What is the evidence that sound travels as a wavewm w4 w;79+wm9dce vv8(s jvas?

What is the evidence that sound xkt 8 p(q)6le 8yif1.q l)cy(w5huvndis a form of energy?

Children sometimes play with a homemade “telephone *jo7eavgs -8e” by attaching a string to the bottoms of two paper cups. When the string is stretched and a ch-*j7 sg8ae eovild 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 t4tuc p,,r(gw4n l2uoghe frequency or wavelength to chano w24,ul gc(n4pu,trg ge?

What evidence can you give that the speed of sound in air qlf w1p dacu*/-a-sw,does not depend significantly o /a,u1 swd--wf alqpc*n frequency?

The voice of a person who has inhaled helium sounds ve m18fq 885lwbk f1bablry high-pitched. Why?

How will the air temperature in a room affect( r: s:ofhqpzkfe5satf96wn+ c6bt** the pitch of organ pipes?

Explain how a tube might be used as a filter rb 4mjrtm la7.l::kd 9to reduce the amplitude of sounds in various frequency ranges.k7: jt mbmd.l:49lra r (An example is a car muffler.)

Why are the frets on 9c(w8 trmelqw em+7rs+4w- eb6ac5rya guitar (Fig. 12–30) spaced closer together as you move up the fingerboard ts8-caw6tm5errlr4ebw9 q+ (7me w+y coward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but 1 ws,kc piman-uf 0 n4zfomfc3e35(mj1j w25hcannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [ma13 5s z 1-j5fcnpu,2ofh fi cj4em0w(mkw3nHint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beat2eeuplycvhqkb rf 55b)*/8 n k/t2 pr5s can be said to be due to “intek)85 /ceehv5/ 2uqyl fbpnkt *5brp2rrference in time.” Explain.

In Fig. 12–16, if the frequency of the gln*eb9 :zhcftr :;a2 speakers were lowered, would the points D and C (where destructive and constructivez:*erg:an2;b tl9fh c interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas w ev uf4ag3q:hz8 vo ebj70. e(un8gj8iith very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technolog. ngu8eae3qi4 e7jo80fv hb g8vjzu :(y, 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 irho.eonz7;1gq3 tz9,6.1myh izj qjfn Fig. 12–31. Each wave 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)fh zzh1;qy9omnoj.6t iq31. ,g 7zer j, are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and0nlda ;t.z(ii:2mpc r observer move in the same direction, with the same velocity? Expl al0i:r.it (;2d pzmcnain.

If a wind is blowing, will this alter the frequency of the soundotrc-u b8 +buqx5-(l*wdly 7w heard by a person at rest with respect to th 8wc* -y -o5ud7 bul(lw+brqxte source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mo6k:aqx4 1vllrt (a 8ofj h,q0rtion on a swing. A monitor is blowinj6:l1r8qt laqof (ax4h0k,rvg 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 whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of +ijoz2pc ap6+ ,4u i dysyib-1her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. ias6z ib2 -py,1y+c4 +ipujdoEstimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He q5z 7vhats7ay / 8,ufvhears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with77uyz v a hf/,t8avs5q depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air /gq.q;posx, 4+g xnyn:zb0xr 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 i1+yf/l. 6dxi4gj(pjl(pk8 cgz b(bs f s drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurbp(gb kcd 4pgfz(j 1j /l.8yf(+i slx6s on another boat 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 + vs0gankvp2pxt+ky3 .h:g 5sthe top of a cliff. The splash it makes when striking the water below is heard 3.5 v:ths+kpxgvsk a3+5 gpny0 .2s later. How high is the cliff?    m

