What is the evidence that sound travels as a wavedq1n;nl 93ys d;q ook6?

What is the evidence that sound is a formetpyjo ;6mct)p9 7f.o of energy?

Children sometimes play with a homemade4.s 0fy(sl mvgm9n./9jvbx-nnei n)f “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave tra(0fm)n igfn/vms-l ej.y4s 9xv.n9 bnvels from one cup to the other.

When a sound wave pas-ay zhrb2/ii6 ses from air into water, do you expect the frequency or wavelength to chan2yr6zi hbia/ -ge?

What evidence can you give that the s q ..5/4rjqgvat g: f3dkeyn4vzg3p;epeed of sound in air does not depend significantly ofn4zvp/;r 3qe3a.g gt : qj4kge5yv d.n frequency?

The voice of a person who has inhaled 4)yjh affe8ey0-geru-x q h(6eu,e;f helium sounds very high-pitched. Why?

How will the air temperature in .v3 z)3)l8g ol oaiq;2kzquuba room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce theo(jv:d6km qke 6:li 0z amplitude of sounds in various frequency ran0zmik6oj: 6k:d ( qlveges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move yk+b52 vj plj/u.4 jg:l t5ulcup the fingerboard towjp5/:lg2 cjukv5 bl+j 4l.tyu ard the bridge?

A noisy truck approaches you from behind a building. Initially fz0-3 lt2 akiw05vbswyou hear it but cannot see it. When it emerges and you do see its2t3wkv0a b f5zl0i-w, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be dues0trnkhbf4gpg*:+j , to “interference in space,” whereas beats can be said to be due to p+ktjnrb,f0g*4:h gs“interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,wxtud4-g f2o * would the points D and C (where destructive and constructive interference occur)w2*o guft-dx4 move farther apart or closer together?

Traditional methods of protecting the h2ij/t7zspnd4y,;g .z wfg nru8df69rearing of people who work in areas with ver7fgj;4nzd/ n f. iu dt2g 6rsrp9zwy8,y 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 levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thou,u8 n(,g(fnro4 blyt nght of as a superposition of two8yn,no(4b( n u fglt,r sound waves with slightly 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 move in the same directiouj+vtz(5y aq -n, with the same v+(a-zjt vuq5 yelocity? Explain.

If a wind is blowing, will this alter tg( omywnb: y0(he frequency of the sound heard by a person at rest wiyn(go w:m0(yb th respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a sj9l8:m-bbzr swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whirj mlzb- :98bsstle? Explain your reasoning.

