What is the evidence that sound travels as a wa l 32/bybo uxx3ahx9-aazhd ()ve?

What is the evidence that sound is a x hd.r*jks)*v qc6t9fform of energy?

Children sometimes play wpkt h+* ju2lhs+ 1lf)xith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child s2+sfjux )lhtk1+*pl hpeaks 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 bqk.8w gvwt,(frequency or wavelength totg,q.b w( 8vkw change?

What evidence can you give that the speed of sound in air does not depend signif:va ji.hu +7m+ nil:xocih;o*g(3s c ficantly on f+3c:h n*vxao. sjg(m;:hfilu 7 c+i iorequency?

The voice of a person who has innnzk 4l0 vazya2p-a b/-9 sk5nhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect )g); mafdc 9nrthe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplijd.zoge2(qo o,a1ki * 3jonw.tude of sounds in various frequency ranges. (An example isdej k(onz .q*w2gaoj o,i3.1o a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced r63ftk f 0 l8odv kt4bavl(n+e)m ;k3mcloser together as you move up the fingerboard toward(3f4ttlkd6k) 8+mnlomkvf;0b a e3 vr the bridge?

A noisy truck approaches you from behind a building. Initially you hear it butsuo0oep t1 41;v sbh)t cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequenctso41;hp) 1o b s0uvtey noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said v2qgq*0o-llsl o(q ,vto be due to “interference in space,” whereas beats can be said to be due to “interference in time.” E-0(lv2 q*osllqo gqv,xplain.

In Fig. 12–16, if the frequency of the de 8mx8pe6ia/*eqjasod7 p w06 at *jghw:u/1speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togethe6wj md 7u xiwgt:8da/1qopa/**p 0jhe68 seaer?

Traditional methods of protecting the heupm2+qpw ;m2:bq 7oymaring 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 aqywpmo b 2mu7q2+ p;:mmbient 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 wipg /:nrpr-vl9g/ y /have can be thought of as a superposition of two 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 //pir9lpnyv g:g/r-hapart? Explain.
(12-31)
(12-18)

Is there a Doppler shift iva46pr3qwuzw ix9r ,(02 w;hzzbsm 4ef the source and observer move in the same direction, with the samrz e w6vhruiaxwzps0 q m44 w,32b(9z;e velocity? Explain.

If a wind is blowing, will this alt m/)2x wy4+v 2i 9xoz*86pd neycceotgjm.t; ber the frequency of the sound heard by a person at rest with respect to the source? Is the w/.o2t bnm y 6pze2+9w ce tgm4oyxv8jcid);* xavelength or velocity changed?

Figure 12–32 shows various positi4a3jvx34e evorf*z 7wej/k- j ons of a child in motion on a swing. A monitor is blowing a whistle in z4/er *jjfw43-vovee j 3 7xkafront of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shof 4olu8zzeyj9g69- nput reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the l- 9nejgyl fo4u9zp6z8ake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below /ng*cy:0gpal 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? Ass0g pg/yalcn :*ume 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 wavelengthsa2bngz3mlsrw6l6o :) 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 schoocm9 j rf4ia(*al of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fr(jac9* f i4maig. 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 cliff. The splash it makes w, xxxg-44cpf5fn npnq/wk*: q hen striking the water below is h ,* x-ck4npwnxnqxq:p4 /5ffgeard 3.5 s later. How high is the cliff?    m

  A person, with his ear to bd .;:tvilkji0u5l7ethe ground, sees a huge stone strike the concrete pavement. A moment lat0: livldi5.7 kj;tbue er 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 did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile (*n5jsq/shh.ahmh4b y s+t,cof distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30hbchas/s h 4.(q+t5y *mh,s jn $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? 2+;of u-l00ttoo oi-ua spe:3qj +cct   W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level1btjd hs/yle v,8v kr*. n*jmim))i n/ 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,)l-wpo :l/gxm9 y1 o/li sysd simultaneously at a certaigl/s lx,)w1: sop/oly-9 dmy in place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wup:f :r; jfd,rith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Addjr ,:frpu:d f; intensities, not dB’s.]    dB

