What is the evidence that h4u e5.ovvi4isound travels as a wave?

What is the evidence that sound is a f )3v kc365 hrnfhzl:koorm of energy?

Children sometimes play with a homemade “telephone” by attachi : a6t3ad o48tqu(sun)kid 7hcng a string to the bottoms6t:7o tcu(8sd hd )4 iqak3anu 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 travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wicu ppw 11k37 rlz1:en8uyq,javelength to chang r7i1lp 8,cjy wzq1eu31k:up ne?

What evidence can you give that the speed of sound in air does not depend sp+ k f3qgsiz b-t;6vy.ignificantly o6py;q s3+z.i -ftb gkvn frequency?

The voice of a person who has inhaled he6b 8*lkpcxz rw5n(fewthw 8:g+:b e )rlium sounds very high-pitched. Why?

How will the air tempera / a.zax+rhih, q;pu8 t*ws00bho1j oature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ahp3k+88 qm j l2qjbg3vmplitude of sounds in various frequency h38kj3j q8 +q2gpvlmbranges. (An example is a car muffler.)

Why are the frets on a guitar +x0wrtfgi4/n/d ogo 2:f4tyy(Fig. 12–30) spaced closer together as you move up the fingerboard toward the bxyt:fr0gd+ /yfwi/ 44ng o2otridge?

A noisy truck approaches you from behind a building. Initrwk b-brm * k62 .7w;1dxhlpenially 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 h1bw .m;p-b* 6lk2 x rer7wkdnhigh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,ls;j;id wx 8jpnh1g90” whereas beats can be said to be due to “interference in time.” Expl;;8w1jj il px09shngdain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points mwjzc)0)miv o xi/ 6/zD and C (where destructive and constructive interference wxocj i/ im 6)vz)0/zmoccur) move farther apart or closer together?

Traditional methods of pq ta/4 v;lxvp*lk mkq0 ok*vrv ,s738brotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or re/4kvmsk0apx o*,vtl r*q7 qb8lv; vk3 duce 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 levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thouvbo;o, 9n g(fe4xdijx z tt963qcxn)0ght of as a superposition of two sound waves with sx)o i6;cv4,onqxzefnjdxt99tb 3 ( g0 lightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mov3c 6/g*thg z(d ctt:roe in the same direction, with the sameg(gt 6 t3*dcoz:trh/ c velocity? Explain.

If a wind is blowing, will this alter the frequency of ib80l- *opspgf; ai py(o; 2xxthe sound heard by a person at rest with respect to the source? Is the waveo8; ayil- ipp f;0*p(xso2b xglength or velocity changed?

Figure 12–32 shows various positq0oq 1xi0ts.vions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which posiox00 qv.1qt sition, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sh,g4cqxdf/5ffaex v28 out reflected by a cliff at the far end of the lake. She hears thfffaxd e g4,5xq 2cv8/e echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his f7up o sc mo6hey9(qy:/-wwm+tm2t(gship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean w:umo yc+-s(gy2 mef moht/7 (p6t9wqat 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 wavelengy;f qk wpq)4g,ths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna bl sxma1n,y -+vb o75bon a foggy day. Without warning, an engine backfire occurs on another bm,5+bsb1 ay7-nolb x voat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clp*2 tm /19n5uxb3xnfj qyv2aliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cli n5nfp *xauj2ylvb9qm1 x23t/ff?    m

