What is the evidence that soundnrh *fnoyx5a /5 ltg;q5 /ils( travels as a wave?

What is the evidence that sound is a form of energy ar 5)4,kammyq*hhz /e?

Children sometimes play with a homemade “telephone” boej4+t,j2vykg1(u ncy attaching a string to the bottoms of two paper cups. When the string is stretched and a child spea 2( 4ektoy+ vc1gnjju,ks 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 yo5:pu go6nm vh7h ec:v6u expect the frequency or wavele76e cghhv5n6 :: mpvuongth to change?

What evidence can you give that the speed of so r9akam 4hiq9-und in air does not depend significant9mrq9hi4 -akaly on frequency?

The voice of a personhsy*;1p :rprptx0x d ; who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch9nt7 *epoq,-iq2 ffhu of organ pipes?

Explain how a tube might be used as a filter to reduce the amplit;0ci 4 h0qrlvt98toiif /hay/ude of sounds in various frequency ranges. (An example is a car mu8i0/tilhvo9qh ty/;r4 a0ifc ffler.)

Why are the frets onzja woh.y5,m /25gqm eysg5h2eg )lj4 a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the brih z5 e lg 4q/5gmheojay2)5ywm jg,s.2dge?

A noisy truck approaches you from behind a building. Initipwm.0 f5e/e j9b6 cdqhally you hear it but cannot see it. Whehmjfe0wb5 cd. q9 pe/6n it emerges and you do see it, 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 due to “interference in space,” wh.;2nsbhtt.zcw s. y9w ereas beats can be said to be due to “interference in tims2w; yct.twsb9 nz..he.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poinak.a ,bhf(-njts D and C b(.ah- knja,f(where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectise dv3p3ic(q -ng the hearing of people who work in areas with very high noise levels have consisted mainvcs d3i-q(p3 ely 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 can8mex(ywf f(3x 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 apart? Explaif(x( yf 3emx8wn.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sazwb5lj:5 t1n6sk:zca me direction, with the same velocity? Explac1:wa5jzb6n zt: l5k sin.

If a wind is blowing, will this alter the frequency lohp.ou-xbpj67 x9k;of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chpxbhl6; up9k x.j o7-oanged?

Figure 12–32 shows various positions of a child in motion on a swing. d/2hw - ai/ :vxyysa4gA monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the high4ig ay/-wxd a:y/sv2hest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lf * 04ikhir2cfej0/ 1p1pgdhfistening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shop0401fdch i2ifg rfe 1h*p/jkuting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hil) o; plr;jtc+ .t2fxrs ship just below the waterline. He hears the echo of the sound re;t.r xcf);+pllrtj2o flected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths gklrluw+n 0lvq ddxn,* 6+b* 6in 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 e9i3t 8w(fzp cjust above a school of tuna on a foggy day. Withoutf ic93p8et( wz 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) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splmml f.gkjtyd- (j*-k n5v-8ii ash it makes when striking the water below is heard 3.5 s later. How high is.mny livi-k5d gtkf8-j -( *jm the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the+da9 )avvo zvxq 5l.vysp/k 35 concrete pavement. A moment later two sounds9ys5v3z+ x) v5qalp dvkv/a.o 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 on79ua 5rh,+r wb2h g)6)c-rmddbe( gtdm 4myjke mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) mdywhm5 ) ,2bct9urj(grgdhm +4ekabr -6d)730 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitwb yo3e+je2f +y of 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 z5a:6ty*hif twhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fiu5s3oeuc s ti b2uk08v5.(ngajg1.;6d llwppred simultaneously at a certain place, what will be thivgapjpc0; .nwdkgst o6uu (s52u.b15le83 l e sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an pg d1cun1; 5-qd1. jtliqb7kf airplane with four equally noisy jet engines is experiencing a sound level bordering on pacqd-.t ilb ;j151dqnu7gk1 p fin, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to /cx9ktc ao*6j3kmqwt3y +2//i gej qj/ayw a:have a signal-to-noise ratio of 58 dB, whereas for a CD ajjoi gy3/mwayc9 j ck/:k/ 3t a2x*6q/ew+tqplayer 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 oq+3zb 0ikk u+)gg5ewjutput of sound from a person speaking in normal conversation. Use Table 12–2. Assume ze w5 qij0u )k++3kggbthe sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area /uxxy40 3rdz n 7vu8hir3bo9his $5 \times10^{ -5} m^2$ (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 mo4.8-ncgk diudz/e0 kgdest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in g8d- cg0idk.n ke z4u/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 registereddgh (u(*rvi j)buk.ou+uz z86 130 dB when placed 2.8 m in front of a loudspeaker on the stag zbj (.6kvz(+d* ruh 8ugiou)ue.
(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 ihdr rd .w)3/glk2y *r6xqlc7vn sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differlw6/k v d3*lhrrcxr. qg72)dy by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will ogfv/ilnk8h .-k 0rmf 29*spfthe intensig8m*klo-fv f .inp 2k/r9fsh0ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dg(jcbdyv 0 s f7fvrj),p:0ui9isplacement amplitudes, but one has twice the frequencyj0 ds,r(v: 7yjv ibffp0g9)uc of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds .y g 33 ll6g/(qdbmai*g3kjp fto a displacement amplitude of vibrating ai36 ag*3 gdi jl.y(gfpmlq 3b/kr molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sou8n(g. 4l)u c4i0:dxdf ,k)cvcl duu fund level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12l,:8(0 4l)ufd)u. d4fcuicu kdxg vc n–6.)    dB