  A cassette player is said to have a signcesw5. *g. + ly:0ne fgb9ftntal-to-noise ratio of 58 dB, whereas for a CD playgw9fgy :t +nte5 csn. e0b*fl.er it is 95 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 output of sound from a person spe l4hbb +hcsr(lc6mxp av .:ij7c6; )hoaking in normal conversation. Use Table 12–2. Assume the sound spreads roughl7pb 4cmsv;chr(jl. oi :x6h a6h blc)+y 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 qwp * 9d xev xy5*+fu9cq b43f4ygux/twhose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplwmlug f/ +*vd0 nnrv2;ifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect m*vnw0/u;ngd+v fr2l at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front ofj7mp(-ec0 8yq( w0s5zzxy dme a loudspeaker on the stmmxcy (jeq w5pe (70 s08dz-yzage.
(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 dc:ee w,tw2hd(m su0 nj+n+g e*q+s+zvetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]ns(mne: + gjevde*t+ 20,whqcw+ z+su$\approx$   

  If the amplitude of a sound wave is tripled, (a) bx+ cc876q ggy grg2/pty what factor will the intensity increase? Increase b xgqrp87t6g/2c +yg gcy a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampj7od zj t,n7jkam)15xlitudes, but one has twice the frequency jt )k5zdjnmoj1,7 7axof the other. What is the ratio of their intensities?   

  What would be the sound le3tv uzrd- )z5fvel (in dB) of a sound wave in air that corresponds to a displacement amplitude of 3vdz-zr5)ftu vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see7kd3 t/emscn wvjj*m(4tq*pmx32w)gm as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.4sm cm3vjjgt n/7e 2kqx**(dwwm 3pt))    dB

