What is the evidence that sound trav1ebr /3g3sv dsels as a wave?

What is the evidence that sound is a fu3-p ,.oe1kge1mm 8y,d mpdn g0h u,evorm of energy?

Children sometimes play with a homemade “telephone” by attachin+yeev od(ia( h- y.v2dg 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 tv-ed oyh ye((2d+i va.o the other.

When a sound wave passes from air into water, do you expect the /pp . psk.m9pxfrequency or wavelengthkppm. p 9/.pxs to change?

What evidence can you give that the speed of sound in air does not de g72*m6w,genqjk h2i tpend significantly on 72n* mgq,jikwg6teh 2 frequency?

The voice of a person who has inhaled helium sounds 4(o w3xdbiu ,gj.l7 ggvery high-pitched. Why?

How will the air temperature in a room aq ozb.rr: lg,uhj31ix3y o0x0ffect the pitch of organ pipes?

Explain how a tube mig p5lcsl.4wc j.ht be used as a filter to reduce the amplitude of sounds in various frequ. sl4c5 jpl.wcency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you *m x(e fwfia5:4 nsai.move up the fingsnew4 f.ifi(:xa5* maerboard toward the bridge?

A noisy truck approaches you fruyw4k+1ph h f5x bow.0om behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter+owpb 4f1w.xku5h y0h ” — 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 spacel:.wy34sx5 bh2rorb-fkr, u a ,” whereas beats can be said tobrlh4k, fb.xas o2y - r3ur:5w be due to “interference in time.” Explain.

In Fig. 12–16, if the fx h1ifb.;y6nf;l cws 3requency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apar;f1xlb. syw3c6fh;int or closer together?

Traditional methods of qonh h8 l6*1uuj; 9pwmprotecting 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 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 addi*8huq w;n j1o6 hlp9umng more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thoughtnp 9sh3d1z7zo of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two componentdzonp h37sz1 9 frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mo: 2hvy5y hato0ve in the same direction, with the same veloci2h5tv0 h: ayyoty? Explain.

If a wind is blowingd(gs(ihw)- her i2 41x lyxk: kci1l.a, will this alter the frequency of the sound heard by a person at rest witr )k-idye(l1ia hxc:.1sk2i4g(lx hwh respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in m: rs b7c1ht-ter58qb.u5yzbc otion on a swing. A monitor is blowi- b7h ctycq85.bsbez rr:u5t1ng 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 your reasoning.

  A hiker determines the length of a lake z w9k:(xpxt*l 7tz+6x nj*nnnby listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears 6xn xz:tj7( x* +p9w*kl nnzntthe 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 belo*z4 52ktz) jse4nnt8bhxvb- yw 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? Az2v84ktj)n4 t 5- ysb*xbenzhssume 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 wagm t/2infom,* velengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna o6 +ks/twgd7x 6i kch.gn a foggy day. Without warning, an engine backfire occurs on as67kiht6/ g+w gkxc.dnother 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 splash it makes when striki.relknq05i7u +i fo6yng the watere+ki50. nif67qy ruol below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone st o8 6sfv6qg-rfg;gbj 9rike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 ;b6ggj9-vos f6rf qg8s 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 disqdfhupl .mj1:s: w1ecuqc 49 2tance by the “5-second rule” for estimating the distance frof u2c:csp9 q 114wq.:d muhejlm a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain l-j tm npe8no o0*qz44gf*z0 cuevel 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 intensj t/ bcp:jd/1eeo 9s82g8kvkeity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soundzjs2+ + v e;oo5ml24vd8km xbd level of 95 dB when fired simultaneously at a certain 25d8zm4ovm + o2ejs l+ d;bxvkplace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jt yf2.4f+mudq iv5dg 4et engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person exper2f5uvdm4 +qdf.tyg4i ience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sig8x :i 7d4pc v5zhsgwc3nal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intens4sxc8 g 5zhci3p :7wvdities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powerrzupxduqfo4- 6 b5;l7 output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads ;7dq4xu puo6 f5zr bl-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 are rg hbyh0w0mo2n8)dd*0 zvz8,ne hzq-a is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modestrhh z b6g8.hdlvdew k+r+y7 *0 amplifier B is rated at 40 W. (a) Estimate the sound level in decibels yo 7ry+l6dhhzk0.d8eh+w bg v *ru 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 13*mx5y yvvtf).:.k0d dm )b0ebpn eb:dk*ukh )0 dB when placed 2.8 m in front of a loudspeaker *.efeumdy0b *db 5y :t)nkk)vmdk 0 bh)p.xv: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 dix-z,,g2fh nf, evj .wjfference 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 Section 1ne j2f, -,.wzf,vhgx j1–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the i4q-u27nu i9hy3hkkbif( ajs0 ntensity increase? I y2kksanh0 fb(ii3uuh4j9 q -7ncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudquxrei7u 3v/(es, but one has twice the frequency of the otheevq7 xuu/ ir(3r. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspong lskvpakp 4wze a2-kw9b08,8ds to a displacement ampka,pbw a8gse8 plw -024kv9zklitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemk,xj*q80iq eu6aj /sw as loud as a 100-Hz tone that has a w k a0q,*su/qei6jxj8 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tha7vrg y c+nu-q:t an ear can detect when the sound level is 30 dB? (See Figq u:+-cv7 gnyr. 12–6.)

