What is the evidence that sound travels as a wave?2q1sg6pu,vtpfj. fyn9 +)spj

What is the evidence that sound is a fovc2taa8,km . qndkk. 3rm of energy?

Children sometimes play w3msgjq1 2gy fwiy3:6(f1dn pmith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from onefsy 36(nd pmwg:ji12 yfgq31m cup to the other.

When a sound wave passes from air into water, do you expect the frequency or :2xdn15 hwhyn)n+6qhct cf k+ wave2x:+d th1 fnq+ky5w hnccnh6)length to change?

What evidence can you give that the speed of sound in air does not depenu1p y95y4lhd;i9soj zd significantly on frequen9ply;soj1yz9 i dhu45 cy?

The voice of a person who has inhaled helium sounds very high-pitched. Wmd6co*5wk(kodl2ir 9hy?

How will the air temperature in a ljyciwh: 09k91k)4e*c en lf troom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplit 8l)gl(4a rte2vm2jhx/ 1kujuude of sounds in various frequency ra 41rl 22ljgjxa)um(kvut eh /8nges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced cl( 0k j.4ffvfye4-xjmsn :q1o1 :b fdo;.wpgeeoser together as you move up the fingerboard toward the bridg newyff10x:. bd-pe.(jo4k14;fes:qg fvomj e?

A noisy truck approaches you from behind a8/6pb, cqenz v building. Initially you hear it but cannotv6,qnb8zec /p 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 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spay+3eq: g2ve:z:z efyzl, 6izoce,” whereas beats can be said to be due to ie+yq,:gzo :v3ze2zz6l ef:y“interference in time.” Explain.

In Fig. 12–16, if the frequencyv lh u6 m; 0 rxxdmm:qv5if,0+lo)cmh3 of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together? im,luh0fm m xq5mx6rl do)v3c 0;v+h :

Traditional methods of protecting the hearing of pei*) 1/sgmp x mv*b8bmoople who work in areas with very high no) gbbmsm i1mvxp*/8 o*ise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it 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.d)5ggbj xlsb;ji 52 5p9leq4 g Each wave can be thought of as a superposit5gi52je ;9bg5d xgspq)b4j llion of two sound 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 j *gdfi8qc i0:cyup1 2source and observer move in the same direction, with the same velocity? Explai*2yd:ujc1g8 i if pq0cn.

If a wind is blowing, will this alter the frequency bg ch pj5emj03v3(d8e of the sound heard by a person at rest with respect to the source? Is the wavelength or jb degpv( 033eh8m5jcvelocity changed?

Figure 12–32 shows various posu,2 wa(epl rfle5a 3z6itions 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 highest frequency for the sound of the whistle? Explain yp(l523rwae, ua flez6our reasoning.

  A hiker determines the length of a lake by listening for the echo of her rac1qp8(.9u7ya ffo *d w+9mnjp yeg (shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of t(a jep da+(q1 n*cf9o8.umry7 py9fwg he lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sikz 743q i,ehsand jfi31h3y.lde of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significdy,i.7n3ki1e 4h l3fs3h z aqjantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in.cy.ika tk ; ;6rw+0+l rbt2oftg:ev c 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 jushzbg68wii*cjm,s;p ) t above a school of tuna on a foggy day. Without warning, an hgpbij8z )6;cs,*iw m engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The sr6rzu7o(jp t+plash it makes when striking the water below is heard 3.5 s later. How high is the7zourr+t6j( p cliff?    m

  A person, with his ear to the ground, sees a huge sto(ls qmu1wp:j8ne strike the concrete pavement. A moment later two sounds ar(:sup lwj1q 8me 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 percent error made over one mile of distance by the “5-second rulw5, p/k -dzfu+mwxi 8ae” for estimating the distance from a lipkuza/i + ,-m wwdf85xghtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound ai( z : x0z6 tftyidsbez54s1h8t 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 jujgys;9a d(5 +z;aat a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levexw.6r)aw a x/v-9w ljhl of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not a9x- )ljawr /6wxvw.hdB’s.]    dB

  A person standing a certain distance from an airplane with four eqrp*1( lj jwzf8.u( gjyually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What soun1* yj.ul8jfp g(wjr(zd 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, whe3fc31 p .xyqnpreas for a CD player it is 95 dB. What is the ratio of intensities of the signal and thefn x.pc1yq3p 3 background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power o in4poks-;dm8utput of sound from a person speaking in normal conversation. Use Tablns;p o48-kimde 12–2. 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 5mtx)bx7uzx 45(p s xvarea 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 zg /:y q1 w:+;w/w8bwidnzfjyW, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound levew;wyq:z b/nf:+jwzyg/w8 d 1il in 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 6p:8n3n k2 wugbkyk8i dB meter registered 130 dB when placed 2.8 m in front of a loudspe:nywiu 32nk8kg6 kb8p aker 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 dif 8:ar 6,mcj,uyastki5 ference in sound level of 2.0 dB. What is the ratio of tr 85a ,: majiu6styc,khe amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inte;px/caks;gxy9,hy ,k nsity increase? Increasehcgs/xp,x y;k9 ;k,ya 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 twice3)qi/-bi wtxxh(dmo . tq4x 8q the frequency of thexid/q 4-qxithwtm 8bxq ).3( o other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wav,a2 6n93osx( fmfg pjle in air that corresponds to a displacemea 9lnms3x p(f ,gfoj26nt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to ses 5u +jbnk18skyka1;rem as loud as a 100-Hz tone that has a 50-dB sound level? (See F;usj kyb8sk1k1 r+a5nig. 12–6.)    dB

What are the lowest and highest frequenci s5s 86r(yaj sy 9kipcu-aav*7es that an ear can detect when the sound level ipvu 6i8ss*9 j-a5yyc ra7k (ass 30 dB? (See Fig. 12–6.)

