What is the evidencedx /7y z0ix0.ghj3vo f that sound travels as a wave?

What is the evidence that sound6h7y bcho1g)-ysfhi 6 is a form of energy?

Children sometimes play *o7dhk 9f;e b8k)lwwgnro*,m with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the othf)mkk *greod;o9bw 7h wn 8,l*er cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or *dlp2m9lxq t+ u byicq;.fq;2wavd 2pf lqcq yx2qb*9m+ tul;;.ielength to change?

What evidence can you give that the speed of 9g3 udz cbl leca61/t*sound in air does not depend significa/ bz*cul1a36ed9 ctlgntly on frequency?

The voice of a person who has inhaled helium sounds verye1 e))8gilm69r( gnhtowr3xz high-pitched. Why?

How will the air temperaturrvm ,kk/wm (6se in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filt;rakn 6e2.wg9+0luq f*mva 2ivq9q k.xuq8sver to reduce the amplitude of sounds in various frequency rangesk9fuvqrn +qw mie. q*v a2a2.0x896g ukv; sql. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spa;wk o2dq1sr+cced closer together as you move up rok+2;dc1wsq the fingerboard toward the bridge?

A noisy truck approachk clf/lec-b(l8.j 4ur es you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hekefl/c(.8jb c4ll- urar more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to b)v 57m)hwxo0nqi0p 0to8mz xre due to “interference in space,” whereas beats can8z o7hvxqprn)w)m t5 mi xo000 be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of theem-m xc/ fm5,3iaav47pi z, za speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closeap-ii fa 35 ,/,c4mezvmaz7xm r together?

Traditional methods *jvko 7f e ddkr3*r n0m7b6zm;of protecting the hearing 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 ambient noise. Instead, a device is used which detects the noise, inverm o r f*jb3*zr;06dk77mkdnvets 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. Eachq) a+db2s,dte wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. +s q)d2dte,ba12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer ml.u2x/b * a fqk17jo*avu3y caove in the same direction, with the same veloci c f b3aq */.a*u17uvx2ayklojty? Explain.

If a wind is blowing, will this alter the frequency of the sound hearyn, s ,b2eqx; g3ccr9yd by a person at rest with respect to the source? Is the wavelength or velbqn s3r,,9xc;g2ye yc ocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor rw.*5 su*i dr0+xykfl is blowki xwfy5ul0sr*r* +d.ing 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 omrgrwh h,4x208okx)5 sdc, fqf a lake by listening for the echo of her shout reflected by a cliffs58r , ,h gqr)chfd2 xx0kmw4o at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Heos +r8;u 1lywcgl z*6r hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawaterw;sz*yl8g u1 o6l+ crr is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthsa aumk( ;2kzc:eu+.i g 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 a yobcuwurs+ v712wp/)bove a school of tuna on a foggy day. Without warning, an engine osw2y cubwu1p)7vr+ /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 t9-b 45 3cot9uj 8mr8 cvulcitlhe top of a cliff. The splash it makes when striking the water below is heard 3.5 s lcc b lvjrum8oic9t9-t 38 4lu5ater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike ve8 vig( d0qpyhme fxt-*h3*3q5 iub0the 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 awa30i*t f*-ixy dv8ee3pqghhq v m0b u(5y did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dist.xz9 n(bghev*ance by the “5-second rule” for estimating the distance from a lightning strike if t*9vng. eb(z hxhe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the ;dx5x c qwykj6*l 52gwpain 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 4-/jo gm y-zy-cbd5iloh lh*(intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dBrl od:7xvmb xs7r7 4pl;7 zzmdyol79, when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]xdpl74ldm:moy, r 7 l9rsz;o7xv7z b7    dB

  A person standing a certain dizl zq8k nmk;x3ny9e9pf4)9j 5g d/ ynvstance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would tknez9/p m;8qndkjx y3z9 v 49n)ygfl5his person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio ofu9;g;oj;fmaz+ po -jt/w q1ey 58 dB, whereas for a CD player it is 95 dB. What is the ratio 1j;oq gwzoj f ae ;ymt+/;u-9pof 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 normal2i8t tp nzl/bg- 8j(zt conversation. Use Table 12–2. Assume the sound spreads roughly uniformlyit j-zb(t tn8 8pg2/lz 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 strikelfrvvd(cv(2 t.6,v lx )1pjtes 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 modest amplifier B is ra),9zo3lf0emhdi pyx0 znp5 ) kted at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each am0p5kzelo0hm9y znf)xpd3i ,) p.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a df2z58dtgw3xx B meter registered 130 dB when placed 2.8 m in front of a loudspeaker on 8txdgxf25 zw3the 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 typicao.g; qj ubjod*t1qs4(mwn3 0fa-ows: lly detect a difference in sound level of 2.0 dB. What isj1 d0o(o*wwtjgs4q u :snm.f ;ba 3qo- the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trips p, a,m*wnty9led, (a) by what factor will the intensity ipant*m, s wy9,ncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have ik:bj/ u(o ap.equal displacement amplitudes, but one has twice the frequency of the other. What is the ratio ofpi /:a ujob.k( their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correru61v mznedkc.i tw33e6 :5hu sponds to a displacement amplitude of vibratingt1kuu r c3 z6eeiv.md:w53n 6h air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level(7 7qru rf 9jujhmy. i7f25ygz to seem as loud as a 100-Hz tone that has a 50-dB sound level? 5 j z.9 hgmr7u7if27(yyrfjuq(See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when p2k xkrs32 e20 6fs4jkwu:ahg the sound level is 30 dB? (See Fig. 12–6exark2j: kwsu3hsg2f602k 4 p .)