  Your auditory system ca k2 ;af ;rsgiw8iy.fo)n accommodate a huge range of sound levels. What is the ratio of high;r8ogkf)s w i2i;fy. aest 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. Theid/*e 90hass p length of the vibratip0ssea*h i/d9 ng portion 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 audit0tp5 w.- 3i/v kqdwvrble overtonesvv 5 0-/i3pttwkwd.qr 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 expec,yt,m*dm8)e w zmyr.. nkfj+0f7 h lyit from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wtfy*r f.h,m yy)ki,jzdw8m . +ln7e 0mas 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 rb2pw(w/ tx w:organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of p(rwpw/ tx:2 wbipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third ha*t-, 5m htfcrla,/ ujrrmonic. What will be its fundamental frequency if it is fingered at a length om ur,c t,5hj/a-rl f*tf only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long ot(25x pb+ijs/ qkw5aand is tuned to play E above middle C (330 Hz).woxq a k sp5t2i(+bj/5
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emit/t3+wic c2ujvso qg87fz et.;s middle C (262 Hz) when the temperat ctt/7q.z8s2ue3w;j g + ivcofure 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 z::7d,uihcd/h k r4qjat 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 should ta5hjl7p3 9mrrhnl3w ; he hole be that must b 3h pmrj97ra5n;lh3 lwe 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 resonaxzmzt:ipb ml1*rz: ujx gq c*u1+v-0)te at 264 Hz, 440 Hz, and 616 Hz, but not at any other fr+ )-jvzq *1ut uxzxi*:p0mzb1g l:cmrequencies 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 lon -lpwo fy9es5 6v-y1ni1i4eizg is open at both ends. It resonates at two successive harmonics of freyv9ey5el-iz 16woip1ni - fs4quencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 tr-5q7 7 mr9 wyb x6lg1jb4fii$^{\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 preseoh*f n8a,ud2.e e:w nh lqz)q4nt within the audible range for a 2.14-m-long organ pipe at n hoendel8qf)4zu,a2w:*h q . 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2ef4(xp ) o/0w:betlat.5 cm long. It is open to the outside and is closed at the other ena:0w)tf x/oeet4 bp( ld by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears +hd;-ltzcc 0l one beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How farh + -t;zldl0cc off in frequency is the other string? ±    Hz

  What is the beat frequenckxe2 v0houe;mgso; ;/ y 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 23.5 kHz, whivi.hna ;98x2n4. :c cfuxuox4y /pruzle another (brand X) operates at an unknown frequency. If neithea icu42.x nu/8pzcf 9hxoy:ru;nvx4.r 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 -qi1i,cdq,y htuning fork and 9 bhdc1,i- yqi ,qeats/s when sounded 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 freb gr2-lh: 1hf/me goe/k:g0khquency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the tw/e/k fohg10 l -gmr bhg2keh::o strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each t, q(qfsbu/ewj2k2(sury to play middle C (2u/q q,su( bk(we2js2f 62 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork q0: oqzmsmgvx(e- rfa 9+)tb6 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 fr:t b(qf qv0-m ms9o)z+ra ge6xequencies 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 sta kzkx gn3if( q,c43o/xiy9w 2nnds 3.00 m from one speaker and 3.50 c qkgzo3(i39yxfx ik,4n2n/ wm 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 a-lk; skvj(f iquam ji;1 58:tzn tf//kt 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played togethekkiqn zjtst/lf 1(uij/a: f-; 5m8;kv r. (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 wavelengthsi:5b.8gvfn)d2pq -c+p w-q zyco ;ney 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = )8 nyi+wbpc. 5 qfg; pcvdo :-yzqe2-n20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1 xjf4c0p 9fz-a550 Hz when at rest. What frequency do you detect if you c- fa094fpxz jmove with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whopv1o6 gule/0pg k04ov se siren emits at 1550 Hz 1g/0u6o l 0vvgok4epp moves at 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 ;mqxc i138on9lt b c326 campqyou at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are the9 1;coxpli23mm nab86 cq3qt cy 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 eqrm ehlm;9gak)vwx4 u h1:j2u2uipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at re leamukj:9r h22)hw gm1u;x4vst 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 ultrasonic sound waves at 50.0 kHz and zah/qx a(8o;c receives them returned from an object moving directly away from it at 25 m(z qh8acaox;/ /s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an a32lg ixp9ebnoeb:tf-4.o (bultrasonic sound wave with frequb2nebol4 tf o 3e(a:xip.g 9b-ency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tube-l un0-t ya p4y3v7 al34wctca 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. 4t3n0yv-ae 4l ucyat3cpl 7-w What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter(hakhf96 je1 k uses 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 2 cm/s directlyj(ka6 hehf91k away from the sound source?   Hz