  A person, with his ear to the ground, seeqhie9h9,v a5w s a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they9hhw95ivq ,ea 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-sezuv,t+8 y1ks5 1dmoaccond rule” for estimating the distance from a lightning strike if the temperature is (a) 3k 81causy1, vt5dz+o m0 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le3hd, zxea5bv dh*8 od1vel 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 intensity if1 4p ,qbhe-jw4b5 fges $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at2pjezm(9a 7 awvpyn.v 7mpl37l7u 4tt a certain place, what will baept7u 47 vtj v 37(pnl.pzywmml9 2a7e the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wi6 oiwo/fg4v0bm qi-q//bg m wxr(7 ,vith four equally noisy jet engines is experiencing a sound level bordering on pain, 120wio4m/ /bg7/qvw-rmqio6 ,0vb g f (xi dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a g2d +orlbbf7t1s su3hw ;klo)vo(5k;signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device?rdo5u ;g kbkh(+s73o2lw1)f olbt;sv 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norma5-kr x ocp;,kyl conversation.ykprc;k -5o ,x Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose ar 3qu c4 xl) -pzwrrp1zia4fj28ea 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 modvv k:rq yo8)i*e9cl ;nest 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 loudspeaker connected in turn to each a;v icvo 9key)nr*l8:q mp.$I_{250}$ =    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 1/ j5 g oydsd 4eh1l*md3zu+3ln30 dB when placed 2.8 m in front of a loudspeaker on the stage. *dd4yjz uno3dhg3l5+sle1m /
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level n,.r8 p lpj2dp kupy-/of 2.0 dB. What is the ratio of the amplitudes oj .rp2kd uppl-p/n,8 yf two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is2x8 fort(k exl2q3)qq tripled, (a) by what factor will the intensity ik) lfxq22q3 te(x8qo rncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twic2xcg 1j29a+mn(cwxcf e the frequency of the other. Wwc c manj(g2fxc19x+2hat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sounc dfn34p/oca6:3xn vf d wave in air that corresponds to a displacement amx o33n46/ cfa vpnd:cfplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lckh ;lu9k)-txfx +4o devel to seem as loud as a 100-Hz tone that has a 50-dB sound level?f l ; o9d-4ukt)xhck+x (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sounr 7k7jzir3kosffqm(.se*i2 m:d;+p wd (jpiekm:f;r*q.s7zk7m sdrfi o w+ 32level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accomqa,5-diiv66/53 8g u6xboq gn l)o lefh*hympmodate a huge range of sound levels. What is the ratio i5yl ,5 vf-bmag3oh q*x )u6iqdne h/l6p6og8of highest 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 fun 5bu:vp* 7hs rh4ixs0dkr:; sndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 u nssvh;xbirds: h 74k* p5:0rg. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three9g* d.gaqlsfc bh :-*c audible overtones if the pipe is :l* gfca. 9*cs-bghdq
(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 topnhlp/n;vo +3(ii i hu5 of an empty soda iin lni /o3hp+5u(h;vbottle 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 pip6yczv-rytffkf6)w :j4wgj:jia6 f 9- es spanning the range of human hearing (20 Hz to 20 kHz), whwj-)yzf jc :66-f6 k:4ga9vy wrjt fifat 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 hara0u6*qx aezlek/ n kv(h-jr2-monic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengtj 6a2 -ax 0euvek-r*/hn q(klzh?   Hz