What are the lowest and high1fzxyzgi-l ..aqi0 a, c-fv2 hest frequencies that an ear can detect when the sound level is 30 d.g0fq- 1,y -clfaz.zai 2xhviB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thb8*bqg) )z1fpp +1mrecm5ftoe ratio of highest to lowpo 1b8mfgfb)ect5q1) +rmz*pest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has1 z nhapu/;syx c:k6c3 a fundamental frequency of 440 Hz. The length of the kp1/:uah6xzync3 cs; vibrating portion 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 thrroz2d6) i7j 1 3jdsuf9qq6o h8w yi3ieee audible overtones if tii 6i)owh ojqd6ezud783y9rf23q s1 j he 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 freqaid2j s x063aj)ivw8 r zy3)hmuency would you expect from blowing across the top of an empty svd xrw 63s20izi))a8jmahjy 3oda bottle 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 26r7gys h vem)5+2v eqr6zuvna pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be th2su26ehze5+ rgyvmvn7 )r6qv e range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenc-kdc)a6.jv kn z+ ,o fu2.btdhy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingejhta )2kn.b.zd,ucd-6+ kv fo red at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play9 z yo7pxno* c-ed.kk: E above middle C (33zdo:opx- *. ny 9kcke70 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that ezj::975 bvkq o y4tnzumits middle C (262 Hz) when th7tbznj:q z ky9v5o4:u e 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 0l 54av vy1so.vikq2sat 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 shoulkc zl2 d*c.o8g78v fqqd the hole be that must be uncovered to play D above 7*82 zodcvkqf qg .l8cmiddle 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 resox plfd mv)qng8 1)z3r(nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open f (mrnz8xl)vp)d31g qor a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m lon1mv;5(zps g ami3po4vg is open at both ends. It resonates at two successive harg1 p; 3aomvp( imzv45smonics 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 q lfz;k z rd/7n( mlw3yoho,,*$^{\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 audibl0awlfv0kcnt+d hm3 32e range for a 2.14-m-long organ pip2 0wkltv0cnm3f +3adhe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside :jro tvx906rtzz n(m5and is closed at the other end by the eardrum. Emj:o6rt5zx(v9n0 tz rstimate 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 graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beag;sn 2ka/nuo1 p*khrf;gdu 42t every 2.0 s when trying to adjust two strings, one of which is soundou;2na ;hd1f 2*kggr ns /4kpuing 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middlg(2olfxkoqya4-c2q qv /e2op+ s47jfe C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while an6u:knerjm2 a. f:m2 (gtc-qyp: mu2prother (brand X) operates at an unknown frequency. If n:n mua(:-q t rm.:j6pce2g 2mr2up fkyeither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produftqqu5 8awwzj- h4 ,4 /z.)f)vhjosvrces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-84 hsa,fq jv.u-zfh)ww4ro5) vtq /zj Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 mijl0 06oqqh0 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togethero hm00q06iqlj? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flut 9,kvfm( ixuc.dt r,;ws2:mfbes each try to play middle C (262 fvkuc s:9,,wm2 .d(btixmf;r 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 frequency of 441 Hz; srha;:kj0e*e 1mgl2cwhen A and B are a*s eegc20k;:jl hm 1rsounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded 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 onezgg v k8bd0 e:u f2k)(k1f3txt speaker and 3.50 m from the other.(u 12g0k)3k xt tdeff:gz8bvk
(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 arex oymmcwy9eyoo:k; l 3c x:6g+ir1 0*j supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratino:6 lik+0mrox*egj1coy:;y xw9c 3m yg 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 m and 2.76 m in air. How many be)uqq8o -; aj nog28gewats per )qagnog -q 28w euoj;8second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency q7q,wqjs (c(a*e hoh-dr*c1tof a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed o 7qthcr -a*jo(qcd *hw s1q,(ef 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequenczjttmnd(f(;8m2+kz (; ye mwjy do you detect if a fire engine whose sire( dkm+n2;8 je(jmttfmz zy;w(n emits at 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 2ae2km:)z0z rk000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exact0:akzze mk2r )ly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same sinwmw), 8z /tht omr;*zvt7.ukb zrvc4+gle frequency horn. When one is at rest and the7*kz,zm8v hrtmur/zcot +wt w.b;4v) other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounf*nnam).8d aw.ak v6hd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is t6a8nfa )v*h..a mkwndhe 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 ult rb(jl olz lb,7*-5jztrasonic sound wave with frequency z5btb l, jr(7l*z-loj 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played wiawsnxx;mhi ir+gg43x p2: 0// 3jh xon 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 /3xiw3:+g xmpj s4 i;hia/xn hrwg02xrailway 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 u4l*,qbeuw.sr ses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and wu b.s lq4*er,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 ultrasonic waves of fre9 aaacbgkba 050*4 vzmquency $2.25 \times10^{ 6}$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 win1 k2; hf6kvmlud velocity is 12 m/s from the north, what frequl 2m16fkuk vh;ency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object movix l7ve:u .+wmtng 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 whe5q l4)s,dvkzw;) gtmmre the speed of sound is 310 m/s (a) What is the ang,ws; tl4mm)q v )k5zdgle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where xiyk(ch.g4:0 :op uu uthe speed of sound is o0h.pkc4xouuygui (:: nly 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. ; qyc/g(7gm,ry,6 rn )meb/h)bhi pwr Determine the shock wave angle it produces /7;rm ci)/)enm w (hyyrg,bhbg,qp6r
(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 6gnhnbbz8 2 h1wg 2l/m$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see iwnsn47z pssgtn 4 -+8a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the soni+pwistg 7ns- z4n4s n8c 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 sej),*bmi 5d n ex8q( .wrxxzp)unds 20,000-Hz sound pulses downward from th z(.nu,x)m8* w5xx) qei jrdpbe bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the gh 0hj49qucozty+y45human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consistq0, nt4u.ikw)l hqnf+ci /g e9s of many plastic pipes of various lengths, which are open on both endsq/lnqi+kwc9g. hie4u,0tn f ) .
(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 o)33wsvtm + m, h,zf3nkfohrdbcb71s7 f human hearing (0 dB). What will be thbo1wmdt 3 7mf s3)s3bc7 +h,,zkvfnh re sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when awtrq6,tefwx. o) 95fvn 82-dB sound and an 87-dB sound are hea wvwofex.9 q5f, rtt6)rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What a: txc/gs;e:vfz9x4 cis the acoustic power output (W) of the spe:xf4c/;ca gvs : zt9exaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 10rac*jx/ rl 1i8dj .a7e00 Hz. The power output drops by 10 dB at 15 kHz. i /e*d1crj8aj xl7a.r What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typ(lghe)3, f klk:h cqz ;ot(/df2f1ug cically wear protective devices over their ears. Assume t/uc(f); c tzg keo2,fg3l:lq hf (hkd1hat 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 at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the ga4rhw+281q qopb/n dafin, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frekni x rld2(2z 04jsnr2quency 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 fixedemqvzlvs ,+ i5 owaf5/ md4d ll+(;s-f points with a fundamental frequency of 440 Hz and a mass per uniqfv /54,5f +i olmsd+ mds-(azlwl;evt 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 abov l ;oxy)47rzhke a vertical open tube filled with water (Fig. 12–35). The water level l) 4rkzy;ohx 7is 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 2u o6fz0kso)1 x.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonan fo0zs6) uok1xce (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resw 8v74w5p;z3 jfuvn zwonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sol86tc)at-4mmuq1wd w9fh ct 8urces. 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 t8 cq-d)l1tcuhmfw98a46t mw frequency of the sound?   Hz