What are the lowest /8n 9rd7c2zjf2+tyx0kcl b.g6jc zl uand highest frequencies that an ear can detect when the sound level is f czu 8zyd27/nj2 ct g+kc j69x.b0llr30 dB? (See Fig. 12–6.)

  Your auditory system can accommoamy0ngjtb h fy.ys/qp :xi*,3o+k9 9tdate a huge range of sound levels. What is the r*qat 0my/+,9: ysnh.fkpj boi txy93gatio 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 of 440 Hz. The: sanuz5v y iwrn11 jw0l;o-)q length of the vibrating portion i:o5 w;1 uqnvl )1jawr yiz-ns0s 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. Wha4ff9em+ (o e /bcwi;jb5r;e tjt are the fundamental and first three audible overtones if the pi +wf;;bj5 je4(f/reo9c tiem bpe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from bk6 2(xx9m nsorwv6j al*)z1 +cb,xk gplowing across the top of an empty soda bottle thwok 6zgml j1, 2+()6sx *rbvx9kan xpcat 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 rwv(d a ;s9cd77q1x(5 r tabeypipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz)cxwa9 vebdr;(y 5d1( t7r7saq , what 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 frequ *6kkjpux+0 gcency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length+kc6 px0j*k ug of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunedkx .xeq(pg1gm h+x.f6 to play E above middle C (330 Hz).kfpmg.hg. 6+ (qxxx e1
(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 a; sfz7 8xseg145a pyzopen organ pipe that emits middle C (262 Hz) when the temperatf7az x 4egsaz 1;s8py5ure 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 s xli)4hw5p r(at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the moutg 7:xztcw2ojxfat h4ksnl **91.p h8f hpiece of the flute in Example 12–10 should the hole be that must beax4wok7gf8 hp t*2sjhf1 lcz: *t.9x n uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hze;u+ 4vsbe a-e cl -xvd9j7(sl, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closedlues b-7e(l+v-xce ;d 9 jas4v pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at tw 77q-syng6xpwo successive harmonics of frequencies 275 Hxyws7-qp7 6gn z 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 9 prgv(b(o+ z,ecio /v$^{\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.d9 j75qan4osf +; jovc14-m-long organ pipe aqj5 csf9no7 a+ 4ojdv;t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It ieetmfe.lxrou 0*;-h : s open to the outside and is 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 relationshilu. emer;0 o*f: e-htxp 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 e n:z6:a, sqeiuvery 2.0 s when trying to adjust two strings, one of which is sounding 440 uq ,6aize:s:nHz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency jc3kkz*ou6bxe5t5 0q if middle 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 2)u/ ku0 ov hy5kz0nwi+6s rypt5+vjr .jx8ad13.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, b8d wkoh. v500js)xiyzn+pu+tj r /yru1kv6a5ut 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 xe0eew /j(dbd2*v wq5fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationbd xj*qeew(/wv 0d25e al frequency of the string? Explain your reasoning.    Hz

