What is the evidence that sounj;jmtxx(,9x m d travels as a wave?

What is the evidence ccln-/., n oklthat sound is a form of energy?

Children sometimes play .kkn q23 o;grg*alk7lwith 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). Explk gqk *anl7g3.2;rkloain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or waz+6bt 3b0tvnivenv+t z0t 6i3bblength to change?

What evidence can you give that the speed of sound in air does not depend zm).klt+nu0u-g vn*m significantlyu )0+-u ltmk* vnzngm. on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Wwk 6vb:(i6j hchy?

How will the air temperature in a room affect the pi,duv0xi1 +s zg d 4kdbb)y;qiav8p.p8tch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude 41fyif: qwno(v :pe/ wof sounds in various frequency ranges. (An example is a car muffleri4(p/fy:: vw1w fneq o.)

Why are the frets on a guitar (Fig. 12–30) spaced closer to, 2 4g0umrhwn*dgi8i qgether as you move up the fingerboard toward t40 mi hq,ru82dgin* gwhe bridge?

A noisy truck approaches you from behind a building. Initially youhy yw )ne n6mhk 9g6-zv*:c9cq hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hearn *:y6m 9kg-hw6zvh9c)ycn e q more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” 1:-/;a7 ruoj lu4 g;aiwyzphu 7bjab5 whereas beats can be said to be due to “interference i7 wpoj;ua-haya7/ig4b zbu51 l rj:;u n time.” Explain.

In Fig. 12–16, if the fre g ,phuxl.cs*jkd0v0+;adi c ,quency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or; ,djca+vd hx.*0pug 0l,skic closer together?

Traditional methods of pr3*x (z7v xgf h:nkbk+ootecting 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 blockfk b:vx h73xz( n*ok+g the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. d;zn k-l0yrpcb./9awbs7x s5 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencied5y /w-alb;709s .snprxbk czs, 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 move in the same directi3l um.jxvh0 *eon, with the same vej03u exhv.m *llocity? Explain.

If a wind is blowing, will thi aci085jto, ois alter the frequency of the sound heard by a person at rest with respect to the sourct jo5 i,8c0aioe? Is the wavelength or velocity changed?

Figure 12–32 shows various posit tbak*(j6j h 8hjnsh)cs/y*i8)t6zo) vfqi 8zions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highesthk bh(j)/o)hv6n8) qj6i saj*fz8csy 8*zi tt frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listenintr5;7v,q66 pjzllw3wkn2 m jvg for the echo of her shout reflected by a cliff at the far end of the l 6jvtjr;2zln57kq,vp6 3wm lwake. 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 bel8 wvbda/jq18now the waterline. He hears the echo of the sound reflected from the ocean v18 b/nq d8jwafloor 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 wavelea01skz. rkph aq 5iu69ngths 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 i;hug2bzh ;g4i s drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on anbu 4g;hgiz 2h;other boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the toeu(i l:n2 v0 g9wajxc8p of a cliff. The splash it makes when striking the water below is heard 3.5 s l (ja nxl8u92 gv:0eicwater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concretde +;df w*5kaae pavemen a+k;5f*a ddwet. 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 occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percentn0l0 rk6rtig36mv m c; error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strim;0t 66 vg3mcnk rri0lke if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity k ztk 82t+;s;r+wepi kof a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensitmcj0ys f *s1k+y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simuv(5jw1r-w. jy12odvoou c t7wltaneously at a certain place, what will be the sound level if only one is expl . vo1u-w1woy t2 odrw7(jcv5joded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanew nk:boe)8nr- with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if nn )be8 -:rwokthe 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, whereo(289gh zl9jaau9j9t wviw)gas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eac8wt9og ljawiah(jv2 9u)g9 9zh device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from 5iol- 1) p3j eesx9vugemn0+qa person speaking in normal conversation. Use Table 12–2. Assume the sound spreads-uv51m+) qe0 olesgiex 9pn3j 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 eardnpiawh e4op2n/)+ uku+)7wrp s9u (rdrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 25fzj 3,1p8bc wt0 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level i 38zb1w ,jfctpn 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 registered 130 dB when place1b rvfal 6n6dzwt 11lum* g/01hk 5n0 af-wcmnd 2.8 m in front of a loudspeake6u fa1wfcdmngr 0 lnha*k z6wbm5nt0vl/-111r on 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 differe ab)wgbw2,ap1z/tuh 3 nm hg(; ruc7,knce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint hr 2;hn,p w z1kbuc(,ug/ga)tbw73 ma: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the int -uwxo(jbmd 8zzy n*)l0 5rfq4ensity increase? Increase by a facw o*zj d(0ml zx4q85yrbf)u n-tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the7*- kxz hhrrxrgmhpp/go +7(z6 c/g. f frequency of the other. W-h kzx.7cg r*gmh p6f/+7zgp hr(/ro xhat is the ratio of their intensities?   