  Two trains emit 424-Hzau opv50+b *i0 (zas rbvmm2k1 whistles. One train is stationary. The conductor on the stationary train hears a 3.+sv 0pbmv5i0k*oau1b ar (m z20-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. Afterkrgznqiip7l./ hr8ak2n4qre7sw :g, 3 g ju:0 it passes you, its frequency is measured a g,rwhiznrk:2i : 7q3qpr/4u7ksnajg0 .gl e8s 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listen qeglg,zl5h5 mlot: m)(r8 0sding to the difference in pitch of the engine noise between approaching and receding cars. Suppose the soun mhz85lgl,:t ) d0gomselrq (5d of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding ts .yfu kgonaa)3 w6m,0ogether, produce a beat frequency of 11 Hz. The shortms03ofkwg6y),au a . ner one is 2.40 m long. How long is the other?    m

Two loudspeakers are ,fph0eo7.o gm at opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he lo me,gh.f o0p7istens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32niv) f4h;x) bu m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were dh 4fu)vinb);x irected along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while)pn-v nzaqq- mvtr;z5.i7i ,t 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 pavz .m;75),qrn-tz vit-n iq wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. 6f3 x+2*ipjkk fabkga4l+ 0etThe pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat xp+j kkeg+4i kl3ba 0aff6*t2 so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 123zew u5o9xhv(–38) was once used to send signals from one Alpine village to anoth9(3v ezwo hx5uer. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which 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 presence of sl.t5t (y(vdg; ilwht* tanding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider i(gtl* .5 hydlv(ttw;a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slend48+ba0okovqf-0qd-dm hu y n,er 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, ringing sound.o+oa4vbduhn-q8y md ,kq f0-0 For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the hhbei b knb4/ ,ss;60sluman ear at a frequency of about 1kle /, 6sb4ss;nbih0b 000 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 hears the sonyqmg2j -+ mn2.vlgi1l w)rj o(ic boom 1.5 min after the plm. gi)l-q+wo (lj1yjg rv2m2nane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbmehuu; q* msf;0-l, ayoat 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