  Two violin strings are td/fru/ do .ubs.nahiw6; oz -5uned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings areu;oar .db sz. /ihn/uod f6-w5 played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fluteshew x6 mainvx /+q4(6o each try to play middle C (262 Hz), but one is at 5.0°C and the other /ae (m+6 hxo4n qw6ivxat 25.0 $^{\circ} $ C?    beats/sec

  You have three tunin,uo: scms*u,20,zjki(e v9k za2m br nla8c*mg forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat fracv n (2 mk,u,j, ral82zsb90 mce*oumi*z:sk equencies 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 apap r+*z5o s-dhwrt. A person stands 3.00 m from one speaker and 3.50 m from th+rwzp-5d hs*o e 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 supposeahi1e 2dp/6i vprsmg 0j2ey+0d to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when t1drh/0y 0p 2ga e2vijs 6iemp+hey are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in1 r6js vdhy85 ;t(ph7xmtiep)fn/k : i air. How many beats per second will be heard? (Assumer;sppvd 1i im tn h65t/x:e(fy7)8hjk T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain 9gc*cua m /)-kb ezcm(y6d.c a/zdw. ofire engine’s siren is 1550 Hz when at rest. What frequen/wc eb6zo.y ac .g cukd*-m9az/c)dm( cy do you detect if you move with 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 detect if a fire engine whose sksf:h ih*19bl6 v-urfjx7 3x siren emits at 1550 :xs iffs-u 17369 bh l*xjkrhvHz 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 movintrl 8: *cgrx*gg toward you at 15 m/s versus you *c: g*8trrxlgmoving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipp ,/ t w dfu)8vh,opnq6wxoj:.ued with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequenotfq ,n x:.o,p)/ uj ww6dhuv8cy 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 wa. f 5f6hcs p*pcv2s;ybves at 50.0 kHz and receives them returned from an obj.v5bp2f scp*;fc syh6ect moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a walamb /,j 1do5zpl at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Whatop5,1/z mdj ba frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimew41i6)xuba pbd f0 zp3nts, a tuba was played on a moving flat train c3 10ai)4uz6w f xpbpbdar at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloocqgy/( xn4w: 7hnr1 qkd-flow speeds. Suppose the device emits sound at 3.5 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 x1q 4/nycrn7w gq(kh: arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency hc(/fgh7q (bfkkl :/h n- -cs z0i*byh$2.25 \times10^{ 6}$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 wifidd2 s4gj*x(kg2 8bjnd velocity is 12 m/s from th jd2sf2(xk8b4gg* dije north, what frequency 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 moving on land if its sw kj 9wp 8o)vw*n n*n06,xcrkupeed 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 sp s09qxe)cpti)eed of sound is 310 m/s (a) What is the angle the shock wave makes with the direct)t xcepis0 q)9ion 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 wu/8ui3gw irz1s 6 om3planet where the speed of sound is only about uim63go iwzs381wru /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 str.nib0 ij d4d3awp1y v/ikes the ocean. Determine the shock wave angle it produw d n0.pidja4vy1 bi3/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 5of4fz 0ipv 9 4brsp:o$/theta$ 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 exact cb3 kq uw.khgz1om vx7zfh(o9,2* c;sly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, ;cwouqo kh3x .9bs(f27zz*h g, vckm1the 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 dev49fv 3cyfk3i5qg) js*0(zq fxs whbw. ice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what 4 3wwqf9qih3c 0k .yz(f s* gbjsv5xf)is the minimum time between pulses (in fresh water)?    s

