What is the evidence that sound travels as a wave gs(r;y() ryg;n u,s:l-ix fty?

What is the evidence that sound is ad9*n ka7hy ulvqv+ +o8 form of energy?

Children sometimes play with s6 aidc3 ,hx9edsu e8.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 other cup (Fig. 12–29). Explain clearly how the sound wavase8x39 ce ds.,d h6iue travels from one cup to the other.

When a sound wave passes from air into watwkfg*m u/i.d7 er, do you expect the frequency or wavelength to chf *gwiku/m.d 7ange?

What evidence can you give that the speed of sound in air does not depe6r 4cw5ks2yu ktt 4ao8nd significantly on freqay45urt s8wkc4 2 tk6ouency?

The voice of a person who has inhaled helium sounds very high-pitc xk2im )b:n(bnhed. Why?

How will the air temperature in a, y 2y1icm /ushz0g6sl room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to re-m v2kly/tx vv6/ kcy8duce the amplitude of sounds in various frequency ranges. (An example is a c kxvt/ly/-k ycv8m2v 6ar muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clo t(ip(2,8inrhx3sly gser together as you move up the fingerboard tor( s8gl 3,hitxp2(niyward the bridge?

A noisy truck approaches you from behind a building. Initially you hear lx,*wo e ,nt 72ntse6nit but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noi o62 ,,* n7nltswtexnese. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beam d/g .9q84qxrim o7:/bqujkc):c t emts can be said to be due to “interfeg/mcqx79:/dimr 4q ctjo8e.b) :q ku mrence in time.” Explain.

In Fig. 12–16, if them3.bo.es.gmvte9 i1 h frequency of the speakers were lowered, would the points D and C (where destructive and constructive interfe3m.t1seo. mh .9v biegrence occur) move farther apart or closer together?

Traditional methods of prot 71q9mkd+ 19e)jikwzk2 dmawo ecting 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, inverts it electronical z 9+79dmmkaie1q1j)odkkw2w ly, 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 cand *f;hyetn1 j6 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 thedjh6* yne;tf1 two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directipig - cmt.rtx4 ipyaoo73a 8*+on, with the same veloog7 8*a4oi .cimyttx3ap p +r-city? Explain.

If a wind is blowing, will this alter b,:9y/3 ue2h q6 da;vi ripcdzthe frequency of the sound heard by a person at rest with respect :3i pez,r;had/b vdiy2cqu69to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monito7d )pj.tir2fa /wh dyp9k/ e9sr is blowing a whistle in front of the ch/ fis7jdh2 p)9eyp/td .r k9awild 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 listr l69bz;zhpq. ening for the echo of her shout reflected by a cliff at the faql;r.p6zhz9 b r 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 wa92rxqmgtatm(+ ( zt 4aterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with a mt(gtqxm (ra+9t42z depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air k z2zgh vs(x,2at 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 driftio*lgs /jp3c i*ng just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another bo*sl/ogi c 3j*pat 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. zw hw-j3own42l y-l+bThe splash it makes when striking the water below is heard 3.5 s later. How3+l24 zjlwbywo-nwh- high is the cliff?    m

