What is the evidence that sound travels acqd) fdjjzt;-r r iz7g: .qg./s a wave?

What is the evidence1x /mhtv u6bz y62yqr/ that sound is a form of energy?

Children sometimes play with a homema58i jwbhk. 7qvde “telephone” by attaching a string to thejv5qw. 8ikb 7h 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 wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect ot3(ivacag- , the frequency or wavelength to change? -g(ai ,a3cvot

What evidence can you give that the speed of sound i5ocmk0pc+), v *rr*a f zcj)wq)iut3 yn air does not depend signifif zp o*j m))*uc kiyc)5w+rtr3q0vc a,cantly on frequency?

The voice of a person who has inhaled hv*cy-uzz ms9 /t om+o)elium sounds very high-pitched. Why?

How will the air temperature in a room aff+.j2o go1u)swy . m x;v7a nc.a 2komyv-vp.bnect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce4mwb8p4 10c nxm5r/tviy0ugxl x o4i5 the amplitude of sounds in various frequency ranges. (An example is a car muffgpix4 mxylv8 xwn0/1445romc 5tu b0iler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer*7-uh/ y wraluq .2;0y nxxupj together as you move up the fingex 0 *7/x -p yhujqya2.;uulrnwrboard toward the bridge?

A noisy truck approaches you f y/ krbndups8)er5h);f 9 ro3xrom 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 hear more of the high-frequency noise. Explain. [Hint: See Section 19)ybkhno;38 rr s)rdp x/5euf1–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatuk+s )n lpyn5(s can be said to be due to “interference in time.n(+y lkn5s u)p” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points sq. adhv,p 3am3lm ytep5i7m 1a9,)rsD and C (where destructive and constructive interference occuras,e lms,mvpmarhd3q9 a )ip.y 31 57t) move farther apart or closer together?

Traditional methods of protecting the hearing of people who workhu1o 8b4skd , i-1yimkq4vp)g 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 1s1uyb, gm4vd -8) k iqihk4opambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. b:ti, .dnhh2fpkwn7-0o 7norp; xd5f Each wave can be thought of as a superposition of two sn- fw:d.h57tnp;o7k,0d 2xnr fhb iopound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mo +u ci+9wfsok:ve in the same direction, s +9co:u+wi fkwith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of thei a v34o0k4toe sound heard by a person at rest with respect to the source? Is the wavelen3ae kvo0 i44otgth or velocity changed?

Figure 12–32 shows various positions of a child in motion on /:jcc+ ejh 0u0aidu1x a swing. A monitor is blowing a whistle in front of thuji xuhc1:/ade0 +0cj e child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for n;j/j* tjyq5athe echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length ofjyn;*/t j a5jq the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sidt:1ayuo/s 4 myy-e*zkeo dt ;-e of his ship just below the waterline. He hears the echo of the sound reflected from the ocean flouk-o *t t/yeze4 ymas: -y;d1oor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airtixxgw.kba*a 7-y+b6 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 das 5d,mkay1a 5by. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heardak1 5m sb5a,yd (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Thskn zp3,ccb r;wfc6/9e splash it makes when striking the water below is heard 3. pc;cbcw,/9sr3f6z n k5 s later. How high is the cliff?    m