  Your auditory system can acu .jga791bxku commodate a huge range of sound levels. What is the ratio of highest to jgxk19a7b .uu 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. T3 (wc)j7n 9pob g (7m1yucbtet/o+np ahe length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what/1bpn9j +cn7)o(yc3am 7tobptw eug( tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three :bqo9:eotcg ; audible overtones if the pipegeqo;b c o9::t 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 blowin b7 *;lu7rcm2+qrjbw og across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed bw;clj 77orqmur+*b2 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 pipos1izo38 ygvpsy ,(vi8zc + 3aes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the le,g8yvp3a 3o +svc8yzi 1z (oisngths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hzyh;tqxr 6 gvv8jzx a38:k1 p/c as its third harmonic. What will be its fundamental frequency v1 /tya6v ;rqhjk8gpcx8z x:3 if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play )*i idgi66inpE above middle C (330i6i*6 )pgdii n 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 emits middle C (262 Hz)v :s)urs2 fei*c:t/bw when the tempe:2*f/vsbsti uwc):r erature 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 8b , k krvq;us 0b/xp,pn-9s2 6ukecmx20 $^{\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 t43hms+.7 5tvrckue se-wby w1 he hole be that ys.rs cthw43e57+ v1kmbwe-umust be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, ke19-ggl h*ywou it v70ume f/m,x s00and 616 Hz, but not at any other frequencies in tf ogk muxw i0*gyh 7vm1 eel09s/,u-0between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It 5klfubrybn.k r eye*)0 4;n2iresonates at two successive harmonics of frequencies 275 Hz and 330 50n.k4; b b* lnr2ykru yefie)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 o9 rtti *uf1o0$^{\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-luyvgxhi+ gml3l. 0p f7fnhl 60 l1jq(9ong organ pipe at 20 fg(96xlu1f3lyvmqi+ h0hj .l7pl 0n g $^{\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*..5bk a)u)g h07q d4jzlugwczzmzb ( 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 t5a0 qhzd(u7lk4b.bgz*. zm) wg zuj) che 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 beatln-8h1rm)bvnnj22w, -g f jwg every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strn 1-gg-wjnfl8 2vb), hm w2jrning? ±    Hz

  What is the beat frequency iw 8tleyk6 u:waunl3lcn6-3 :sz5 4laif 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 23.5 kHz, while another (brand X)c /7 lhli:,okn operates at an unknown frequency. If neither 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 operatin c,ih kln:lo7/g frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-s0ptl)/: 7iz2u usfhj19 tpqmHz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vib0 zt 2197f/ ulqsuh m:pip)sjtrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in kqr t2y.xyawsp8t18 ,one string is then decreased by 2.0%. What will be the beat frequency heard when the two st2qta8twy1y ,p s.xk8 rrings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be ak qnv0lj8em03k d-7cheard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 -3veqc07adn80k mj kl$^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B auio/;m:f;dl. gtac;, 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 frequencies are possible when A and C are so ;;doif:t ;l aa.um/gcunded 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 and rk 8 -tvzec4(ml+pnyh+b gx9/3.50 m frov 9l+t +p-kre8/n(m xbcy4g zhm the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hebix,pzj .o7 ub8zxwtx 3y61o:c09capars wybpxt6 u,0.1zc9i p j8: aczxobxo3 7three beats every 2.0 s when they 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 wavelength93 e:ylmhzch; /wzt *-xymo q;s 2.64 m and 2.76 m in air. How many beats per second will be heard? (As*/-3hmxyto9 h q;emz w; cy:zlsume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certainphd9 7wrntg f,;ws k2. fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed ow;pfwrk.dsn 9,gh72 t f 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. ho1; aohi5*vv3rnzcjv, (hly;pz2 8 dWhat frequency do you detect if a fire engine whose siren ro npo;v ,v;v2 lyh3ih8 1( 5acdzz*hjemits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift ip 5jpu t, y6zytoxa1k6 lw9 4tpp;:7lin frequency if a 2000-Hz source is moving toward you at 15 m/pi4l ptp7xj 6 1;6:95 kp,ttualwyoyzs versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn.5bjc:mcjt;guh i;k5i r cc29: When one is at rest and the other is moving toward the first at 15 m/s the m:gbj:2ic; u9h5cicckrt ;j5 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 oz i -qzve-bts9(d h6ruh /b6:rut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is th h ts-(qr-/ b6izbrhdze:69uve 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 afkg vm7t)(l*2s kth-gn ultrasonic sound wave with frequency 30.0 kHglg7kv( )-*fst mk h2tz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopkp s45bz :*gqmpler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a secp :s kzb4q*m5gond 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 mexn1p6tvf jw*: cu4u 5 8bcg0kjasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to b 61kftu5j: cg0jwxvbu pcn4*8e 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 ultrasonicz5vv hi3 g 8ckayx;oj93s)ep: waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits so+ujy 369vvkwr und of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are locau39v jw +yrvk6ted, 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 lagndh*cndc- ow s/v8 - i ;771wfwqcacz(2e/ggnd if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the spenh y89 67et sqq* 53tmcveerg2ed of sound is 310 m/s (a) What is the angle the sho7ce2 3m ys qrtge 8q6*t9hv5enck 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 +h)-gkbv om* na planet where the speed of sound is only a*- +nhgkvmb)o bout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave angl/ s + ab4pb6e2alyc7vle it prov7b cbaslep4+a2/6 lyduces
(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 n.z:ozhae ): n$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and s28(/dcl* ke ujm qwa7iee a plane exactly 1.5 km above the ground flying faster than the speed of soundmwji2 *du(7cqa k8e/l . By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,00t;crda-gj c 8 i,6;cpg0-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 is the minijdrp6-a g c8cgc,t; ;imum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in8zz iu22lbjb;02n psf the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipelm.c7,v teju+ symphony. It consists of many plastic pipe+,ej .7tlcu vms of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person ma( +sj;dlak j*ukes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 100d*aj;ju+ (s lk0 such mosquitoes?    dB