  A person, with his ear to the ground, s8gzigjum5 3y15j kx:gol(s b6ees 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 b6zk8lm55 ujj o 3g i1(yggs:xin 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 nqjyb84 v03wp error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning 8nv4p0qy b3w jstrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level flb1)+4qdv5:aeg 7o hti+yvv c)ft8w 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 levk7bq hfik /s4z-j tk-9el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta(/gty/9kq2a0 svw8 ki6uhl ub neously at a certain place yusbig qh86/9(/2twvl k 0auk, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airp 38 ldzra)vr4xlane with four equally noisy jet engines is experiencing a sound level border4x3rl r)dvz8 aing on pain, 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 have a signal-to-noise ratio of 58 dt52ahq+h8wzy 9y 1p fzr+9rem B, whereas for a CD player it is 95 dB. What is the hmhw 9yztf+5z rr8e +pa 9y1q2ratio 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 normc40s pobnby6tu6,t8 q kc(x306o efdbal conversation. Use Table 12–2. Assuf80stkc eod,t ( 3nyc6b0xuop bb66q4me the 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 y4a)g4gaju8.5yia jpwhose 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, whil32bjqu:hk by t5khrv-: ev *d+e the more modest 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 conne-kje*hv t3qh:ybv2dr ub k +:5cted in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130zloyr matut 31i m .u*w)5 aknn44+qk; dB when placed 2.8 m in front of a loudspeaker oikt)w lk43na*4 ;5 .yo mtam+uruqzn1n 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 sound level of 2.0 d0jnw3x.0x)f xkr aiuhg f.1pk-pv 1(zB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sect vg1wr0fua()x nkp .1xi jphfz0.x3 k-ion 11–9.]$\approx$   

  If the amplitude of a s f4(jfnm9tt6dc gbl(d: (rr,uound wave is tripled, (a) by what factor will the intensity inc(dfm4nl (jt:trfcd9 b,(u6 rg rease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudevjo4pgj8 9 (fbs, but one has twice the frequency of the other. What is the ratio of their intensities?j(8pb4 9 gjfov   

  What would be the sound level (i5+ ufeeo08t; ie cu4ozn dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 3 tee5uc i;zfo+48uo e000 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that /afic wjuk,. +has a 50-dB sound l+.jf/,iw kauc evel? (See Fig. 12–6.)    dB

What are the lowest and highest fres vhrw. es3hgj)p9ma kke*+00quencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)hep9s0s h+.k*k v j30wam egr)

  Your auditory system can accom 7wk;gch g(mkvaakgm*,3wr 8 2modate a huge range of sound levels. What is the ratio of highest to lowes*m k kg( g7hg ,ka3rm;ac8ww2vt intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violinu; 1ljno,p -rt has a fundamental frequency of 440 Hz. The length of the vibrating portiontnjp;,-ru1l o 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 112il7kux0sjb 9;:m,w,yjcb m 4v cm long. What are the fundamental and first three audible overtones if the pipe is v b7;sw0il9jcmbmyuj,k ,4: x
(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 blowing;;lwekt6(v5g.abtv l 8 k2ku oo hb72i across the top of an empty soda bove (h kk.8g2l wa72vt 6l5tok;bi;ub ottle 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 pippj11::nd, by vpg3vdse organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipesj1 1b3dgnpvvps d :y,: required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What wlvezlop7f g) nz *i2g d9nt3.lgnp2n42rq9)nill be its fundameo3 )dgr7 ni nvzng.elp2f*gqpl l9)24n2t9n z ntal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is; 3oyroji,gu41-dgi b(9nlg b 0.73 m long and is tuned to play E above middle C (330 Hz)i,bggjb9 i ( dlr3no; ug4y1-o.
(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 b7i pri14a53+nnhpll middle C (262 Hz) when the temperinn1 p3+pi 75bllha 4rature 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 ;/2 v3 l,9yi9 ic rmap.pcua6rd ysx**sahx6a20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute inb5 1vm) febbhq1a+v ,q Example 12–10 should the hole be that 1 bfq1+ae, hb5v)qmvb must 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, and 616 Hz, but 8 +;pe3em zbnrqp g(;dnot at any other frequencies in ;rezp(nq8 e3+;bmpd gbetween. (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 tubedaj9frw lcf7:)o5 t )q 1.80 m long is open at both ends. It resonates at two successive harmonicst :9fj5)wadlr7q )foc of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 / 8h( 3uvpm;;li m/md-; q. kdsiubuwx$^{\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 d- ;tn-js ons6 ;0iij )+gfnzuthe audible range for a 2.14-m-long organ pipintjou);fd g- -;ss6in0 zj+ne at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 ch+vdf9 uxx4hb*0q8z p m long. 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 standing waves in the ear canal. What is the relationshi+v8 uqzfp* d0 hbhxx49p 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 beatu u;9tin/0 (y g4/yhgzxq6 mqh every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz.60(gyqxhzqt / /gnihm u;u y94 How far off in frequency is the other string? ±    Hz

