What is the evidence that sound travels yx 2ucs(rc:z)rued ;+as a wave?

What is the evidence that r -8;a-:jk8pcb rn)oto1iowm sound is a form of energy?

Children sometimes play witzaa6obva:9dv xl7wy;6b +m :j h 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 one cup to the otzdaybl9j ;: vx6a +wa6mv :ob7her.

When a sound wave passes from air into water, do you expect thc zayv h;c.h+)e frequency or wavelengzyh c ;+hca.v)th to change?

What evidence can you give that the speed of sound in air does not d *unmo4zl2 v+doh8yb5epend significantly 5l42b*mvnyz+ooh u d8on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. )ncx 1edzt 7:tWhy?

How will the air temperature in a room affect the pitch of organ 8 s eozhxn( wzrm( :j5:8m vs72zv)kyipipes?

Explain how a tube might be used as a +z:/ bsj davyyac915lfilter to reduce the amplitude of sounds in various frequency ranges. (An cdsya/9b5 lj zavy1+ :example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move ua-krj 4 zh.e,zp the fz er-4 j.hza,kingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but c1jnt lc5 p9xg/0z5g )rbbm hz8zif/s6annot see it. When it emerges and you do see it, its sound is su9szzb /ngh/bi 6pm50g8zc15rl tj)xf ddenly “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 space,” whereas be x n7bqi/sjy,3ats can be said to be due,i/3x nbj7qys to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wvah99lh4, v7zyrde 7lould the points D and C (where destructive and constructive interference occur) move farther apart or close4,lv rhe 9d797vyzah lr together?

Traditional methods of protecting the hearing of peo*ntf/iby k q4lh ip32)v0jl(w ple who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. lj n0w)k (ifhyli qtvbp34 *2/How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shos1; s/h 3/w rcc 0)aqb:gqrfpwwn in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the wav;rq)sra/sb0pwgcf h/ :q13 w ces, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the i0ork-xp6+o-zp,sf n source and observer move in the same direction, ix, -p60 zkorn s+p-fowith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard3k-g b s40 onq:dcpw5a by a person at rest with respect to thsoc3 4-pwqg 5b0adkn :e source? Is the wavelength or velocity changed?

Figure 12–32 shows various :61 mc2i:u7vnf 9 tfz2jemnykpositions 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 chfvu n9 zi::cenj2k 6f m1y7t2mild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ech9a6:sc zr3(g 2z nylglo of her shout reflected byra3:9n g2z zgycl(sl 6 a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the w -d/tgolcd( * a7z)xpcaterline. 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 12a-7cxdp( to)c*zg dl/–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in fv.x c a.k4cswj*2kz3air 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 tuna5xv7 irdbal)vj dveq *4/8c:r on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses befo) *45: ivcdjrrqx d7bvve8la/re the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes wh0,jha7:es8s iyb; knmen striking the water below is heard 3.5 s later. How high isb j;ks ye:s0n ,8h7ima the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the k;pt1d f2amicjtb;n 6l7 ,n4aconcrete 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 ta j4ifatnb;; m t7cldnk,6p 12he impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “l+e1f7 (et h(ql iurt/5-second rule” for estimating the distance from a lightning strike if thetl1 ql fh (e(e/u+t7ri temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun/ibo c6ojgj(e*jj l38d 16 s3 gtqzov+:v ow+dd 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 sount qu v*afsac-y1y+8 j-d whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prod czen3yo.i,kq/ciq. k8p)7pvtx9f ; sds :vz1uce a sound level 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 d8 .:y 9/ k q;qi3 vvze.)cfx1c itds7o,zskppnB’s.]    dB