  The Doppler effect usi6iho;,ni u -kw 44u/p0jw3 k wxeyid+jng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequiz *c .kxn )s6q*ipjt0ency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hean0p.xqczitk6s**j i) r 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 mov f/)m 9 bsj9srhbemc5b- :uo7sing on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where tryl1st d6gv.h8yh,o/8zr 7kvhe speed of sound is 310 m/s (a) What is the angl/zt 86ho gdvh,k .1vr7ylsr y8e 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 ofh9ok 1m/u(zw(lff j 6z sound is only abou w6l j1k(9z/fohfzu( mt 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 thu cngqm7x .d6);ehc- 8g wzgc3e ocean. Determine the shock wave angle it produces ;m7)-g6e3 hu c czwdgx. qg8nc
(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 :xo) upd6mti( $/theta$ 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 exa lb9*i;o7)mabb ehwa)ctly 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 horizontal distance of 2*bia9 )bl7o;bwaem) h.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downw 5 +kg 3/-jplta,wwoppard from the bottom of the boat, and then d3-j , wwt l5/opgp+kapetects 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)?    s

  Approximately how many octaves are there in the1eqqz/t dl/lud/v +k gsos9:,x)tc 4 f human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of8z n);aw, 5lirzhg5 36( hfmdcyrr7zq many plastic pipes of various lengths, which ag3mna yf i)q5h; 6wrr 8zlhz75(d,zr cre 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 perskh/ :26 so36 -xykhvbnd-odojcu.zxj f;on9 ,on makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 10:f jx 6-/3o-.ko2hoz,sycd 9dnju;oh xnbk6v 00 such mosquitoes?    dB

  What is the resultant sound level when a9w2ylanhx j:(yik( /ozw.k,ye(o jfcus h /65n 82-dB sound and an 87-dB sound are heard simu(// y,hlk :cu.5(h69zywwjk a i2onjx ysoe(fltaneously?    dB

  The sound level 12.0 m from a loudspeaker, plac fnxbjv07f+l*ed in the open, is 105 dB. What is the acoustic power output (W) of thexjnfv0f7 b+ *l speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The sal aotr+p614 )hf xx,5zq ov0power output drops by 10 dB at 15 kHz. What is the power outpuh6504ax)foz+ q aop x1r stlv,t in watts at 15 kHz?    dB

  Workers around jet aircraft typically wdceykh5* 03jt ear protective 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 effectiv0j3eyt5hck *d e 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 communicaan.l cpf.8z:gi+2p x ltions 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 violinh.)sysww6 d9 y is tuned 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 violin is 32 cm long betwe oy27n6jdk +4uo k;ajten fixed points with a fundamental frequency of 440 Hz and a mass per unit lengda;ykk6jj uot7o+42 n th 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 filled wz eis j)( 75)wl95a8lp:nj atcadzxe:ith water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, thea)is wja: x:pndt8 )el(l 75zc5a ezj9 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 string3h7o2see 4ug f of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in thee4fsh2e g37 uo 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 resona: n1ejndajc um cmyk2 e94:n49te 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 t/p,mdkqs; 8qfg,7vr dhe 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that thfmpr8vkqd / gs d,7q,;e 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. Onerw3xcfj l)cp(5 -:)lar eet 9c train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency whencrr3 )fw (p:xcle e5lat 9-cj) the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steaemmmx3y)b9ylra q 5/w 3+p ne9m train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast wa+yxm3 5m qay e/n3l9wpmbe9r)s the train moving (assume constant velocity)?    m/s

  At a race track, you can est c*y:z7ag1 pxgimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a ce zp x:ggc7ya*1rtain 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 beat frequency of 11 Hf;m 2;tp 1cypo4pvjn9z. The shorter one is 2.40 m long. How long is the otherjy4m;ftpv9c po12 p; n?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past ;ybmaknf:;yg *dl 6 .ua 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 theklmg;nf 6y*d .uy:ab;y have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what be3jr2u )b9uwxz +b; bzqat frequency would you expect if 5.50-MHz ultru9u )r; bqzjzx 3wb+b2asound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the bw5 awe 8h;czb:at at speed 5 m/s The bat emits a sound w;c wb5wz :eah8ave of 51.35 kHz. 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 sound pulses as itk7/ynym vfv--uqrzm1(r 3 ob0 approaches a moth. The pulses are approximatel ryoq0mkyu n1 -v3f7-b/mrv(zy 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 to send signals fi . (gum(o:at odcu/9from 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 which overtone is close to F sharp? (See Table 12–3.) Model as aufodm a. gi(ct(:/uo9n open tube.

  Room acoustics for stereo listening can be compromised by theqh8i 0gpwk:-r 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 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in kq8p-wg0hr:i this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratirg.*ussd4v5i ( lp m p:odml56on, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,d:*lv( 5pp m.ug56drls4iso m
(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 thm4 wlw 3/jfi*dgp9 08m8bcngae human ear at a frequency of about 1000 Hz iw 4j8i*gf3np8cgwbml0 dm /9 as $I_0$ = $1 \times10^{12 } W / m^2$ 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 travelingf.(3ke dwvskz ;tb 0-g at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plaf 3z-gd0ebtk ( swk;.vne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isy*qun68 on47 1qjmwgs 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