  What is the beat frequencik/ p vvpca .,+xfvq/;y 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 operata)f1*w-e.ownnj o v dklsa 9 sxs//5q5es at 23.5 kHz, while another (brand X) operates at an unknkqfwsnv55 a/s o .e1n od9-x/as l*jw)own 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 operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sboxd5ulwnudh(i0;(lb 01n bsrlg.*- ounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tun0igln.uxl50dlbd bs( nu-w br;h1*(oing fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension5lf -dz m8vnf. in one string is thenf fd.z-mlnv8 5 decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identk dw, z57dh.g c-g7mnbical flutes each try to play middle C (262 Hz), but one is at 5.0°C and th-kg.nbwc7 z,gddm57he other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441dt wuf ( sv;6bw/wo6k+bi3yi.n s/8kw 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? Wha6w ik.vw 8+tyw3ni/sf6;kws u/(b b odt 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 y33gyw0lej +f. A person stands 3.00 m from one speaker and 3.50 m from f3yjg+0ly3w ethe 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 he( tj2boybp5p1.b gq* gars three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be b bgt. 21q*g5(pjbypothe 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 wa:; 2o cbzpyn,xvelengths 2.64 m and 2.76 m in air. How many beats per second wi :ob,n;y2xpzcll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certapuxcri2) ja mvxu;k)2 7z 4ch3in fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move withc7c3ihxpkmj v2u2u 4 )razx); a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still.stptoc,4.h rny8 d4* z What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speedz,.p* thd8srty c44on of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourqtw brc7,f-f fc2a dgib** (-rce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencieq,2-fg rcf brtbc*a 7 -wf(*dis 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. Whenr: f,su q.jgz5 one is at rest and the other is moving toward the first at 15 m/s the driver at rest hea5.gq ,suz:jrf rs 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 receives them re73c6 ly* btbzrk0o2wfturned from an object moving d k60ry3 b bcwtf2zl*o7irectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the j gyjd)/um :z5bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in :juy)5j g dzm/the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pl0gfsd 0 *gjzyzk-v2 e(l. ;jvlol if-qty/8i/ayed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone whji fjflig8qz*d -vo t-/2sel.yvygl(/;0 zk 0 ile 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 wavecskpo0f3/,k i mtud2u 2w4(aks to measure blood-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 arteries at 2 cm/s directly away from the sound sourcu/,2a2mkpo (03ui dkkstcf4w e?   Hz

  The Doppler effect using ultrasonic wa7:xbb 87v4lyru yvn /nves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of f lf;gp9q fu(q96hkq -frequency 570 Hz. When the wind velocity is 12 m/s from the north, (pf-h9; fkf6 ql qgu9qwhat 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 itoz8mhz(7w91qov 4ksbq 7t l7ps speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whlk*u. fl( qvs;at is the angle the ss.(lk* f vq;luhock 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 o0ohi68sy6e e2ndiysr dnj6; g4b /s5ff a planet where the speed of sound is only abo i/dsyr6 8 sfi;2 h6jybdng0e s4eon56ut 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 .w+vz wvl rryhn2qe*e. 4 p09kthe ocean. Determine the shock wave angle it produw.vv 4q.lw ree2h 9kpnzy 0*r+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 3g9cq orgw ):uw2ug;s $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and 0jef4iq3r7y6 d8 cy f(c,2 6 yflpxhoesee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear lj6ff3c cer xhoqed(y y0p6i,4yf 728the 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 tqo,qkyy) o gwxt(1iw(t ;m3f 9hat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then dq;)1wmf3gwk to(x tqy, y(9oietects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octavesv /s- tdm )iu;habr thc--6pz5 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. I1h,wi +( )nlayajc,o ct consists of many plastic pipes of various lengthsaa,l, ohy)in (cc1+ wj, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresho)gw i;f,f/ xkwld of human hearing (0 gx,if) ;k/fwwdB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound uffcr1ik 5;3 kand an 87-dB sound are heard simultaneouslyfi f15 rcuk;3k?    dB

