What is the evidence t, oj/d6)iixethat sound travels as a wave?

What is the evidence that sound is a form of eneb)f8s5jgoy7va tco 5-ej.z2z rgy?

Children sometimes play with a homemade “telephone” byx beg2kle+w, : attaching a string to the bottoms of two paper cups. When the string is seb+e2,w: xgk ltretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave pa:+2 xfyz5fydosses from air into water, do you expect the frequency or wavelengtx5dfozy+ f2y:h to change?

What evidence can you+- xu pwkz98tnn )2s4uu k+tiw give that the speed of sound in air does not depend significan zki42uwwt- x8)tkp+uu 9n sn+tly on frequency?

The voice of a person who has inhaled helium sounds -u g3xu8znkr0om7mbyn;y-(g very high-pitched. Why?

How will the air temp/on2:rcd9, 7p: nc jk b1b livdl-sm)qerature in a room affect the pitch of organ pipes?

Explain how a tube mig 9:mtso)a0w6-ie9 f st lpyp,hht be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is yeop :p6)m99-halt0w ,ssfi ta car muffler.)

Why are the frets on a guityi/y(1mie66 4ezxe d jr,dro3ar (Fig. 12–30) spaced closer together as you move up the finger6 r( 16i,4 dmdx3yr/e eziyejoboard toward the bridge?

A noisy truck approaches you from behind a building. Initiifo/fj/ny y;p )zp:s /ally you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sectii/ /f )njzos;/p:py yfon 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherbl9,af+0c 8 1xdeejfddw* q ba42ku/zeas beats can be sc /kej2ul0d 4d18fbwx 9+da fbz*e,qaaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequ-go3mfqp/6c k ggbu24ency of the speakers were lowered, would the points D and C (where destcg o3ub6/ gk g-42mqpfructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting tgjk x3y5 ja)6chw il,+he 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 ji+3) gxla 5k,jcwhy6 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 6n,9hi::ikvh8lz2mi (/g qdjx3tmle Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), ar h32hitg( :96vk / ,lide ijm:8lqxmnze the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source aoazhpn6 z51xo */ -od *4 i2lcnfah;mynd observer move in the same direction, with the same velo5*/ofhlpohy4 6 aic-n2m d;xon*az 1 zcity? Explain.

If a wind is blowing, will this alter the frequency of theash ;ff /npd5o,d7f )zhuw0- c sound heard by a person at rest wfnuwd)fhf7/h s,z; o-d c0a5 pith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in2c 9b20ga/ 0 s4ffuvd0ptknxx l ;ojv- motion on a swing. A monitor is blowing a whistle in xn us2xvc bo0 a;2dkvftl00pfj9g-4/front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of as3l-hj 2 rn /ghf,sya2 lake by listening 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 shoa2ysg 2-j/ 3hfnhrs,l uting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ecoo9 )ywm,k)qu(eiz 0kho 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 significantl, koe w 0m9o))(yzkquiy with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths )ayd6mu(;jb x in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy dayi wheb6tq)g7iq- olk 23qt1vc9iu--u. Without warning, an engine backfire occurs on another boat 1.0 ki12lh-ub 3kuw 9qg7ot-vii-c qteq6 ) m 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 splash it makes when strikingi6k dtstxk8 16 the water t8t1 6k6sd kxibelow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone str.peyu8gkz c57zy :qu9ike the concrete pavement. A moment later two sounds are heard from the impact: oneu yck. 8 zpg:e7qyz95u travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dista j q4u y1c yr*akd-tqq;p0k6i6nce by the “5-second rule” for estimating the distance fry*6k6pjda4 ukq q0 qc; iy-tr1om a lightning strike 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 of 120 d d0929sm hyynsB?    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 d3en8yf /o g8qhy5j 6mj* 4txssound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a so*gh .f d.sc28k6o1ylgceig l0/1 k jwbund level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Ajic w10.2 /kf yh6gsl8l1gg.c dbek*odd intensities, not dB’s.]    dB