  A hiker determines the length of a lake by listening oth9fs c4rl8f:tz0x ;azp o+-for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 clf4 tt9oo:+-f0rsa;z8z hp xs after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his;d0o l1:xha72x grmgy o)i3vj ship 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 at this point? Assume the speed of sound in seawater yxjg)vlx ;aodi:1 o 3g0m hr72is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelen 4kxidp.24xtw0ml:kz dpw/+ogths 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 jd8.. im 4kcu)- hhjc*d2 lhcquust above 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 elapses before the backfire is heard (a)d*qh.km84ch ch . j-ilcu ud2) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes tkjjm -4gs0 lme*nm-1when striking the water bel 4-mkl m0-mnjsj *t1egow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone 2loi9xfv ,h.s/ *r tnrs/z;ef strike the concrete pavement. A moment later two sounds are heard from the impact: one travels intszhx fif n9/2;./ vlrre*,so 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 oc(ti id m;.p+;+dhlrok : f.0kfv )alfne mile of distance by the “5-second rule” for estimating the distance frhkodtif( )r kl +pavl; dc.;ff:i0+.mom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atyn 3,zyk3 :ln qx bbp5+so2,eg 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 nym(8 dae*p:e whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when4yda/l* h8z ce8a5now fired simultaneously at a certain place, what will be the sound level if only on5ona/zc4ly8*8 dwh e ae is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eqncpkwcky ut 4(;4(jn +ually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would thi4kw4n(u jtk ycc( +np;s 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 signal-to-noise ratio of 58 dB,vp(k 0w0z3y m a gf:pc;ncg(vn9 by2;s whereas for a CD player it is 920yf3p9c ;0(msvk g(n;n zcy v:abwpg5 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outputx2*9yexm4c ,x vsgklcl9a.p+ of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly x2 .mxkc 9+s9l v*p,e gal4ycxover 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 strike(j a*2rwmv ;rt: u wp)d0hvxo2s an 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 mod.qg( kme2 h nkc6ens qr/a2q9)est amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from anemqr262n/ (gq)e9hcsk .k aq 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 +p: h :b (b l8priutnkz)7zwv1registered 130 dB when placed 2.8 m in front of a loudspeaker on the stawztp 8ubi+hbvr):: l (np 17zkge.
(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 of 26sp z(9f8 r5afuzott -.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this 56t utf-9sa8( fpzrozamount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intnk: :jx.rt;)v vkpk.g ensity increase? Increase by a vpn ::r kkkxj.tv.g );factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equyge6y.am v lz) h,*fw7aon*i9vft.6e al displacement amplitudes, but one has twice the frequency of the other. What is the ratio of9e gfa,a6 y*of6*t i .)vzew .7nmlyhv their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds .jwa dnp:oh+ wu*/3u4c xffm;to a displacement amua*ujw: + nf;o4/cmdf3xw. phplitude 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 100-Hz tone th6: m*svq5i.vvz;aqb2 ydii;l at has a 50-dB sound level? (See Fig. ml vi;.viqdq*; 5ya6v2zib s: 12–6.)    dB