  What would be the soundcalt5 h ;o5;acupo( u, level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm atac ;(uu5,p5 hc;otaol 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 10(h:g, qaf-tqs3dx*: u*ajcfv 0-Hz tone that has a f sd*:3* ( jgca af,-uqvqthx:50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencixg:wqd,*:texb y)-s d6z 6 ksves that an ear can detect when the sound level is 30 dB? (See Fig6gxky * eszqv-b:),d6:xwtds . 12–6.)

  Your auditory system can accommom rja *7t mlvvw 90y-/szv5t-sw4of o/date a huge range of sound levels. What is the ratio of highest to lowest imy tf/va/ *o-v5l07jsr-o4 m9wv tzswntensity 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 frequ4 +0h*gjm)ndgtun gi 3ency of 440 Hz. The length of the vibrating port 4) i*jgun+hdgn3mgt0 ion 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 112 cm long. What are the fundamental and first three audibew;*;.xydh: r whz ;sjle overtones if thehxyh*.jww d;res; :; z pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from bxv 5 2x rtcrt6a::he0f. p+ululowing across the top of an empty soda bottle that is 18 cm deep, if you assu0hafx u.puc6l:rt:5vt2 x+ ermed 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 spanning the ranguo0mlgp mz,3; e of human hearing (20 Hz to 20 kHz), what would be the range of mz3glpo;0 m,uthe lengths of pipes 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. Whaqk;7z p ncv75mt will be its fundamental frequency if it is fingered at a lengtz7 ;v5kmpqn7ch of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle C ekikj,uwg0 6m2zl.h zrd 2,uir.g; -t (33w 0 jie-ri;l z6dkugkz2g,r.h,m 2u.t0 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 openloq) yy amci(9 l-xy.4 organ pipe that emits middle C (262 Hz) when the temp -.9amc)xi l yqo(y4ylerature 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 8 4 r(onvr w)vdzd.wfn5fmofp)v n )-,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 9 cvhyx e (rf:j4/dg*:nm5shishould the hole be that hein/ (x m cfr:v4*5 gdys:h9jmust 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 2645pv 1 -i,cze4s:vuf6u oo0m mp Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Sh,1c6evs 5fom iz um40o-:uppvow why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It rmnm8b8 p b6 xi-g*k.jtdrh b;+esonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wm xb m-i6kdn+b;gb8pht .8*r jhat 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 q ;dtutzf):9dk hi.w(t0 q8 rc$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14v gvet7wcfp) orr7;5*z. il5n-m-long organ pipe at 20 7fi5rwp l7g.ro;nv te*v5cz )$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.dbzeer+3jo u (.3u3ie5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate thr.uj3b3 eze+ o ude3(ie 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 11 ygdof/k -lxj,ose;when trying to adjust two strings, one of which is sounding 440 Hz. How far offkelxjy-1d/s, o fg o1; in frequency is the other string? ±    Hz

  What is the beat frequency if m5,*t ksgwvrfhnu) 5k- j)upf6iddle 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 23.0l: q e ril./*(ey ajhwbkq+/w5 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 occurs when they are played simultaneously, estimar/wq(e y *jhl0qeki:+w.l/ abte the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundedy3i(d us.wb;i with a 350-Hz tuning fork and 9 beats/s when sounded3( i.ibws uy;d with a 355-Hz tuning 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 tension in -qm7 hq1)xtw sone string is then d-1sx tqmh7 w)qecreased 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 hse te9 w-.qqf:/mg i9feard if two identical flutes each try to play middle C (262 Hz9 f.sq egmqe -f:i/t9w), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuninz(2 lgmhk*6 odg forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A o6z2khl* d( mgand 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 34f0.2 ;je pme3vgspxl1ex a (j7wmnq* .00 m from one speaker and 3.50 m from the other.va;pqjwxgf ee7*l nmp2j.3xs1(4m 0e
(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 piw0k.c uolat /(ano tuner hears three beuao/k l .tc0w(ats 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 wami8o5 5b kz8+hcyb9acvelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Ak8mb+ibyhco ac z9 585ssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s s1xevq7vf3r6lu2 8m( h wghc t6iren is 1550 Hz when at rest. What frequency do you detect if youm62g17eq vxhr3vf 68t wchl (u move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wher48wqts7n6 a+(+q jeeec6 jhat frequency do you detect if a fire engine whose siren emits at 1550 Hz4njeqws6qe78+ jtce6ae+r h( moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fxf,6*jb7p ikirequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward i,6f kip7ib* xjt at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is68 h k .f;tj4*mgdrxbb atjdm;t*kf 4.6r8gbxb h 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 the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends outqp 4dlg9b f2ouc;sn9jaxz 4; 9 ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received s94zgd 2lscqxaufn;b9 o9;p4jound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emipx0xqg3 a04t2 r e1ydpcz4g+wvp j8e-ts an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflecte8aj+z4eg 3-c e4pt0 pxrv w20yp1qd gxd wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flatba jxkc. ;;hd5k ndes 3u-6v+t train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at re +t6dxk3 d a-5u.esbj;vc kn;hst 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 8ehpx.ud3eo+xu , sw) waves 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 frequeno8ue ush 3,e.)dw xp+xcy if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequ urrok .tm-*3k6ze; osbu0-nnency $2.25 \times10^{ 6}$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. +d.e 4o ypvys1i n6nxf+8z ql)When the wind velocity is 12 m/s from the north, what fpi8d6qn) f l xnvsz.y4+ye+o1requency 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 sc:il0,ri x sv+;zh/p19z fmr20 $^{\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 3hqz7d*hzdx)es :tv 9(a) What is the angle the shock wave :e79dv)z sh*q hdxtz3 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 n fdb9l(7;gzluv t1ybk ,fprz a1(6./zkn0fw thin atmosphere of a planet where the speed of sound is only about . ;pn,b(d/f1gbzrtku k769y(1nfvwl z l a0fz35 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 bfa)7x -yfsi28500 m/s strikes the ocean. Determine the shock wave angle it producex isfb y-2f)a7s
(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 .z5ii aeu i1dm/klx )*k2h6g t$/theta$ 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 the grogv)i; *x 3bqpcc i9p5uf-g ap*und flying faster than the speed of soundvc* ifxp9p; uqi-b)a53gcgp *. 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 se)hm e-6) p:lwl;rhr8va kw0dbnds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is design rwk:pldw a;0rvh)h8e l-m6 )bed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many geh;34yjt43ee jk g t0octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony2lvc7wt )0u3t ni:8p3veo 3a qvm1gty. It consists of many plastic pipes of v: a)w eocmn 08pu32gvtvt 73i3q1yt lvarious lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thbyvwbd8 /6nee/sw e 0*reshold of humave6w*ew dseb//b 0ny8 n hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level hgcvs9/f5 6nawhen an 82-dB sound and an 87-dB sound are heard simu vf9n6h5sgac /ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i. 3 .sl*vetckps 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiatekl.*s3.t vcpes equally in all directions?    W