  Your auditory system canofn16ma m7 /yb accommodate a huge range of sound levels. What is the ratio of h mym1f7 /ob6naighest 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 frequency of 440 Hz. Theoi (yo;5l ,uv 8(swaso*v7oom length of the vibrating portion is 32 cm, and it has a ma5oolovs sum*y7(; o 8i ,wv(oass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lo0 rghbj18y 0lhng. What are the fundamental and first three audible ove br1 h0ljg0yh8rtones if the 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 expectz e9r)iq0efz( from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it we(r)9z0 z qfieas 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-tudg ,w.swb*)s91p/ z e8gxqip10r zkobbe pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of w81) zwpb90x zk*.oqs pe,/gd1ibrgsthe lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz a-6ob qc tsea.sj3s,g7s its third harmonic. What will be its fundamental fe 37tgsjs6sb,a qo.c- requency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle u1ms wy/gn e*vm7)kxmp/ag+:C (330g ym7u1g en/w*mamsk:/ p)x+v 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 ofj jeo,,osl)x)v5 xlfnma- :k2g z5h :m an open organ pipe that emits middle C (262 Hz) when the temperature is 2xzkxo5melglv, 2ms: ja) )5 oj-nh :,f1 $^{\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 a)z2i +s6a c1viyo )kr nl+oyg1t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece:yzi10qwwq2ysn; * lb of the flute in Example 12–10 should the hole be that must be uncovered to plalwz0;*q yqws 1 nb2i:yy 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 2rb a ivi: ,9jfmb jc i:,f6mt1uolm(5564 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Sv,fr(ti:,5mm:ja fbi ulc9imb615johow 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 resonatmrqo1 85.d bc9)dgubo*3 a3yfq v3.owg8du cx es at two successive harmonics of frequencies 275 Hdb5a.8u q.g9 8uyro3d*1 )3 d g3wmcbfvooqcxz 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 ene7v2 *4evr q$^{\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 presentbqp6v3bu4 r7+ 1 naxvr within the audible range for a 2.14-m-long organ pipe at v vb1a rn+q 6rx7b43up20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelyjn/bwdpgo( 5) 3b/ix,k9 c pwy 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 informationy g(p 9x/ d5jwcpob,i3/knwb) 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 when trying to aw4to l;eq xzc4o* s.*sdjust two strings, one of whichx*sso*l4c.oe;q4 zwt is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and 870ek/rd /xfxb :u8 twd yvc0yf/v *yn$C^＃$ (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 (br pq1. fag5*waoand 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, estimate the operating freaf1go*5q. awp quency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded+sv5x1h-e a )d: hdw:s u(huhp with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of+:sh-h ) hpd5e(uwd xsa:vhu1 the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the *l:)i7a ,6d;euybxafoi r i(wsame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heardda6:yorbl7 ;,xiawii*feu () when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fg49oof6fh sp* lutes each try to play middle C (262 Hz), but h6os *fog4 9pfone 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 frequency of 4+k ec*r2bdlt d/ed1 b-41 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, l+2t e-bd/r* dbked1cthe 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 one sp1og7 q.9sfgsbc )v/sw eaker and 3.g/sq vb9wgcos1f7 s .)50 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 v3y ytw0 y:7q6z jmky2ea (8ceHz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one6yqj yve8:0tzyk am 23wcey(7 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 wavelenm)e12)7rn x)m/l*l zz fgixit gths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 2lzi)) lirg2)1 f/ *mntx7 ezxm0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’a.avrc **j5bys siren is 1550 Hz when at rest. What frequency doyv 5a*ajbc*.r you detect 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(kd 5,o/+dxmo fr(fxnx:rr 7nn) 0bxq do you detect if a fire engine whose siren emits at 1550 Hz moves x0q5r bx:x(nf7mofndn/k (+ r ,o)drxat 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 p( fdfk;ge(3 3 ijq; lcm52tlwyou at 15 m/s versus you movi f3;k 2ll im( 5f;3dwcpgeqtj(ng toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single freqfg bhr -mc.6l9uency 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 obc .glf6 9r-mhf 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 h 96lp7o3n cwvkHz and receives them returned from an object moving directlon9h clp67w3 vy away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall aw+4mto2f7wjhu 6n2zk t a speed of 5 m/s As it flies, the bat emits an ultrasonic soh fu6w22+ zo47mwn tkjund 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 expers os5 n4vn,er4ut6fh v t1v8+uiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway uh6u5,sv8vetnts1+ n r44 vof 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 speeds. S 2jy3b3h+wcd qoakf36f//x9wtsa hr +ypo* 7quppose the device emits sound y6jastfxqc+ob9fy273dh p k+ 3*ora/ 3 wwq/ hat 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wav *4nu+gtgb1yh de:(-fmx v5 mges 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 wind velocity is 12 wv:+e mn:y4qfdku;1 :a pxi8c m/s from the north, what frequency will observers hear who are l;uap:xi81n qdcyf +:: wv 4kemocated, 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 apd1ej33hi iq+ud3g 3s 4k n7az7mv 2eat 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 8 qat7trjx3 j3speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpx3aj t j7t8r3qlane’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 atmnymo4dte7p)61am2wh/0z ruk 3ah 5n cosphere of a planet where the speed of sound is only about 35 m/s0twr4ozc5dhp1 h3 mym) 7ke/aan n26u
(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 q 4iz8k5d ji6w7lsostg l 3l074 -fpjyocean. Determine the shock wave angle it produs37j4 0lf dist8qo5l4pgj6wzy -7l ikces
(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 b4 y1ux3ca f 5gg54sha$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and sehwi pku: 1dswf9 -49hve a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizonta wdh:f vhi9 1w-pu94skl 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 de+c0i (u0ig-5 flvhm,ztezll.vice 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 is the minimum time between pulses (in fresh water)?u5lv(tfi0-+z 0hizl cmle g.,    s