  A person, with his ear to the gro9 6klu)h)lgw; r2 epolund, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact ;wllh)p2 eul go) 6r9koccur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one milef()2k h4onvke of distance by the “5-second rule” for estimating the distance from a lightning strike if thef( hovek) n2k4 temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lfjj) m*oyfi9uk(l ,j5evel 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 x *8u)e cwk8*evof 7 lhger-.rsound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dBi6 qftsm.k7umi5pw3mo (+xi - when fired simultaneously at a certain place, what will be the sound l3+. 7(wp uioif56xmtq km-ms ievel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airs l 2cbc6szd s(:vb:.z26 av56 gpbuqrplane with four equally noisy jet engines is experien6sspz2g.:5bv6r c sbv6dbqu al(z:2ccing a sound level bordering 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 dB, v 67 cej(99lywpp 5co+0lmd;m3u tt frwhereas for a CD player it is 95 dB. What is the ratio of intct tempjd;u(cw3 9l5voy 0967m+ f lprensities 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 normal cml8 88ecekelq6.4jxjjj)a7 *g9 jg ugonversation. Use Table 4.jcjg67q8 8k* xg9jejl u aej lg8e)m12–2. Assume 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 whose-aiu 9h;t4p0n 1lggqc 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, w qh- zkwducyx)easdq**cz ((-4p z( s2hile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in q(4w* zs)sh((z c-dqzdyp2k* xcaue-decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter re crf4c6p:v- wob m4l9jgistered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. c bo4 f-lm6v rj:c9p4w
(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 differe nrf6eodk 382ynce in sound level of 2.0 dB. What is the ratio of the amplituo38fr n2kye 6ddes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (avnt sci/nc(5e a74zg3) by what factor will the intensity increase? Increase by a factor /t3 47zngcna5ve (sicof    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one ha+pczm59tj+jaan, o r(g js01ab4 zkw)s twice the frequency of the other. What is the ratio of their intensiti0c w)b ,jaj 5(kzag4n 9t+ar jsp1+omzes?   

  What would be the sound level (in dB) of a sound wave in air that corrk;iauc s0: 3-rwy- fyy1nmrd -esponds to a displacement amplitude of vibrating air molecules3s d-wy ya :ckm0nu-i;fyr1-r of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to x4 k9zthv*q m+xo+mh/seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12t z k*x o/h49qmhmx++v–6.)    dB

What are the lowest and highest f3mnle9()ozog xb, +3h1j 3q n6d,vtdktuqxw ( requencies that an ear can detect when the sounj1ndnu93qx bgo) tt3q l,mx(ode36, (z+vhkwd level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommb v ,ee3hbj-6b5c* gkgodate a huge range of sound levels. What is the ratio of eb ,ec6-bkjg *g3 b5hvhighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frv y9g*ezop ecvc/ob1(we,6a :equency 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 the string be pgcv:p ozveeca,b9 6oyw( 1/ e*laced?    N

  An organ pipe is 112 cm long. What ar q/c)sc) ux)o ypw3xz(yg/yt 6r eo*1ke the fundamental and first three audible overtones if the pi1)ux yo (x)ztpcocwg*/yyqsr6e /3k)pe 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 expect2gj5uigtku8m2g2 c 0k from blowing across the top of an empty soda bottle thatjg02t kmi2g2u5cgu8k is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes sp//phdp x*y yj8wz(e; cmsg.+w anning the range of human hearing (20 Hz to 20 kHz), what would be th*w.8/pep j;y mx/(d zs ghy+cwe 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 c (/ksbt5qw rc/h:kbp7 fp,t6as its third harmonic. What will be its fuf/(5 pkq6t, b p7kstbwc/h :rcndamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar1wt vi)wi s36r string is 0.73 m long and is tuned to play E above middle C (330t 1w iwisv6r)3 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 5 xzl zg80(zdbthat emits middle C (262 Hz) when the temperature(zzxb0g 8dzl 5 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 elo9plsl6 bnd(m aecv7l i6x)*5m n)/at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 opal b53ov6x /should the hole be that must be uncovered to play D ab5va/6x lb poo3ove 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 peuuz52079qg0 aqcbt( na +olg)n e4 ekipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why th ag42)0eqeoeutnbgn q9c( z l 0k75u+ais 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 ;d8 .5r1)mz iw it/3 gr)crcsdkwx9.iqw jv)n1.80 m long is open at both ends. It resonates at two successivwr.i53ni9dvcrx rc 1qz)8g)s.w );mj i kdwt/e harmonics 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 9hlow2 5v58x9 xrbmf r$^{\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 aurf/ 3clyq; t7kdible range for a 2.14-m-long organ pipe at3/tyr ckf; 7lq 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apg4uxwk-z rvp+lawg3.p0 x + z*proximately 2.5 cm long. It is open to the outside and is cl*gw0.4rpk wxuaz x3lp +z-v g+osed 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 graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s f :0 y w:e,52luy:jrax*e /vh9johmehwhen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stjahr0e2yfj emwu9*5e hlovy/:,x h : :ring? ±    Hz