  A person standing a cert*ri7 od 347l/wo8* e0 ew*o otljhjhceain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Whl d4o3rh otoeli/7cwjje70 8**oh *ewat 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 sfk-1) 9bt cldjrg+up8 ,ttzp5 aid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devi5b 9rp+pz jktfud1) -,lgctt8ce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of x /xx)-zjmwgf:ck6 ce)f,z)fsound from a person speaking in normal conversation. Use Table 12–2-cwxe) 6fgx,/mkz zcffxj):) . 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 strirexnrixz-b:7kzk/ no39s: l 9 kes an eardrum 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 250 W, while the mo( lgbo 0vw 9 hy)xj)vu.iub(1ire modest amplifier B is rated at 40 W. (a) Estimatvh v9.b(wb)iojyilx) gu0 1u(e the sound level 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 dB meter registered 130 dB when placed 2.8 m in front of a vl uo:vf/n3 ,;/j7 p qapo8w fq(pvr8eloudspeq8 ,fprv q(/n8 fow3avp/ov:le7j u;paker 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 ob8p *o4dhb1)f* j*rfe,vrkxdifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectio*db* b fvreofjkh4)p, x or*81n 11–9.]$\approx$   

  If the amplitude of a sound wave iwmdpar 42rj/57mtl0w s tripled, (a) by what factor will the intensity increase? Increase by a fapmrm54dt2a 0rjwl/w 7ctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has t81gs/du b7g ks5kqs5kl -qh6qwice the frequency of the other. Wha qg -d675hkq/sk81 qgkbls5sut is the ratio of their intensities?   

  What would be the sound level (in d gc6wtre3hl 3opx,sjl ,tu*4;B) of a sound wave in air that corresponds to a displacement amplitude of vibrating ai6prwx,tslcle ,;3 to3g*4uh jr molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem auzah*s h9dq: dqe z* i9y*+z5ys loud as a 100-Hz tone that has a 50-dB sounze5**yhzqzsq :a * iuh 9+dd9yd level? (See Fig. 12–6.)    dB

What are the lowest and highest ob u-/l1zyd +x;ojo1p -nb(pyfrequencies that an ear can detect when the sound level is 30 dB? (zo/ujd po;px-1y +by n-o1(lbSee Fig. 12–6.)

  Your auditory system can accommodate a huge range ofj+tfgzghx) 7a2j9 m3r sound levels. What is the ratio of high73)jgx h9a jg +rzmt2fest 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 funbu:lj / poj 5dk*q9wtu+4/higdamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of d4 *jgw5:/lb tpoiukjhq9/ +u0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fu, w20bme) hgzpndamental and first three audible overtones0pemz2w b,g )h 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 expect from blowing acrosvn- 2 +.qzin3s ttt0zcs the top of an empty soda bottle that is 18 cm deep, if you assumed it was at3-ctv+2sztq.0n nz i 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 spaj *51fwbwqsm8nning the range of human hearing (20 Hz to 20 kHz)8wmwqfj* s51b , what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has 3av)9fjl gf o tzoc0, .xo/iis4xoi; 9a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it ;j9xo9sti3,zf )fogv il 4ica0ox ./ois 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 abovz e)niq4(ew5p keo;4ce middle C (330 Hz).epew e54kn; oq(zic4)
(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 len p-dxu5k +k8twgth of an open organ pipe that emits middle C (262 Hz) when the te 8 +dup-xkwk5tmperature 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 a5m2 42ro8*duw b3hs ncrdur 4ot 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece f.m -yy edoo*6of the flute in Example 12–10 should the hole be that must be uncovered to play6-ooy.em *y fd D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hzyknuv*o n5s rf8 8.sm+, 440 Hz, and 616 Hz, but not at any o58f+vnr*o.u syk m8 snther frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both / k/0iptd8v eoends. It resonates at two successive harmonics of frequencies 275 Hz aot0 pke8 v//dind 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 h 9 (am rn+9dpkm j/ (ft;qqpuon/4ql7$^{\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 a dnkz0;vht ki lsc3hi*8. ft-,udible range for a 2.14-m-long organ piptsifl.c 0;8 z *,nv3idkt-kh he at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to t mxa)n2p2r u(.vf fi b0ov70pwhe outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing w2f0pbanv )0rx o7p. ivfu2m (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 when tryi f nz29pn(wvj2ng to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string?2jzw(p 2vn 9nf ±    Hz