  Approximately how many cz 6ak4+ldp; -jbkqz9 octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a: y3 b :cicf)qxjr9s/d display called a sewer pipe symphony. It consists of many plastic pipes of vxrs qjb fy9:dic 3):c/arious 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 a1:sfp8dc0 q-y nau-xi person makes a sound close to the threshold of human hearing (0 dB). What will be the sound 1-afuni 8 0c -dqpxs:ylevel of 1000 such mosquitoes?    dB

  What is the resultant sou-6n x pyu3wxbztpzayfb,2* /x:nb4 e*nd level when an 82-dB sound and an 87-dB sound are heard simultaneoe*6y xyxppt-, nzn bbb4axz23:*w u/fusly?    dB

  The sound level 12.0 m from a loudspeaker, pla-poc gh 0*5zse;s 1fj,rfpyk,ced in the open, is 105 dB. What is the0 k,fpr 1p-g5oc *yf;sezj,sh acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is ,qn9kr5m fgcv) grxzjrkn8 )q*7 3l 1irated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outpzqx1n 5r,fv9kqrn 8rg 3 )7gkijl)*mc ut in watts at 15 kHz?    dB

  Workers around jet aircraft typi oa3r.-v3y rdl.. uckzcally wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effec .3rvrkzoy. l.dacu- 3tive 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 s2idwc41 3g kdt.mw8j 0l s6a tellj:x5ystems, 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 q qe+zrk0*2p kis 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 betweenm+ zh a/y3aom8 fixed points with a fundamental frequency of 440 Hz and a mass per ho+m 3aay/m8zunit 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 d7a9nu5dp 1 bfm:s3oc a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance fromcddm a5s3 p9ubnf71 o: 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 totr x42m2v:hsctsb gf mibu27n s0lz f :0:,4qhat is open at one end and also 75 cm long. How much tension should be in the string if it is to pro4h: t:2st bimmnl2 gcfsbxq0vs: 24uroz,0f7 duce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to repz,tdwn)6 -7mezjdhu( aqz 59 sonate 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 fro0wrpacd0dv . pek:) n7m two sources. The sound is loud0 vdr0.p)7a dk pcw:enest 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 sound?   Hz

  Two trains emit 424-Hz whistles. One tf8n oke tc619q 6s3wysrain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approa1yct6e8snk9 s 3f6q woches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afte jrdiw 285yx/sr it passes you, its frequ8jw i/x2sr5ydency is 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 just7wrr5k80npaqaw* w + d by listening to the difference in pitch of the engine noise between approaching and receding cars. wakwqp rrw 85d 0n7*a+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 a beat frequency od3ab5w dx l2(uvv- x*vsdy-; mf 11 Hz. The shorter one is 2.40 m long. How la*v3bvwm5l;u y-x dvsdd-(2x ong is the other?    m

Two loudspeakers are ad1u5ew8ozjkh.g3yp (1z o*)rc5wbpr 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 hear5(gp51krjyp3)* bd1wzooz.we r8u c hd by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normalgsh qih .s- fif939ufuws w;nu;-od*8ly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speef.u9whs-9 -8 ous;wsq;f *dhiui nfg3 d of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6co -)c(bx: jr x3akk-p.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detectedjkkx--)c x br(3: copa by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as 4o4cf: txxkacv:3ky7it approaches a moth. The 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 so that the echo fromkoa :v x3c 4k4xyc:f7t one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one A6 e. s8vrc/ekwlpine village to another. Since lower freque6ckse wver/8. ncy 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 ster a5*1y)u vyogje*9hv7d 9jr- mv2 xmfheo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 y -euj)hmxg99f7v*1* hj vymr2dv a o5m 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,kbsd- /ade( q; 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 ksda/ q ;d(-bemade 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 for thx9p 2 szsy-tjs3sn2v 4e human ear at a frequency of about 12nt ssz 9y4s32s-xjv p000 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:urb.scr8g4e gr0(e h:* jhtg observer on the ground hears the sonic boom 1.5 min after the plane passrc g* (0j8sr4.gg :etb:ruhe hes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatn8lm5s -n htd: 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