  An unfingered guitar string is 0.73 m long and icj.d1 vj 5w b z809v2uoheqk mee-91kks tuned to play E above middle C (330 Hzhe-bcv.1z1kk9j9dm k vo8uw 52je qe0).
(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 len unz*ue9mfk,.yb3994. irjgqz wq)x sgth of an open organ pipe that emits middle C (262 Hz) when the temperature is 29kez) fjur39in*z9u xwg4ym b,q s.q.1 $^{\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 ad3km(90ty6vs)io gv50dfcnn t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ofgv9wv.:p u8o /in.+f ,ccv jga the flute in Example 12–10 should the hole be that mug,c8 vg :nw+opcuf/v.9.j avist be uncovered 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 resonatvp,zren t6). xlqy0(d0bfc) se at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an bvedqz 00 ,rt ( sfncxy6l))p.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 resoc6g5 ae;qxq,1 b-(k svdm5bmt nates at two successive harmonics of frequencies 275 Hz and 330 Hz. What iq-515kqmbmxgdc6( ;av,st eb s
(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 zd0zf8qn y51iuf;ov9$^{\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 pre9i h8; 7mgeuylsent within the audible range for a 2.14-m-long organ pipe at;gi 8e h7umly9 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to t :yzwk,c (ti4ghe outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) tgc4zykiw, : (of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears l;vtu(6e y4 iged a(.rone beat every 2.0 s when trying to adjust two strings, one of which is soundi ;l(ayvd 4.eg6ture i(ng 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) ags;yl+0 i mzqt7(hp2znd $C^＃$ (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 gz revo)c7t7w-m+y4k23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whist v gmc)74tw7z+ey rk-ole can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuningzbgow s*xfcinrf: ie-7 -7;f1 fork and 9 beatszw:ib*; fcxno-r7 ig-7fse1f /s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tune lr l/vj09ow:k3kemi 5d to the 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 skj :ml3viowk/re059 ltrings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try tzfzpd6e.gu4akyzy 4bg v+b :45 +wrp1/ajss.o play middle C (2624e44.p gy +us.: kya/rda6zzpzs bgw5vbf j+1 Hz), but 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 freca9 *lzx i-gm1quency of 441 Hz; when A and B are sounded together,ixc- 9a lg*z1m 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 together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are z/;lur:yz +ioj:8 dzs 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m fr yulj8 iso+z/dz::;zrom 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,vun2rs2 .v7 9m / n kusw1ms:*aukpe)d but a piano tuner hears three beats every 2.0 s when they are played together. (a) If ovump 9:)km uur2 n7a vs/w*ssk2 1.ednne 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 waveleng+w p-x) ,iaztsqd31xhths 2.64 m and 2.76 m in air. How many beats per second will be heard? (p3 -aq zd)xt,sw1 hi+xAssume 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 rw9whv3 zdf: ,mest. What frequency do you detect if you move with a speed of 30 m:v fh9w,d3 wzm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Whao:f cj5h.+k8sh-g lh53 lmqgi t frequency do you detect if a fire engine whose siren emits at 15k5h h ci3.o-sg gf:+hj5l8l mq50 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20k/ ;:;m,xpw*cpip v qm00-Hz source is moving toward you at 15 m/s versus yo:*p;/, mxvq;wi mppkcu moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equippedi7-ck47xi 4s ( fri7pizsowlu 5(/ua v with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at i(lsa 4u7-i(v7zr/u fpi w 4xok7 ic5srest 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 ultraso70z f 5vmfe 95exys3ejnic sound waves at 50.0 kHz and receives them returned from an object moving direcyfes5ee5 m7vx j09zf3tly away from it at 25 m/s 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 emits an uykg 3u --ixumq(gju 0yt6by gi(yu,;7ltrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave? qju;k- gmt0-ig(,i xub gy3yy7(uyu6    $ \times10^{4}$ Hz

  In one of the original Dopplerk.nq8tz0 +epy 7qkp a- experiments, 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 station atpy.+k 7ap 0teqq nz8k- a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedsw)q 4br:6yslx . Suppose the device emits sound at 3.5 MHz, and the speed of sound in hul4y6bsqrx) : wman tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ult p)h9 7)wbm3: 8u:svrbou7nz3aedmmi rasonic 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 of frequency 570 Hz. When the wind velocity i9p/rx q7qhs s0s 12 m/s from the north, what frequency will obs qrhs0s/qp9x7 ervers 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 objechg ze(+6yjp b;t moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 wherq0r z1c5w wmwc /-4oww hw;.mre the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction ohwwrw/0cm1ocq;wr wz 45- .w mf 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 h). l y.ej.r:x -xo(fgt-yeagw lu5 +iatmosphere of a planet where the speed of sound is only about 35 l +5eggj.l.xr: auyh-ty(xo-f )we.im/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. Determink- hpqb 4a (fwtd/)-fxe the shock wave angle it produces /ht4kwffp )a qdbx-(-
(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 y44 l-rpueuc-3q(jol2 zj zm.$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see 6zfbb ..lsby-lwfb;q; *2ng y a plane exactly 1.5 km above the ground flying faster than thebfbs g b*wz.;6;y2y q.-nlfbl speed 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 sonar device that sends 20,000-Hz sound pulses downw v9pmy;/s 3u0rzx f:) g+5wbub(hlgw card from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desi wuz0 mcslp:y)wbbvr5+ g/f39;g uh x(gned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves ar-j0 xl )vr (rtp.uj0binyp. 3ve there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dis( v./e(gwqmtaplay called a sewer pipe symphony. It consists of many( em. vqwg/at( plastic pipes of 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 to the threshold vrrxq5c:- pr b56w/oi of human hearing (0 dB). What will be the sound level of 1000r 65ir5r/p-q:cbw ov x such mosquitoes?    dB