  What is the beat frerbhk 1s*f8, e(wsetd.quency 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 operates at 23.(g1bb1kmb mw : e f9mlh*cc a:v7izh035 kHz, while another (brand X) operates at an unkbba3* (0k fzgb 1c 1:lhmi9: vcmwmh7enown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning foe,hxgr1z0 l ,n6c lv.0n.sloxl7/a fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency ofrlhcnoox1lgz/v.f 0a.6l n ,,xsl e7 0 the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frpo g1apg,m*cu9 ri1,p equency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.] 1 p*pp1gg,mr9 ao ui,c   Hz

  How many beats will be heard if two identical flutes each try to play middf r :9/hfs1uj rj-7mcxle C (262 Hz), but one is at j u9 7r:/sx-fmhrf j1c5.0°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 441 Hc mgxl;gjj1fa5s7xhb 3,wb-/4fx ed 5z; 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 a, j7c-x4m1es5;g5 jfbablhw dxxg/f3 nd 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 -eg9kqv6zo,fs-*u-kjf aw 6 jfrom one speaker and 3a e- ,gfk9j-6qv*fzsuk jw-6o .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 13dl64po ut;+e o2 Hz, but a piano tuner hears three beats every 2.0 s when they are played toge;ol toduep6+ 4ther. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many b k/1sxv;kp5ateats per second will be ;x kst15pk v/aheard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wheb,g gyvkqblc5z9 9q1z-78 tjhn at rest. What frequency do you detect if you move wgq59k ,9 8tvqzz1blj7b-chy gith 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 si9z tst/)p j7 d)vevb26dxww85ycp-ok ren emits at 1550 Hz moves a2j5 7)tpoyd9ckwz)6ex v8bw/p v-dstt a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a g*po e15x79r2vxfg6qsv0wvc 2000-Hz source is moving toward you at 15 m/s versus you moving towaw1ce2vxgv0v7r6 gop5*9qfs xrd 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 frequency horn. When one is ah zjl1k 8u7(jtjy+ai 8t rest 8ji+(tuzjy1ja lkh78and 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 out ri(ez nx7 o1w)ultrasonic sound waves at 50.0 kHz and receives them retur1n iz x)re7ow(ned from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 55 :p+r* b5fwx0hsiwyy m/s As it flies, the bat emits an ultrasonic sound wave with frequenc5ybw:i fyr 5 0s*xp+why 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Do/;ui4d q/o ulnppler experiments, 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 station. What beat freqld4 on;q/ /uiuuency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter 5 c1/hov;cvl p;:qpwjuses ultrasound 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 frequency if blood is flowing in large leg arteries at 21ohcpv ;j /pwc;qv5 l: cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofjtqxk;7;qm z4 gd o4p9 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 qlu;: z d;kyrop *y ny;o7v(j*the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, pj*;kq;;*zv yn(:r 7yduylo o
(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 .gc2h*,qs - x,a bkd7rsok1iz 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 2d0m.8z.whtwm p3bgq ug*c +6a.3 where the speed of sound is 310 m/s (a) What is the ana .m6gwbhd w.cp30mqg8*uzt +gle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed*doio5n- kgc y:3 wh,z of sound is only abohi5,zd3 y -g wn*oock:ut 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 the shock v.pvgjylpc 9 7h8901hd, esi zwave angle it produc0hsd1,ze l7p9.9 pih vgv c8jyes
(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 yqqgve2;+ -b b +o h0adgn5o.k$/theta$ 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 grou7f :m5ud(mzm8 q(jrpynd flying 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 Fpzum7fm(d:j8q 5 r (myig. 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 20,0s kd1j. nm*p/d.x h76du wjoc r6,5kaf00-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for whic.uod/k njfr w5d6cm*hs k 67p,1axjd.h it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the -., qjpraj 1 eit2(pubv (egy/human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a s g9 dy.1cdy g-let*;ouewer pipe symphony. It consists of many plastic pipes of various lengths, wh.gueyc 9o1*ld d;t g-yich 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 ilwrgdtds953 p6 (jd; threshold of human hearing (0 dB). What will be the sound level of wj(dgl; 6d3r5 9t ipds1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-d :88tq wd7++xw9msgutbn;q caB sound and an 87-dB sound are heard simulqxq89dt+7nc; wbu: g8 a+tm wstaneously?    dB