  A person standing a certain di /wh v19);m0lcy92y cllwupgz;b mh2qstance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captc l9y2v; h g2zpm9bw;0y) l umqc1/wlhain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-n jx6a.5 ow;6tr)zsyk coise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devic wrk5 szj66.;o )xtcyae? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person s min1n epnp0)ap 2 lm3p2qnv7,peaking in normal conversation. Use Table 12–2. Assume tnpn3702me pp 2 ainv )n,qm1lphe 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 w:iuxx-9a scm,m.+t9cccc j j 5hose 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 modestoh 9. *nfzt6tbc2cjbu(. n/h e 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 otu( cbjnz.. ehf6/nb29tc *hin turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when plack8cn pdo 52c;3jvnpm 6ed 2.8 m in front of a loudspeaker n2o5c3 n6;jpkv mp c8don 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 dB. Whvk. 4ogq+kg 3rat is the ratio of the a4qgr okg3. +kvmplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound;rskyum(j qt./3mz : m wave is tripled, (a) by what factor will the intensity increasemr ;my(mq. skjtu:3z/? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tz0o)3u 6za1ad iut9x twice the frequency of the other. What is the ratio of their inz60d 1xtuz9u3i t) oaatensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds trl4g5pt*(az qo a displacement amplitude of vibrating air mp5agl4q( zt *rolecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lolgwlh)1:iive9(1r xr qgk 1h2ud as a 100-Hz tone that has a 50-dB 1hik)119ighwrlr(vq lx2e g:sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect e:17ou,r ytj; h hotc(vv-ws, when the sound level is 30hohjtte (y: o -,,7u;1wcvvsr dB? (See Fig. 12–6.)

  Your auditory system can/ioz,ge7 d :c+xgcd7k accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity atx/c : odecgg7i+,7kd z
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a vib s4dfqk;(c+m( ibl-yolin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must 4f;( b(yl qcmski-d+b the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firsuemn l y)jpk-n exj(k5) s*m3/h,p6wu t three audible overtones if the p3nlj)kxpe6whn /,sy5p ) -u(km*jemu ipe 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 fro4 (a i8/42gobrxhgva z)lk pwiw(g 06jm blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube?4kl/wo a hj(i 2)(wix vb8 6gzpa0gr4g    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanjty;jj r-jvua 5:j: ;:egdk-nning the range of human hearing (20 Hz to 20 kHz), what wo;jj- jjvgyneu :a dk;:jrt-:5 uld 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 frequency of 540 Hz r2ne(v b* wnh)sxe0(s as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lenghsxe n) nv(esr2*(b 0wth?   Hz

  An unfingered guitar string is 0.73 m / g+fjhx xu-jxp/6d 6along and is tuned to play E above middle Cx+ a /x/xfhd6p-j ju6g (330 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 opt3gq.k- ,y 7b dybr-qtsnw2 xoc:j y:-en organ pipe that emits middle C (262 Hz) when the temperatur-t , 7brjk32 d.yxy cgqwns:qt -:-yobe 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 e; +3( ijtkhbcf s2w,x20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Ex/ns z8 3 xc(3v5nzlryzample 12–10 should the hole be that must be uncovered to play D abov3/svzn3y 5zl8 crnx (ze 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,jlie3c enfy7 ,,cl3c178fuc y and 616 Hz, but not at any other frequencies in between. (a) Show why this is an op,f if 3n1lluc8y7ycjc cee 37,en 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 resonateswxu.vzg0r+h),:af/0kfo v u0ztpq l 4 at two successive harmonics of frequencies 275 Hz and 330qr v/xz fga kpov+u)ft,0:00wl4zh u . 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 .nfk)4 hqjx4jm y nd9l +ae(8cp c8u0r$^{\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 prf5 c26.r.cwwf kdrk+sesent within the audible range for a 2.14-m-long organ p.cf2+kw r5f 6dc.srw kipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatev+1l ph o:*rjyly 2.5 cm 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 relationship of your answer to the information in the grappojl*rvh y+: 1h of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every*l wiq.ik00axfdn 5m1 . 7ycqe 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. nq .0wdi1ilkc qem50a*.y x f7How far off in frequency is the other string? ±    Hz