  A person, with his ear to the 6ln9/ynlpf a*ll ;9 nrground, sees 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 they are 1.1 s apart. How far *l flnap; 9 9/n6yllrnaway did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance 8.ia9ikom q+qby the “5-second rule” for estimating the distance from a lightning s9k ai m+q.i8qotrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity o,so sh4hq2xt 4gfq(smh/ 5 wn+f a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity sqm95 y*k *wnv,msui s l5m;q.is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 956 27qt*;jmpyac8k m8i3vphp e dB when fired simultaneously at a certain place, what will be the sound level if only one is explodthkc78 pm68app ;ym *je2q i3ved? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from2p.xj zbs sn-/spm:8p an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine?pbsp8z/ np2 sxjm: -.s [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sig6,s guq3 e hlbadiw(dy6*+2jnnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the r uy(blq2hw 36 gni+sdea*d,j6atio 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 speaking in nor )o:iaetxw)v1mal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the moutaox :wve)t1)ih. $\approx$    $ \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 stlax1xztqa p)y(3 q. y2rikes 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 model;.7 8g lrxopwst amplifier B is rated at 40 W. (a) Estimate the so.olr w;lpg8 x7und level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter rego9nfv hh7phz8++2qoz istered 130 dB when placed 2.8 m in front of a louds h+ozh +nq8ovfp9 h27zpeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in soun qfgrim5a; )q91o5: +shnqn ry35drrjd level of 2.0 dB. What is the ratio of the amplitudes of two sounds whosermnnr 5q qsd+r1 ghr5yjq );o:9 ai53f levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soun*hebuw 5 u5q8arg*3 ; jffebsd*1bi /rd wave is tripled, (a) by what factor will the intensity increase? Inc*j85 f*fa dqbhe ;berbu3* w5s1ur /girease 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 tw w56v i07ur/cozxk-wd ice the frequency of the other. What is the ratio of their xzirk67 0co w-wvu5 /dintensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds tvou q(z 5mw(q0bt l02zo a displacement amplitude of vibrating air molecules of 0.13 mm ml o tuzvbq0(25zq0w(at 300 Hz?    dB

  A 6000-Hz tone must have what ytyr mtqn-6 6(/xfal;oe3 r-bsound level to seem as loud as a 100-Hz tone that has a 50-dB sound l /bqn ey-lt6 at6ofm rryx-(3;evel? (See Fig. 12–6.)    dB

What are the lowest and highest frequezs 8dszw +.: zo5yg*sencies that an ear can detect when the sound lwez8+*:yzdo. s5sz gsevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate adsubqin800 e3 huge range of sound levels. What is the reui00q b3nsd8atio of 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 fundamental frequency oh 0- yjlmo 0kv85ertgmea+ r3)f 440 Hz. The length of the eojrhrl5830m0 )t y gk-ev+ma 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 ad-t3 , t n0h-rsm (yeqolxb)g*nd first three audible overtones if th( -l y0qe3grhsmn -)totb ,d*xe 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 ejw;u r p:mol(cnb1,r1;ums s oy68l6gxpect from blowing across the top of an emprmwb1 ( mglu yo6scs8olr,; 6p:j1u ;nty soda 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 a pipe organ with open-tube pipes spanni jsg3puh5t h 3xtyf:9-ng the range of human hearing (20 Hz to 20 kHz), wha9 t xs5-y:hpfg3j t3hut 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 frechhaq(akl/x49 - t:9qz0bydjz0 r1 wxquency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length oqz 0b yj9hct(ax4q0-dkrl x 1wa:9z/hf only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plawkv (yzh9*p+ wy E above middle C (330 Hzp k yh+wzvw*(9).
(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 o*xp5ser43vmp f 7rh5yrgan pipe that emits middle C (262 Hz) when the trmxepv 54p*f7h3rs5yemperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at lh:pedvnfj8 cyff 3*h,0;.og;c 6hxs 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 should thew8czu9h) k+ lk hole be that must be uncovered to play D above middle C at 2+khkuc98) lw z94 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and /a jm9h o-:uix616 Hz, but not at any other frequencies in between. (a)o-xmu:9 /ja hi 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 loswn ywpyp -vdwe-r-yqo. eod)72 /-q*ng is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whynw- pqd*/dv)- wo7oyws.q 2- rey-epat 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 4m wf-:;h2 d4jxepcvokg4 vs +$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long ou 2cnugn9t *)jrgan pip9nc) n*2u jgtue at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long.i6mbp9 h0,k/ vyeo-s k It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the st,yop/ - vkhes0ibm6k9 anding 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 beat every 2.0 s when trying to adjust twowl/1uwfj 4r)t h q0vo. strings, one of whiwltf/)hjuq1 .ovwr0 4ch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2k, yf8y -c;i jdqgl29u62 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 dq84 kx:ywesg 7 p1 ttpz):or,at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle cap1k q8:)x wt:sd4rz ,ep7tgy on 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:m k 4;h w,vs.;knafjw 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationakfw,sj4ah n. m; v:kw;l frequency of the string? Explain your reasoning.    Hz