  What is the beat frequenrg1q, (- ex uy(jogc;hcy 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 oper5c5z9f ft w*vrkpu,2 cates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occ, k pct*fzr9fvw552ucurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a z2v 3hd9aw95a p0jfmp350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequencz3jp95fva9p0ham w 2d y of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. T lubx*(lt h4qaxf11.lhe tension in one string is then decreased by 2.0%. What will be the beat frequency hehbl.1au*flxl 4t x (q1ard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play midhkl (8c9jyef6l *iup* dle C (262 Hz), but one is at 5.0°C and the other at 2*y l9(pijk* 6lce8fh u5.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forkimkq1j 2h0 i4tpd7ws8 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 a7mt 42idiq8s w0kj ph1re 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 p,eef:rp et+9pwl/ j pti+ ;0f1yy5sb gerson stands 3.00 m from one speaker and 3./ bwf;ytep+epgj r tls+1if:y5 p,09e50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hea:+nslhd k-abi8 z(13 y2fryix1y8i m yrs three beats every 2.0 s when they are played together. (a) If one is vibrating at + kiam (i1l8yys:if- byn1 2rdxz3y8 h132 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 in air. How mans*jk) o)j2qhpy beats per second will be h)j osh2qjk)p *eard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fir: 1hbb exe9b 7fid,e(pe engine’s siren is 1550 Hz when at rest. What frequency do you detfd7ebxh1bp9 :ie(e, bect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose silck+e a+cy9* qren emits at 1550 Hz moves at a speed ofk*caq+ l9ye+c 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 towau ax7tkn g6.b 5hj6m2ord you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? k2mh un6t.ogx bja756 $f'_{source\,movine}$    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 equif: t:.q n (/6jg,rvo+bgd ctktpped with the same single frequency horn. When one is at rest a(:dkq+v6ng,:ft.cjg /obt r tnd 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 the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends +e:ty2nmeej; k+0 mb yout ultrasonic sound waves at 50.0 kHz and receives them returned from an object mov+eyn m2j;: tky 0ebe+ming directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a walle5.zlkv) 2hfn; ebk4b at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wavef5blv4 b2nz)eek .h;k?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba11fpvhz,y)hw was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while1z pvhhyw,) 1f 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 ,6- ahnm42 1g ngq ja1hvepte)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 tgjpa,h- hn2)qm4g v1 1en6 aeis flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of* )/y5 evhjhnaoe*p. x8pm/zo,ip 3 wt 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 wi3lvv:, fhx pj4nd velocity is 12 m/s from the north, what frefh4xv, 3lvp j:quency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 2w 3s0) dn ig0(h*cssy ur(8xps0 $^{\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 whevpe0b6zq:s5woo q+ q6 re the speed of sound is 310 m/s (a) What is the angle the shockw s 65oq6oepv0q:q+b z 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 atma /3o6et64) yzl2wh w4itpwrfosphere of a planet where the speed of sound is only wi /zfyeww)h6 l3ota6rt 4p 42about 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 e0m vl .tz,z8ithe shock wave angle it productm lz.,z8ei0 ves
(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 -f;df84v ubez$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and seeb) ;n 9jjxn7n75yo qcp a plane exactly 1.5 km above the ground flyin 5ojn7) 97pncqy;jnbxg faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. 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 2jl9 8.w ngi ,ji,e 1vw5bm8bpo0,000-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 is thevw1b 8 niwji,o5e.9 mlgp,jb8 minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there iju) +m ,aoagz:n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony 1e2nsnn5ccmdc5+ k2q. It consists of many plastic pipes of various lengths, which a2c2eqn 5nskcdn+5mc 1re 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 makecd1pi ko+d1c )/sb+ sps a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosd1ps+ p+/ok)1ccsdi b quitoes?    dB