  What is the beat frequency if m(bslshb i12(0p/pl 44snk ivyiddle 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) o-+yoc3v1cnu 8- n2f1+nt7k:3zt gwrqxypia iperates 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 opertyo1v: ncw+1y2r 33zakg-+ nx7tpi-fc iqn 8 uating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning forp5+ q d0w d*0mdh.y*ln5ty usdk and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoningl055 n .ddy dyh0+dqpus**mwt .    Hz

  Two violin strings are tuned toz ca6b )xj88jl the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when t lcxz88jab 6)jhe two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical1;5d07 lpy lhqi l:f.,l jcoev flutes each try to play middle C (2p1 l7o:l,jf ;he dli 50.ycqlv62 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a 4 ntp q8syst 896f9zlgfrequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. Whestl6 f8 8nq4z9sgy9ptn B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from u+lv7 /f2 qe1efviszskx3j:, one speaker and 3.50 m from the 2vk 7qj,vs /x suil31ff+ e:zeother.
(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, e1ih)vo 6emd(but a piano tuner hears three beat16d hom e(v)eis 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 wavelengths 2.64 m and 2.76 m inyxwt9 (ut0 fb .n/tfl.;1xihd air. How many beats per second will be heard? (Assum9/t0 uwf ti1xtf.ynb.d lx(h; e T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’fz s p8+. ;-t8wewpaolj. kn(8g5)a ldczz+vls siren is 1550 Hz when at rest. What frequency do you detect if tlzg +oaa;)lc jk-n8lsewwdv+.f 58z ( p8p z.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 d s 0v(-pc)9s8rlipvdz pqx6zopg ght7/.i g; -etect if a fire engine whose siren emits at 1550 Hz moves ag9/ p;8ts- h.6l)iir -gx7pzv p(o0q sdzcvgpt 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 moving toward yo-j j,gw 4, l,t,jq teozahl,.bu at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies ewa tjjtzlg b4h.eq,l,,o, -,jxactly 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 si3pt6lfjm ,ti(ngle 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 frequency of 5.5 Hz. What is tt l,i3t mp(f6jhe frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rq6w+gax /x s q;5-vmf3bkzmo uq-/ m+eeceives them returned from an object moving directly away from it at 25 m/s What is the receivez e+qx-aubw3sg;+qf k/- /mvom6 qm5 xd sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5y5- 0 3yaoq y+ykgjy7l m/s As it flies, the bat emits an ultrak0+qygy-7l oy5jyya 3sonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played od hm/2bwody0slw h*u4kj8bj6e5 y 9q4n a moving flat train car at a frequency of 75 Hz, and a second identichy4dq2bjle50mw s*b/hk9y wj84o 6ud al 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 blood-flow spk( z08,xgcy+ lbi5 czveeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in humangz ki0,y zl(xcbcv85+ tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usf -iwm*u sfk4gqoq 464ing ultrasonic 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 sound of frequency 570 Hz. When the w73vv ezp 8xpt6ind velocity is 12 m/s from the7 x6v 8etv3pzp 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+3xmo e clohx)85guy ytmip5:t .h6*s land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) es/ 8:1bh jpac 5g rz/d-nf2ymWhat is the angle the shock wave makes with the dire1ra/ghc -d:/8zp nsyje fb5m2 ction 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 plane/u ,w2qz)wz / 3kmjlzu-mp1 lbt where the speed of sound is only about uz, q )/ bpj2w3zwl/-ku1mzl m35 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. Determi+2 w*kf v knsu5()szv hf.mhp7yle;4qne the shock wave anglew2zy kk+;sp 4qlmnh*vf5e ( hf 7uvs). it produces
(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 x6i /fi d9pemiw5x98a$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above . aaez4vgd uxpc+g2w,k(x (( hthe ground flying faster than the speed of sound. By the time you hear the sv.((ud zw2 ga4+(page,c xkx honic 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 def p8rggv*y)*3 cgv3 myvice 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 g833*mpgrvcy* gvfy ) is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in th*d .ubl72voo*v,ex 5 he/azkl e human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists 1 q 9(w;gtwnnv20f nda3cq6mr of many plastic pipes of various lengths, which are o q1 nv3g wanm;nrt 60(29dfcwqpen 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 uw(cp zy 8lz0r)tdg): m from a person makes a sound close to the threshold of human hearing (0 dB). What zgr )zpw )(y8t u:l0cdwill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dBbwo auav0b3hd 3b3 m3iz*). er sound and an 87-dB sound are heard simultaneouslyuib)eba. zma 3w3 *3r3d ohv0b?    dB