  What is the resultant sound level q(1.m8ovkoabnz ue4/when an 82-dB sound and an 87-dB sound are heard simultaneously?(m q/v en4zbk8. 1auoo    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What i u :xper2/,upl9my e3mg5/fy js the acoustic power output (W),59g m yp x f//pl:emy3euj2ur of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Tc di(.pcnlx6 9he power output drops by 10 dB at 15 kHz. What is the power output in watts cx (p nil96dc.at 15 kHz?    dB

  Workers around jet aircraft typically wear p7h5:pv (fsqa mrotective 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. What would be the power intercepted by an unprotected ear atq5:(maf h p7vs a distance of 30 m from a jet airplane engine?    W

  In audio and communicati+.jn ; /ana+ofztl/x9 p; wgktons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to afrfi/+g7 wg g+6 br8mi 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 poi v fhr0uw/m j;byeefe (ou420:(: ccoints with a fundamental frequency of 440 Hz and a r:mfie/ 0(c b 2wo0coh(f 4;euj:yveumass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical opeu;0l19r2fz )fn8u nznl4f nkfn tube filled with water (Fig. f82)41 nlkz;n90n nzfr f lufu12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one endajyh.l5 dlfs(/ad*05t h m; ws and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third har5h*aa 0dsm/;jys5w l .d(fl htmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one6 n yc /s45tsnyc.o)qn 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 two sourceep)q;(a *a c9gv9(hjsf3ezka s. The sound is loudest at points eqee9zj hg(a*(3ca9)p sakq ;fv uidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conducto(o(pshzgt/ m d cpaqy,x 9b)kwkr:+4 :pu p8.dr on the stationary train hears a 3.0-Hz beat frequency when the other train ap)k/shbay :r:g zxc9 +(4( pm wdt8puq .,pdokpproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whi/r6y/prcl*h,c nz1j o stle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving lz/ ro61 p*jyc,/nchr (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by 47oml zj0/d vllistening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a ful d/0zjl7o lmv4l octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soa ha,6 3q2/o/3dqa gs-*4ovhmfb lcld unding together, produce a beat frequency of 11 Hz. The shorte24h /lfl3 6 -dbacaao/,sdqgoh mvq 3*r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends fycw9tz v w068cv,7 tkof a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have iy0z7fc9wv8 ktw t vc6,dentical 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 speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in t bb4li9/ux/a phe aorta is 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 from the red blood cells? Assume that the waveibpu/4axl 9/bs travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed b /w*wn 2-fvtv6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound w ww/t*v-bvf2nave 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 frequi((cxd dm;5k cency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms a(; ikcc(dxd 5mpart, 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 5gl tcur9v*mm -;lo3smo( :za used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtonet9ml5:( crm; 3o-vzoum lags*s is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be c7,0jz6aurvyn( 0 dtfx ompromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a liviny fd7(a0 ujrtv0zxn, 6g 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 rod46(;xdxxogrw *cdmx5kxy5k . s,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Witd5 xyw;ck rm*.xd(x 5xokgx46 h 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 fo x)ca v/lrlbaq .(yf2h: r*7anr the human ear at a frequency of about 1000 Hz is )2*:vbaq (h.n r l ryla7x/caf$I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears tnae.c .yus8,e he sonic boom 1.5u,c .n.8saeye min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 hd0y89q-tl p8ag ou 3f9tp i.s$^{\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