  Approximately how many octaves are t::dmmfq/9 6 p,hrlefd*r tjs 2here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mansv(2l ) 4/o9 :fysxzrmxdgb6ry plastic pipes of various lengths, which d2mgrz6vol 9xbf: )/ss4y( xr 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 threshold od, 446/qkqvd yja5*-+va/tk hclm jbaf human hearing (0 dB). What will belj- v 6qmdqj+a4kay d/ba,v*k4c/h t5 the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hea zh3uyrpmn 674 .gu)kard simultaneou6ha43 ygmpuunk . z7r)sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What icmr +, xcmkm8- r8b6 n*+tzgvbs the acoustic power output (W) of+bcmncg+bzvr - 6,mx8rmk*8 t the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at ej+n6ios 1va6 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powaei j6vn16os +er output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear qy(j84*+pp+ 9wekc+:j l7dyjj okpq:pss* e gprotective devices over their ears. Assume that the sound level of a jet airplane ej9 c sdjyqpe::p 84jlse7g**o +kkyjq( p++p wngine, 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 communicatiomjocik 5q +7i.ns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a freque1 ucljd/ 1hs0gq1-q3wv.fg s mncy 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 zy 2niw g06kd132 cm long between fixed points with a fundamental frequency i6 gnyz20wd1k of 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 vertical ope mf)rn 2pws)u n28+mjmn 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 tju2mpm rwn))2m+8s f no 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 neppa v9 sde/e4 az+e2:rar 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 ee9pz avrd4+sp 2/ea :its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f v:ls zkmjugd3psr*)j.;( f2dull 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 c3o* ivx8jh:mw oming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of 3x hm:wv8oj i*the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. T pp6bk7qz .q6ehe conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mov b6k7p.qqp6 ezing train?   m/s

  The frequency of a steam train gj6py4wfw l /o9(z+g pb2dl;f whistle as it approaches you is 538 Hz. After it passes you, its freqbpg9gw pdf46(wl2l+;yjo z /fuency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to j2bcd huf+vt8vw4p+ :. xp:wk the difference uwxv d hk84:p fvjb+.wt2c:+pin 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, sounding together, produce a--ufnj(k. j tmusav /: beat frequency of 11 Hz. The s/. f s(j jkanumtuv-:-horter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stavd5 .v+0vnc 14s- n(wbrq q viwbk(7votionary 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 qvn-q vk7v 01 s4bovi.(rbc+vdw( w n5observer 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 aorta is normally about 0.3 yp t+pvstus*c2g +x 6zy/k*-j2 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and refz+-*pv6 yxk 2yjt*gcsps+/utlected 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 toward gn3 ryo/xmz:- 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 thatm3yn : rzo-x/g wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses af(n9hsy-af1+ vhhop2 s it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth b1ha f fvh-+o(ysp9hn2e detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig.aj1;:p w vig8t2e eg5t 12–38) was once used to send signals from one Alpine village to another. Since lower frequency soutj itw158eeg;avgp 2:nds 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 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 cx 6(oph)x,gzy ompromised 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 mxhzo,)6 p (ygx 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 “singinhoa2h4* hxav rday.*6g 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 pract6r.o*a4dhy* x a2hv ahice, 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 t5 .h8nu q58l)l,2;lp2hcfc(pqgm yedu t pe9uhreshold of hearing for the human ear at a frequency of about 1000 ,92hupm8t5lfu8cu5llpgh.e2 q(ce ;ydn p q)Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hearoy 6/j soa5n3ys the sonic boom 1.5 min after the plane passes directly overheyo nsa y36oj5/ad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 k3on 2rh er)u0$^{\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