  The sound level 12.0 m from a loudspeaker, placed in the sa)frm y8.1 x ozsyld,:-1 vhfopen, is 105 dB. What is the acoustic power outpulvf).8xhyarmoz:- ,s11y sdft (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output 4k(kh*b 4td 8ians dn:at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at * sn4k(8: abintdhd4k15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over u i3hz,xi :1p-qprvtp8; jb +gtheir ears. Assume that the soundvpiqu;g,b 8ipj-+ 1x rzh :t3p level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gaingp:i.r 2xf*0. dw lz+xsyyd ,d, $\beta$ 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 .yjpp;8g2 sdb)r..:6z* bhtdpbacxwto a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fi:)08:lkqqn ijzvu2bbg e.id* xed points with a fundamental frequency of 440 Hz and a.v d2 g0 uj:qz:ei*kbiql8)bn mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fi; av3+df2 at2iawkds) lled with water (Fig. 12–35). The water level is allowed to drop slowly. As it )3a+d ws;k2ai2ftvdadoes so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at5xev5lihqp(yx( - gdtw3cz3: one end and also 75 cm lon:tpl-d (e3gy h x3zcvi(55wqxg. How much tension 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 fuflf q4er.zhs0 9fcjlzztq8; 3 7zp6q5ll 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 5000x xzi4gp-5ijx( ckc 5–1000-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 and finds that the sound level is minimal at a poixz-0k jc4xg(5 icpix5nt 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 conductor on th(,g3 tc ),xq trly2rhbe stationary train hears a 3.0-Hz beat frequency when t)(3qc t,hr yb rl2,xgthe other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you 8ojq x6e1kmp93snhc1 is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant9qmen 61j oxkp8s 1h3c velocity)?    m/s

  At a race track, you can estimate the k4q9-o,xcvonj8 2 jfzspeed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car cj 8x-ozqo9nv2j, f4k 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, soundigbfdtr2/ p ,(24 xodomg2 igk.ng together, produce a beat frequency of 11 Hz. The shorter one is 2.402(fgtdgo2m ,b d xr2/gpkio .4 m long. How long is the other?    m

Two loudspeakers are at opposit3j ltg hsze);1e 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 listee tj;)l 1zh3gsns from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally abo.yd++:i -ho u8 vrwbukut 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves werer8b+kw iyuu+vd .-ho : 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 speed 6.5 m/8kgb; -wcqgn) 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 detected by the bat after that wave reflects off theg-bwc n;k)gq8 moth?    kHz

  A bat emits a series of high frequency sound pulses a*u;qzpe 5hkti ciz7 3*-a9uois it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms lon5zi3u*cazei9 -qo *p7tku hi;g. 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 sign cuabtp 0c3h 84kg6mo;/ /eomaals 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 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 frequency6oammoch0 ;e4ckbt 83pu g// a 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 prpia1vhpi-: b 1esence 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 m wide, and 2.8 m high. Calculate the funhi: vpbp1i -1adamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, callemz31 nflpi6 3ee:* k/-gcklxp d “singing 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 little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod, k:nxl6-ikp e1 z*pe/33flmg c
(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 fieww hg:au8viy )*b 9e2a(b6lrequency of about 1000 Hz (8awb*ea wig 92b):uy6vehli 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.n8ls1 o,oyq,b An observer on the ground hears the sonic boom 1.5 min after the plane b,ol s,oy8q1n passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 116reo3 o xj4iw5 $^{\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