy *)* e7ajuw ,hp +):-cu)doation at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spee:xrjcy c,pn4hy9i o+9ds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s Whatc +hiyy:o,99xrn pj4 c 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 fre .un :4e+l;ypr3y8xetgoos) cquency $2.25 \times10^{ 6}$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 frequ/zfrbmgp43 mg t9;9fzency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obsg9 349 b;zf/rmpmzt gfervers 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 rlmv3 t/ 9gg(qpux ,1tits speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speec4 t/aow*(m ijve;4yzd of sound is 310 m/s (a) What is the angle the shock wa vzmj/;twyio4e *4a( cve 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 atmosphere of a planet where the speed of soundl vbb1wsm*ndo9/g.4( dn*9st h lil h1 is onls1l*(4d ogh*bnl ldbv.h1n/t9ws mi9y 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 ocean. Dq se*,vw3 7f vuncmwpu63vt;6 etermine the shock wave angle itu3w*v6;p7mv v6t u en3c, sqwf produces
(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 svlzs0m uw(-4$/theta$ 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 exactlyi v.qy c6(t0gzbz01tg 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12igz00tt6 cqg1 .yzb(v–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 20,000-Hz sou.v go.ff*t e,knd pulses downward from the bottom of the boat, and then detects echoes. If * fgk v,tf..eothe maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hzfl:7 fcomw 9i oq/4n.qap;v,uman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of m+,-bi(gk ikc4+g w6fh zv *iuwany plastic pipes of various-u 6b*( gkhk++wv ,fgc4iiwiz 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 to ) kz *k2pu gpwxfk545hzdr45othe threshold of human hearinz)pw5p ro5khkgduk*x44 52 fz g (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 y x,tdcxz6tgg1); (bwsound are heard,xg(gt yt) 1xw6dzc ;b simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What i,+ai*cq kcuc9 14x tyis the acoustic power output (W) of the speaker, assuming it uck y q+1*xiia9,c4tc radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops bfpp17 okgn exs+v*x0 9y 10 dB at 15 kHz. What is the power output in watts a1xpf n 0x ks+7*9gpevot 15 kHz?    dB

  Workers around jet aircraft typically weara8lw6z80 gevm/:;d:nyyhu v q protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What8:/nvqe :yug;m0vazdlhy 8 6w 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 gsdk3ern)j inna-a; .: ain, $\beta$ 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 tunbzyhq 6c 1*2ijed 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 isn2 z3r*uh m,w8romj)f-x qcwn9j q(5d 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unitwn j u r,oj2dwr95-8mn)qm3 c(fzh *xq 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 in3p:u ov s.yqr7r30bzl cv63mhto vibration above a vertical 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 withcbrzu0olv 3phmq33v6. ry: 7s 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 that is open at one end142uk3yeun mn and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamenenm 1u3unk y24tal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full m bmkilre7f dkb);,e9 e+f7p9loop ($\frac{1}{2}\lambda$) 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 500–10w zcn((d5agjuxg1e/vl4bk + 500-Hz range coming from 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 thgvkd(l c /a1ngex5j5 b(zw4u+ an the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The cod/f i4/hnzcfk2y94s v nductor on the stationary train hears af4 z2ksf4vycdi9hn/ / 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 whistle as it approaches you is 538 Hz. After x k):uadqld +h(0vp3s it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume cons0 xha u3k dpl)+:dsqv(tant velocity)?    m/s

  At a race track, you can estimate the 067f a apg+pjxspeed of 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 straightawa 0+apgpj7xfa 6y. How fast is it going?    m/s

  Two open organ pipes, sounding together, producmnp*5n:fukrx 7 8se z:e a beat frequency of 11 Hz. The shormk: e8z snfx7u*5r pn:ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sta 7y*qn6yw/v npkngfje*1s / 5+arnl(ptionary 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 sqr716+/e/(npa *jn lwv5 kypn nyf*sgpeakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta icyk9/r4o+/ k6 dxng mvs normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected frocy/ n gd9 vrkkmx/+46om 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 atnf5kvjzb:f4b , k9 +mk 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 frequef,z+km: b 54kfbknj9vncy 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 axr )ktou7emo x9( toxj6.3um3 moth. The pulses are approximately 70.0 ms apae73.6ujt( tuo rx3m o9xko) xmrt, 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 oncod;e5 / bsj.5em5o0khq; yese 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 5.;ckes;h ebd/ 5e mqjyso05o 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 stcr)em it2dx -2ereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.m )2i2r-c tdex
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratiob(jjl w -.x)um,4xlkfn, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoif,ml-xjb.l4 x)jk wu (nt. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearinahp)yq d:) 4o6fjv, ckg for the human ear at a frequency of about 1000 hf) aykovj4 6qp c:)d,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 heanz x3d f + z,e1;e-qaejgc*jo;rs the sonic boom 1.5 min after;ocze-fge,q en1zj3xaj;*+d the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat9h0wo:n z-hdnkf9 q ;0k(ig:ksm nt(d is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h