  A stereo amplifier is rated )zw/eew qs+g* at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz/es eqw )+w*gz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectic t26b7x*z li gps;i+ove 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 from a jet airplane engipcg+ bi6ix t;*zsl o27ne?    W

  In audio and communiczrg kl;/wiv3 b3 ,,q;ozpl9rcations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned3:bw8xwdirklq;( rk ( to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violingawre-84dh,/c 2w xh7) f cnte is 32 cm long between fixed points with a fundamental frequency owhacg4w- 8h7x)en/ e2df ,crtf 440 Hz 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 above a veov9dhvuym( xp6,2a l kfbf9.)rtical open tube filled with water (Fig. 12–35). The water level is allowed to drop sa9p k2olf.yf(v bmx69u) vd,hlowly. 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 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 9vqi3 j* bshh5n8,puj near a tube that is open at one end and as v,j*h8i5nu3 qbh9j plso 75 cm long. 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 reso d4vr(6miv j,cnate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Ta , pv2mar*:nw (qx5hehe sound i xp,2a5*a: hewvnq mr(s 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 farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Onhb4lkpw1ks( b89 e 4yqe train is stationary. The conductor on the stationary train hears a 3.0-H4pykseb4q 8(w 91 khlbz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approache,s csi- .u* -cl;b.x5jwoeqfx s you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the traicbfs,; iu* ojc.l5w-qe x.sx-n moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lisb s-z-aiv 9u0)gjse9htening to the dif-)9 jue0gsh b-v izas9ference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soun6feiy i v4b7w 5p:a(nlding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lo p:iya7wn4iel5fv6b(ng. How long is the other?    m

Two loudspeakers are at ese/c *ia wwff+wl3q -.rmeb*6u1-p uopposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12e. ilfu +bwee* cqp-f* w-a/1urmw3s6–37. 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 speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the q9+yx0qeyzm2z - r1avc)qku4aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow a9 )0q cz umykxr-yzv1eq24q+and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying tnksh ly( lz dt,7g85p1oward 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 w ztld lsh1k58n,gy p7(ave reflects off the moth?    kHz

  A bat emits a series of high frrp6d mt68j4 2aiz ,gehequency sound pulses as it approaches a moth. The pul h tz4e268gajp6r,idmses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used 0ocik 8vxo1.lto 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 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 f ki0vo1o8cxl .undamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pregqvphcuyy +:,- 2 cbal;9ue. nsence 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 fundamental frequencies for th a: b9; vuquhc ce+yply.-,2nge standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumqp zwbq+z e/6n; -wgvg5. rgsk5w 3v h2qco(3ainum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Wirk.v b6sa+ gqg3o 2qn5h;z/(we v5pgcwqz-w3 th 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 thewcw kyx+3 3mc: i5v;+f0vvmob human ear at a frequency of about 1000 Hz ycwmv3+w5ib 0m;x3k v:of +vcis $I_0$ = $1 \times10^{12 } W / m^2$ 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 thhnv jju0qojd ,kt3 /2dgzsc* e7d.y: 9e sonic boom 1.5 min after the plane passes directly overhead. What is* j.ksjz2g3nth,oe9u70: vjy/ qc ddd the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb j-0jc+1cnsqqm- gj 2soat 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