  The sound level 12.0 m from a loudspeake wfkh 6deb 9t:w02is5ar, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuifa20d9 swbh56:w ketming it radiates equally in all directions?    W

  A stereo amplifier is rated at mo t np2jup/61150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 1 u6/1mp n2ojtp5 kHz?    dB

  Workers around jet aircraft typically wear protectivmk98x aj/ajt( e 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 radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m fro/tx aja(8kj9mm a jet airplane engine?    W

  In audio and communications systems,2c/+v 5wajn0p-(i xs) j hiboh 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 fjriw.du6 n exhw :ii9hq: 922irequency 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 fiyvk /dn4 z0dsur6 xmnti1k+z(.m xi46xed points with a fundamental frequency of 440 d i1mnkmy/ vnxzku+4 s0(6zx4i.tr6 dHz 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 above5 nbv1nh5w)dwvp mi* 5 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 w5h 15 npdim nvb)v5*wis heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at dme1wku*/v a;:ebh grqg.i32epn-; yone end and also 75 cm long. How much tensia ;e;*pqyb :mvein kgwg/3 1r2d-.e huon should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full ldn-6vgd0s/r5l1kvs m 6lt.( encid 9uoop ($\frac{1}{2}\lambda$) 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 cominr1m 6t q nb9igf),ysv)g from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farthe1 qybgv,9i) rs6t f)mnr from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hilpd,s 7-3b6w/ i;nj9efie hr) iuy+vz whistles. 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;,ifhdnl w9 i6 uiirje- b7e/p3s)yv+ the moving train?   m/s

  The frequency of a steam train whistle as it approaches ylw*o: kfzu-9m ou is 538 Hz. After it passes you, its frequency is measured as 486 Hz. mw*fl-:zuo k 9How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of xgun j,t2 *u.06vm*/yksb vz pcars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a fu.k0ugy ,ptn**z b26vvjs/x mull 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 of 11 Hz. T-atyb4kj)k8cgrd 3b (he shorter one is 2.40 m long. How long isg8ab) 3-jc d(t4rkykb the other?    m

Two loudspeakers are at oppoiwmsg 3s .9+lgsite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between thws.gslig+39 me speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blo16ck5f7bs /kzl-/ px9sbr zapod flow in the aorta is normally about 0.32 m/s what beat frequency would you expb xz- 67p z5rspk/lf/a9bsk 1cect 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 speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at spee ikcjqg;bx1s .v*;bj1nm qq- 1d 6.5 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 detecte bnqxk-i;c qm 1gv1s*j1b.;q jd by the bat after that wave reflects off the moth?    kHz

  A bat emits a series tmxw3n 29of7k v uq3/k2kmt mwtq7 6/yof high frequency sound pulses as it approaches a moth. The pulses are appro92tk3ot xmk u//nktv qw 7qm2m367wyfximately 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 uslu3 a-kiwe3o:g;o(u ged to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones gg3(3keuwo-u: ;laiois 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 stere5x fas(:t726vok rec19wo ic d6kfhe: o listening can be compromised by the presence of standing waves, which cano1 :7(w66 kdto:hxr ecsaf9k5 e2civf 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, ca5z d5 52gjfmv stl-5fulled “singing rods,” involves a long, slender aluminum rod held in thf25 zvus 5jtmf5g5- dle hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. 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 ofuc5fuyf qt1**4hmgyy u0t/. u hearing for the human ear at a frequency of aboutuq0cy/h5f 1.uum4 f u*gyt*ty 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 observer on the ground hears the sonic pz5a87dg,g fe boom 1.5 min after the plane passes directly overhead.8efd, ap7gz5g What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15xy7d)y unn+hb-f kk)cb i4*iuqlhc* +m56o l* $^{\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