  What is the resultant sound l:y kv5mk)cberrii 1/x: -a6z bevel when an 82-dB sound and an 87-dB sound are heard simultaneouiv/ak::1 mz by k6ex-r5bc i)rsly?    dB

  The sound level 12.0 m from a loudspeaker, placeaa 4fs k0l . mm;ufs/gv+1x8twd in the open, is 105 dB. What is the acoustic power output (W) of the speaker, ass+;s41mf/af8wt0avkl.x ums guming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ojjznq 23+ 8.(afqwi jbutput drops by 10 dB at 15 kHz. What iqjw 3q+.j i8zja2 (bnfs the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protec 2: 0doaazdm,htive devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective rad :a20aod,mdz hius 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 communicsj4s2 fjh :3ybb caj-ojb5+ p5ations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequencymfz:pv62 (e gf 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 betwuzfonf2 t300 zeen fixed points with a fundamental frequency of 440 Hz and a mass per unu o0fn3tzf0z 2it length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tub( afgn 2fat4t 7;bzrs1e filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tuf;2n sf z (a47tbtrg1abe 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 muvy edr9w9t /:ass 2.10 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 produc/twuy v :99rdee resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to 1t4i zs nkkt; s ak5qf::-y:suresonate 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 to 0mbgjzv -+;94jt(v vfadfk5one in the 500–1000-Hz 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 andvd4-fjkv(g5vtb 0j9;oma +z f finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The co3 +/fy8nah rwi2jjzy3nductor on the stationaryy8j ji/wnr+f3 h23zay train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam g n7 v,vkdnm2s5:3qrm9l yk0jtrain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured s: j 32vk95nr,dkl0v7ynm qmg 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 by listening to th 0kd9eepa* 5ehe difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octak5ea h edp*0e9ve (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 frequ+fl5 5nb ushf3ency of 11 Hz. The shorter one is 2.40 m long. H5uhfnlf s53 b+ow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it yw9f .gr6 32g:sureoxmoves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in 6rs9yow xg.rgfu2 e :3front 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 ie14vkq 8j d,uzs normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were 1v8 uzjd, q4ekdirected 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 the moth is+n-p5lw q8n5-hi rpjv flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What pj5pn- +iv wl5-qrn8h is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. T )rta* bl,eew9he pulses are approxb wte),ar l9e*imately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals4h6k /5l6ifrkm9 gks1ud7g rj from one Alpine village to another. Since lower frequency sounds are less susceptible to intel6 4kgj/rk smhif d 19ukr5g67nsity 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 s oj ;a/dfz.1o y- 6:s:czzgmpdtanding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. 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 roo/sdzyo.m;a 6::c z-zf djg o1pm.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “sin*yhhc1dr 8)nk0l ci(tging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a lithncd0 hlytr)(ic 18k*tle practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a fru,-otxb se9 3b8e t2( btc(ulelvp tl+( aw:a2equency of about 1000 2wtvb,((u lsclp a:tu l (+tb2-8 eo9at3 xbeeHz 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 +4ip wmu w4k:dk/-7n)ipxa vgground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’sa/47n)u div : k-+iwk4 pxwpmg altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iswx-qd dxm-d 9 8q b. wrg3dgrrl;n4c/8 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