What are the lowest and highest frequencies that an e39w7 okdmn/k r 3etb4nar can detect when the soundn/wktk b3rn74e9o3d m level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is th;x8ppj8pf 0-6n:p) ufy d6btbpqk jw1e ratio of -pjwbkqpny f860x p;u8 t jb:6p1fd)p 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 hasn lcz39y3d0sr ts a , g/mwbejqe1x;6) a fundamental frequency of 440 Hz. The length of the vibrating wmg6yqsezle3b 3d, cr0j;ax9s )n t/ 1portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first ,p55. z2yqlo hq )yaqlthree audible over)y 5 pzlq5aqyq,o2 hl.tones 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 expt g(1c1jgzy3iect from blowing across the top of an empty soda bottle that is 18 cm de1 jg(tc1gzyi 3ep, 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 7r*sfo8:kh) xrjw- tcopen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes crrhst8j* k:ofw -x7)required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thi 7)mwlvm vgz yu+,d(j(rd harmonic. What will be its fundamental frequency if it is fingered at a lengmul(jwz v(+yvm)7 d, gth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 f4m ut. f7quh+m long and is tuned to play E above middle C (330 Hz). u.h 74fq+utm f
(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 or3 q+s,v8m85.e9kxny erl . mszg d9ykygan pipe that emits middle C (262 Hz) when the temperature is 8xy,skvg.l z ys9n.rqyme 9 5+3dmek8 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 atdi ana n 4kzgt:pe(hvq,a2s0gl3)/8w 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shov9m.i qp5 u5 *f nax6kzrim;r5uld the hole be that must be uncovered to play D above middle C at 294 Hpi56kmux9f5qira.; 5 nz mvr*z?    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, and 616 Hz, but nxz(ztr.73q0r gvrke 6ot at any other frequencie rgvtr rk0(6xz.3qe z7s 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 lbnm*vv(g o28as1:m x,j i.xm is open at both ends. It resonates at two successive harmombgjv,i.an (x 8o*lv2 m1m:xs nics 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 b*v7w v;oul0zgz(k6etwy6 zby92f,k$^{\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 withitb zn0yc,52pg t7yi gb 3r2*;aqmm5gy n the audible range for a 2.14-m-long organ pipe at 20r3 ttzm n5* bbg,7igp 0c;yg5qy2yma2 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside and t:ipqr7z4u,fis closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the gru,:7pqr ztf4iaph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when t0dvnx 4-wo ij7rying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency4 i0-vxw7o dnj is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz ocgxb nhilj.w4e8555) 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.qm 4rmbi x(8yy5o-7u8cat q-;u.jh cw+fbsy 55 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, 7o- sih5xqaw.y+8j(85ry cym b f;cmtbq-u 4u 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 tuning fork and wv)0te aibh 0 l.s7.ge9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your re7alvweth ).igb0.0seasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensik0b/x- /r+/kifdp pgwxel3x c6b ub5;on in one string is then decreased by 2.0%. What will be the beat frequency hearu 5 gbpc/6x/ elb3kfk0i rpd+x/bx;w-d when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be t4pwg;yb 6ch87: fkdy f4y/ lcheard if two identical flutes each try to play middle C (262 Hz), but one ifk6:yy4;cg47f/hbc 8y dptw ls at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, s:+*p:6asajarjjm e1 pldo7) 4ogn-lB, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frel71s : aojjnrjg4dl *):-o 6pas+aepmquency 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 1.80 m apartal45 5hjadgmlk0k u 15sz1n h3. A person stands 3.00 m from one speaker and 3.50 m from t ah5hm0l3nk4 11gk s5dlua5zj he other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano thg u-li(ie8( huner hears three beats every 2.0 s when they argihi8(e (lhu- e 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.+q(/hf lb0wyk64 m and 2.76 m in air. How many beats per /y lw(bfhqk0+ second will 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 whkg9 0a.-xf dc(fs21zuf wnu0cen at rest. What frequency do you detect if you move with a cudxffs 9a-2. wgk( c001nz ufspeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you dete 3 5teyl tiiye iy3f55rk1:/rfct if a fire engine whose siren emits 53e eyl5:1 ktirry/fi 5if3y tat 1550 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 2000-Hz source is moving toward youce** re9v (mrpqzrggs+9y7gyl us)1( at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they closeers( 9urv+gz ylyqgrc *gs9)(pm e*17? $f'_{source\,movine}$    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 sn ms59 *013h ol8noqouwkvah7ame single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the fr87oq1s a0u*l ok9hho m3n n5wvequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives thejw:eau xe:, -sx.cifd jej;09oz8f(rm returned from an object moving directly away from it at 25 m/s What is the received sound frequency?: 8 ee0(-wsu9acjojz;xrd, .ei :ffxj    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emxdi f 070 8oueprj6ldk:n*p3gits an ultrasonic sound wave with frequency 30.0 kHz. W*78j xp3duo in0fkl60g der:p hat 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,z d l9xi(p hsr072ojk moving flat train car at a frequency of 75 Hz, and a second id2(0rizd,o xlh7ks9j pentical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wj6 cj5luk4v3 y*o/u nb x9v 1.va+duvzaves to measure blood-flow speeds. Suppose the device emits sound at 3.voz3 al*xcvku./d uuj49 1b6+ vyn5vj5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ulxp ) g(lms2ft+trasonic 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 ;w(9dv9b ctol ir2ize kp jo. m2t( 3ervvk918570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest,re2i;l rvbv(3otkm( wj89ivop c e.t21dz 99k
(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 onya9qk x/ uvvk9v /x6k5 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 where the speed of s9m f qfq*ts( ;k ij tqabv6,f81cje *.t7pmq;bound is 310 m/s (a) What is the angle the shock wave makes with the di kq*7q;,v6a m1fejt8 .tbtcm*fpqi 9;jb(fqs rection 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 of3 jkstm2u,q ,i( t8gzw a planet where the speed of sound is only aboutm ik t,g8, zqj2ts(uw3 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. Determine the shock wav jfh/t yc02oq s(u-ht(e angle it producef 0(hj ht/su (ycqt2-os
(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 cdsysbe bp1 w7z 54s01$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a+0-m (ekx j -corr+kel plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travelee(+0r+e - klr xokcj-md 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 downward fro z;sq x7a1x/njm the bottom of the boat, and then detect7xa/j xq1zsn;s echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are/fjn+zw d+pnn yek6** there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of e*+g:/ujucbfdf :b x 1many plastic pipes of:gf bbdxj/*fec u+:1u 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 osq/y/ e oiam39f human hearing (0 dB). What will be the sound level omy /qe9s/aio3 f 1000 such mosquitoes?    dB