  The sound level 12.0 m from a lzfg;s.l( 6a yot;p. zixh dy-3oudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming .ihz(; f.zp3 odsyt6gy lx-a;it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The po 0csdsokz0 76t d,aci6wer output drops by 10 dB at oc06s0a6,sz i c dt7dk15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. A +le*mrb6l7qb byf2vp m/hb7 1ssume 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 v+e1hmy bf rlpb6 /lb27qbm 7*by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communi: k.n6zc b rdjug wk2d7;:b2yocations 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 frequetssfwimx+:i/ pv 5 l1uw+g4p(ncy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm l pkowaj3a92f29iwck; k2m 7a*utpk, gong between fixed points with a fundamental frequency of 440 Hz and a mass per unit kmt3p,9w2k 9ca2*j7 ak;af gwk2iuop length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fille0p: n ro. kqutgi4 x 9gz0*ho5(9mtcovd 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 * unxzogr 4p9 t5t0g(vmo:o9ki.0chq 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.u*zl ( 5*w-fzz qc9uxa10 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 ia-x5wzz qu**lcu9z(f t is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loz efyl 53rqv 3wcf292(c,az biop ($\frac{1}{2}\lambda$) 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 sourcesfi v jyt.jlfu3bd 9rw/1zpa m4d8m tp-*f,2u.. 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 3twr 8uj-f. *b9y ip 4j lma,f2.dzdp1fu tmv/frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is w zoxbkm4 x40 a9nn 4e/2su4mrstationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving 04rz44x9/esxmkwnb4 2au n mo train?   m/s

  The frequency of a steam train whistle as it approaches you is 53jsb0o* zr eb5mkb- u-5;xdv5d8 Hz. After it passes you, its fr-5u 0d -db;ejbozs5*m b5vkxrequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimagrd x yjo jm ;dhs- i9fzht8t7b18+27ute the speed of cars just by listening to the difference in pitch of the engine noise b7jtjh 8tiuo; f9bd81ymsr2+d7-hxzg etween 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, prodrg2 jov 0n.,dtuce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How g2 orjtdv0,n. long is the other?    m

Two loudspeakers are at opposite ends of a railroad carclqu.h.cne 6 5 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 speakers, at B, and (c) he hears the speakers after they have passed him5.c l hce.unq6, at C?

  If the velocity of blood flow in the aorta i4gl2 kled, n(iuxg:8gs 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 blood cells? Assume that the waves travel wnguglld8x ,(2gei4:kith a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m oqygpke/*nr/b*r/; h/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz.qe/ hrp g*/y/nbo rk*; What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency so . 1wwe8q9lr/w 1sepbtund pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far aweq wr b8 s91.1ltepw/way 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 on3 31;s onuga7, f o92fuxtmmxgce 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 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 whxufo 73;tau 1g gxmf3n9,osm2ich 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 presence of si/+jeg2fs yl8an9v6 ztanding 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 frequencs g+j8z6fievny/a 29 lies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rodt++lp0ijr eh7s,” 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 practi0 i+l+ h7rpjetce, 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 h+ mb ijv6jeoh l*g2yxal5v k/1i+k0 :tuman ear at a frequency of about 1000 Hzvkhe*l j2+:5gva o0l +1/mtxiki jy b6 is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears th6ogn9a9nfgs6z c gxjgd:k2 ut/) 0y(ze sonic boom 1.5 min after the plane passes directly overhead. What i/ (a9xfng2guto6)6 skyjcg:9 zdz 0 ngs the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo/vktb a5 e--yvrzs 6,vat 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