  Two violin strings arc2 fwgbt5l (q:0a -nttw39k wj0ad+kpe tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat f3 ntjp 0 -q:(0w wat+kk 9gftd52wbclarequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fis+ex06kxaq *lutes each try to play middle C (262 *qk06a xis+exHz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,,:bjqlgljz+ iwz*/ 9p A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounde:wlzz jplb*qi/9+ ,jg d 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 one speaker an x;jy o6qcgbyq/; 6:qbd 3.50 o bjy6cy:q6/b;qqx; g m from 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 ky lbugey-(h+:p28kz at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency olbgk:e8 ypk-(+z2 y huf 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 bea aiod)4hbsawl6z, q; +ts per )al,64oha sb w+ id;zqsecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencr0 /7 pfexut1bl 7wkmkh/ 9pn5y of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move wit 19pm/ lb0te7kwu 5pn frh7kx/h a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you de( 7znkgd9g +ahtect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 md( z+a7kgnh g9/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sfj0 8uut3*cgaource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exa0ga *t8f3ucu jctly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single fre e4q-g)fgx:jv088 1ij4pf3 n2l l4zqfhbkalequency horn. When one is at rest and the other is mozff01jg)xfb3nq84i- 4h kvaq ll pg2e l4e8j:ving 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 sound waves at 50.0 kHz and receiv/9+ u6j mih xrkd8iz5nes them returned from an object moving directly away from it at 25 m/s What is the received sounndk h 9i/mj+i5 rz68xud frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s xdy1g-le - l(ke:kkh;As it flies, the bat emits an ultrasonic sounel( -khxge1d -;yklk:d wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experime;ln t:jw(b c8-5jpkbqnts, 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 appt:( jbjbl8-kc 5pnq;wroached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves 8i.) e *b*)i9w0yxslgh0 i eonq4haq mto measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and they*n hqiqsom09ixia8bh*40) ewe g. l) 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 frequency ml0ql2r .x -ow lv-3wf$2.25 \times10^{ 6}$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 frequencn6us2v). ugt oep.h +ly 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who +nlsv2 ueo. p6g)t.uh are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 20-l5/(1 j3tjcdgl8c cjut)hje(v )bjf $^{\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 atf76e m8fd*xai Mach 2.3 where the speed of sound is 310 m/s (a) What is thx8* a7mfe6i fde angle 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 the speed of 4os01u olbw9y sz1g u/sound is only about 35 m/s uw0lbsgo9/1yo1zs u4
(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 wave angle e:0wda8tk7x()ff j ux/hlvt3g kxg85 it produ/j)7 e0w x8(xxk lhft83utgk:5vdfga ces
(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 kxf mv8zuwli c/r jt s.vk4:.;yui 4/5$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1r 2ov.:u fuqk*n( 5chb.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. Se.kroq:v2hf nucu(5b* e 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 downward7vdyh1h47e.)r q awzq from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed twq .hzy4h)ea71 7qd rvo work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octxu 5 pycu :5+2 mv5xiumbd3nf2aves are 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 m1s; (zz b;x 8qyffg/ypany plastic pipes of various lengths, which are opezzpb 1y(8g/ x;;fysqfn 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 aei x,dek 7 *i4;xksd/g person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquiide4 ksg *,7ik; xxde/toes?    dB