  What is the resultant sound level whapn)c7lrg9fwu4s9 s4jug 79oen an 82-dB sound and an 87-dB sound are heard simultaneouugwu9rso9 ) lag47fcj ps74n 9sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opyeo8i+ r ms44ok)4) ufkzxxh- en, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates e)hor4i y8 uo x+mk4f4zk)x-sequally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pow1.7c42alib8t/xynm 4ofd6wxz0e irter output drops by 10 lm rf2wyoi4ax zdc1bt40. e 86/7x nitdB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet airpd xima63ez/2t -ph/f(sh1whiq ()utcraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, iu ih)hwxtt p36adh szp (-2 fei/1/qm(s 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;z z+w6z(2 vned*zjgl, 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 frequency 15nr* justj:qs/ u+r 5y$\frac{1}{2}$ 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 32cs .cn -r-j6ty cm long between fixed points with a fundamental frequency of 440 H -j ycnt6.rsc-z 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 vibra)2moe tv c( m9h y2b2r9//zteen:g ewrtion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water ntmg ywz 2)92hov/2r:/e b ree9m(e tclevel 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 mupdbs h-pw, 94ass 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 produce resonance (in its fundamental mob4p h-9,dwusp de) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t j:6u** phamt u72ywjlo resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pures07 xx. o*f0hno7wr hd tone in the 500–1000-Hz range coming from two sources. The sound is loudestw* 7o0 fhn.do0r7x xsh at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is 2p xx/r,uqo8istationary. The conductor on the stationary train hears a 3.0-Hz beaqiu8/x ,op 2xrt frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle n wx ::r;saeuk1o2 p4imt we,(as it approaches you is 538 Hz. After it passes you, its frequency is measured :a,m(w12 i kpxw ;:nstueoe4ras 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate x28k+wtgxpw 07oey1nthe speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose to8egptk7 w+w12 yxn0x he sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding towkgi.p(0i fk; gether, produce a beat frequency of 11 Hz. The shorteii ;g(.0fp kkwr one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opvk+u mrcs02 g(zom9.eposite 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 the speake0zrmeo g 9mu(sv2 +c.krs, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aore r7f16hi5 if,2vgcnzta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bloo7vzffn6i5 1e g 2hir,cd 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 spepcuhtq qldw-- /(./ubed 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 detected by the bat after that wave reflects off/ t(bq -.dlphuqc/ wu- the moth?    kHz

  A bat emits a series of high frequency sound pulses aw : zi wa djg6k2 nwdwvkg6*cl351l+d3s it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 6w:6lwwznkl +wg 3 5 3ddkji1gc2dav*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–:zk(nb/ u b+yi38) was once used 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 in (:+bzbnu/kiy strument, 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 compromise(sa2,h twz tow8nim(me aywbc 86,9+bd by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0(8,m w b2o+yb,nst iehwzc(t98ama6w m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slva) zjek,be -d+4+wuc at,r,v ender aluminum rod held in the hand near the rod’s midpoint. The rod is strok utw+ )rkav4+vz-,ac e edb,,jed 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 of hearing for the human ear at a 9uks;w+qz5 iaam01j lfrequency of about 1000 Hz ikja+;aqsl1mi z 9 uw50s $I_0$ = $1 \times10^{12 } W / m^2$ 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 s2 k0hwwt /w2pponic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? w2kw/w th2 p0p   $ \times10^{4 }$ m

  The wake of a speedboatud zaw n6:tsc/r:p1 fg ul,54v is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h