  What is the resultant sound le )bm neg7ecw7lrd-1/ yvel when an 82-dB sound and an 87-dB sound are heard sim/cnme7d) -b 1w7lr yegultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in y0ynhcoi9h41the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in anohy4y 0h1 ci9ll directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powerjw 4/ cgn:lm5h output drops by 10 dBw5h nj/cglm:4 at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devpgry/ yb)6csx1s jf-c uvt75)ices 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 byyb 6 vyf)s-c sp7jcu5 rgt)/1x an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications svo zl76ona -,pystems, 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 iqr7;dt 01t1phjf7uuis tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long be b0f,:8ovdt qb37af+dk au5w jtween fixed points with a fundamental frequency of 440 Hz0:8kba + d,tja5 udbo wf37vfq and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tubelo1cz9p/wo0 ,r l6qim 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 waterc pow/lr9moz1 0i,l6q 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 oneod cr4gv* 5agi lykl yrtnx,;;c4/; 0d end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in it5;c /4d tnly;;av lgrcki40yrx*god ,s fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate-yr h5ev- gm9u as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz /qixq(u-1zu9h xgd4 nrange 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 than the other. What is the frequency of the soun(q g91 h qzxd-4i/xunud?   Hz

  Two trains emit 424-Hz whiycane:(kshsb+1 51t1 zztp 3istles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approa+t1sh5:a3 nyci(1zse pzbtk 1ches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After0 /j51 8pwlgpohb cmq+ it passes you, its frequency is measured as 486 Hz. How f/wgmc +boqp1 l0p h8j5ast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cp yvtftp39crq2.f 8e9ars 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 tpy299tq f tref38c. pvhe straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat fr npj+ qr.g(0 f6gltmi;equency of 11 Hz. The shorter one is 2.40 m long. How long is the o;.pm(g6+qjft ri n gl0ther?    m

Two loudspeakers are at o*1 uob*cop eh2pposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency 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 e2b*coo* u1phthey have passed him, at C?

  If the velocity of blood flow in the aorta is normally abuij 7oeq; 1zh vm5f0/yout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected /qejm0yofu71; 5v hzifrom the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s vjpf+7px4wop-tbi + 4while 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 after tha7pwo+ v-x+bj ipt4p f4t wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approacherccs*lsn; )cyt6d 9v ,s a moth. The pulses are approxtlcr9,sndy; *6)scv cimately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was 7,jrq-bfxv s /e5sti9 once 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 overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) f qr7s /,sjv5b-tie9x 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 by the presenku:9 3pes4kf tgr7zt5da/ ,v nce 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 mkdr/tgk v34nu:f7,e z 9p tas5 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 lonp gmm9 azy(a.2*xfhn x919+ aes4hthkg, 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 made to “sing,” or emit a clear, loud, ringingxxs 1 tah+2g *e znhkp.99 (4mmfhaya9 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 qh1;p 8 xsfy*niq +mu3for the human ear at a frequency of about 1000 Hz ihf81+pxmqisy u3; qn*s $I_0$ = $1 \times10^{12 } W / m^2$ 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 bu(d i;:1c 1vwo zqp1uthe sonic boom 1.5 min after the plane passes directly overhead. What is the pp ( dv1 z:;bcq1woui1ulane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 159kb 0lclrp f -g1soh89 $^{\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