  What is the resultant sound level when a h4: 0oz8kxn(29j6z mvjax7 gkk,+*cle noqzwn 82-dB sound and an 87-dB sound are heard 7 zg6m :ecx0qojz*zxk h v4,l9+nkk8o a(w2njsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opejf9 ctomjjtti(5-92u n, is 105 dB. What is the acoustic power output (W) of the speaker, assumingoj mt9tj9t uj-2fi5c ( it radiates equally in all directions?    W

  A stereo amplifier is rated at 1tuw/xb3li qz4 tk4 ,)dntl: f150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts ,itn blx kw):tt1zql 3 /u4d4fat 15 kHz?    dB

  Workers around jet aircraft typically wear protective 0wiihc-vr-foiv) ox 02g yj ;zpc1k-/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 p;yhoijcvcr- 2iz0w /x-1)gvkf-i o0 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 gapp6qk7/ lco 1cin, $\beta$ 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 tzk +v9 es0/9nh-hbq dvo 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 between fipg4zf/c rbs(3xed points with a fundamental frequency p/4 sbc3z f(grof 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a ve2shoh ;0;*rlhjkds qy. emz 2.rtical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the a2h 0hkqlh d;.rzsy ;2e.o*jsmir 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 t+6ow vimzggpce(v:cg ,3 (w :jhat is open at one end 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 i:3cg o 6pwj:(cgv+wgzv me(, third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observee c;; ristc+d.om98uwd to resonate 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-:8prp s:qi twl*2nhg5Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about a phnp5*girl8 :qsw2t:nd 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 whis7n now zw2ki+ev3-k4atles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of kz+ 3nwwkie2n v4o7-a the moving train?   m/s

  The frequency of a steam train whistle as it approaches yo2*urxsd; cb;oj:+3 jbqnt/ auu is 538 Hz. After it passes you, its frequency ia j2:rucj dbx/*qtos +; 3bnu;s measured as 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 byfnglb4i(m -z 1 listening to the difference in pitcbzmgin -4lf 1(h of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce aj/o w ;nc ek0d/l,(sez beat frequency of 11 Hz. The shorter one is 2.40 m long. zd0e j //we,;l(skcnoHow long is the other?    m

Two loudspeakers are a8u ;pftiizy*8d6sl:r d,p jp /t 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 listens from *ij8:i ; zf/r,yppsddlt8u6 pthe 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 app6 (kluinsdrh.wq, 2k4bt4 zwut4;0orta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were d6pr4ht4zls; nq4 0w.id(b 2u k,wtpkuirected 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 wh ,79 q. 22ztfwmwrc bqnp4,gboile the moth is flying toward the bat at2z.q ,no94w7f,trb 2pmwg c bq 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 that wave reflects off the moth?    kHz

  A bat emits a series of 9 pwdh12e sjc;/0iqgh o n5z4ohigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far awad9nzo2/eg15ciws j 4h p0;ohqy can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpifelh:0zpjf dd*m1e u3fq o7 81ne village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 1*8dfp z0e1hd jou1qmf3e7l :f2–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by1kzz8 1m x1w5 clj5pv m/vxdi7 the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes.d5lz7j vx/mx m1i1 vzkp81cw5 Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender dlbhjd98r jd/ a+50 hoaluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rodd+od/harh8 lb0 j95dj 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 0 q3z,b f(zq3bjgfo1 bfor the human ear at a frequency of about g3bf o1z30jb,fqqz b( 1000 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 obse) uklzn .t7p+u gtr(.;ymw*ztf u5ast51 s 1surver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s .u+p a s1. r;sl)m5*z1ktyw7g(f t5ntsutuzu altitude?    $ \times10^{4 }$ m

  The wake of a speedbojooq gli d)sk5 8fc0*9at 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