What is the evidence thabgwf db -d8vd x7e 7iy9(nf65at sound travels as a wave?

What is the evidence that sound is a form of energbrz ev-/5xc6c y?

Children sometimes play with susa f)r+iz59la 7f ):oo2qmb 4gu(oga 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 a 5ur9abg247:uf q)lzs ( mooi)fg+o sother.

When a sound wave passes from air into water, do you expect the frequency+ q)drur7 gj um)(tt2q or wavel(r2+7u )gmrj t)qqtdu ength to change?

What evidence can you give that the speed of sound in air does not depend sig ia*hqj.kgx97nificantly .q hx7ja* 9igkon frequency?

The voice of a person who has inhaled helium sound7 9el4 h umi7c2 k*udo1xp8erds very high-pitched. Why?

How will the air temperature sn,4 c k,0msejgp:mw,in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of so gfu ozj2.,6mrt7pum(unds in varioj6trof pzm u( 2g,m.7uus frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig1fd15.jp c oez. 12–30) spaced closer together as you move up the fingerboard d1coep f15 .zjtoward the bridge?

A noisy truck approaches yo*yl v7 4momwg 8llv*7ku from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on d8ky lw gm*vml7 4lvo7*iffraction.]

Standing waves can be said to be duer 0hpsu ;+( t7qzyjb q+8ha8fh to “interference in space,” whereas beats ct78shqh q;+8jzfh (0b pu+rayan be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speaken rck63bm2n17 8lelaars were lowered, would the points D and C (w7l61ar8c2lam3nk nb ehere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wiz5t9o moh+; aith 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 bl+5h9oia to z;mock 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. Each wave can6e o j:kya5l;m be thought of as a superposition of two sound waves with slightly dife65kjyo;:mla ferent 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 s(d wsm;yd-wj- ource and observer move in the same direction, with the same velocity? Explaidj;( mywdsw- -n.

If a wind is blowing, will this alter theb7 3wddwfshvzf18 -l jc3pfq;sf /54o frequency of the sound heard by a person at rest with respect to tw4wo p 1l-f3bhzs qf7s3 5f8dfv/j;cdhe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mv++bbrel 3c9 konitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequenc3l+bb9 e +ckrvy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fohhn+ ebr .mdqn6el *b.8 d/uw )m/-alcr the echo of her shout reflected by a cliff at the far end of the lake. She hears the edwd+le-mb n mr.ln) bc*8aq/ . eu6hh/cho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jus3 egl 7kjsw-bi34oi 9.* svjyxt below the waterline. He hears the echo of the sound reflected from the ocean floor dg k l4*s-o.9vj3ixjewsyi b73irectly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ;qnejy fb;t u,tv; /3zair 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 3sota+(ivca b(x -y (wju1 +e *ugem7tabove a school of tuna on a foggy day. Without warning, an engine backfire occurs 7i+ ((at3jbsxw+e*c my ut(e 1-guvoaon 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 ob.7f fzlklgj 3pbow i(a .pd3q),/g2mf a cliff. The splash it makes when striking the water below iszfdg)wb,.q i2 .om3gkj7/(3plblf ap heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the gr hr hu-t;4uy:kound, sees a huge stone strike the concrete pavement. A moment later two sounds are :4t-h k; ruuhyheard 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 “5b;ck *ub u xgzck/wt h:c*0p;5-second rule” for estimating the distance from a lightning strike if the tembx0;;uc tgpzk:hb/ck*5w c *u perature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le n24vsup(*z buvel 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 o1 yobrmur 82fr :1fvk:f a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneos 1wn6i ebgf u4z5x:1uvzy9 c ,7iz6xvusly at a certazb 15 cvif:e 6nu9sz4yx 1u zxi7,6vgwin place, 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 wi75 s ed*nh rprya);/dnth four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain )d5nyh7ep s* randr;/shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is ssf/1dxz qnr.7aid 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 bac./rf7zqsndx 1kground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spea icfi +82 wa9-fxcwp3zking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphwx238 ic+-i9afcw fzpere 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 f 3g:gz (zjy;d *pi4);raix l *xaj-owwhose 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 more modest amplifier B is r,rmze /b;ikkew(z) 7 usto/ 5oatedei()wk o/uezbzo7 /r ks;,5tm at 40 W. (a) Estimate 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 1fg3m:unrj1 4b 30 dB when placed 2.8 m in front of a lou:rg41 jub3fmn dspeaker 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 typicaigs.09;(cp7 ooty ax xlly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [o 0o9s 7( tgxicp;.ayxHint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whznboe f);r; yit b* iw(7o8w:oat factor will the intensity increase? Increase by a faciwoi*;t7n8eobw(f ;y:zo b)r tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudel c(jh5 *6ej(j )dawcxs, but one has twice the frequency of the other. What jj(jal56*dc w( e)xhcis the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air y(iy(, yqd t1+:ob, x ldbb0ndben0s8that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?,+e t8b0on yddl nb01ibds,:b(qyy( x    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that / :ay+nr q flrbi,t4 o(qt*mk/has a 50-dB sound le: i+r tbytn / lkra,fm(oq4q/*vel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencieshvj r*ls 9*yl( that an ear can detect when the sound level isylvr*h jls *9( 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodo),ltdl f/ kbwed/4a-cyc, )t.nh )maate a huge range of sound levels. What is the ratio of hw, dk- etfhdtllac)/,)m)/ a.bn oc 4yighest 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 frequency9vj, wj,5gi1ref ujyr7gi 2 )b of 440 Hz. The length of the vi7 5,)eb2g, gyr1 irj fwj9vjiubrating 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 el/+0hskwa uw/ (rd5g cm long. What are the fundamental and first three audible overtonewg/u0( l hk+w/5rsdea s 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 across the top a xl.:zcs3 3nyof an emx .cl3 z:ay3nspty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range ofhve2bq 4r ,s2lnr7,)tz xn4os human hearing (20 Hz to 20 kHz), what would be the ranr2h4b zt,e vsxqn 2,7)4rnols ge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freqxhsh , ;; cum8o) 6fx5etp7vituency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original l85xt;osue7hx6) ihmvt p;,fcength?   Hz

  An unfingered guitar string is 0.7i :xs-wgb)es96dxv l +7(;b kktj xxt03 m long and is tuned to play E above middle C (36eixlb svk)7s +kx-:dxtjtgxw;90 ( b30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organa5 b;ehrb-h-rnpqv9q( ; l i0d pipe that emits middle C (262 Hz) when0 r-p9lehb;r;b-aqidhqv (5n the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 d4pctx-9a5rk $^{\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 shouldm60vln,rzj/a4s e4dd ehdh: d+ghz9, the hole be that must be uncovered to play D above middle C at zh04m,s9dg lhrejaez4nvh/d d, : +d6294 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 pj ql,.q:dxa **-k+qogp gk se,cavb1b 3h4 up,ipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an opep s ,*u,dcle bhq+a3gopjg:1a,*qk.4 bvk xq-n 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 d ,+jtf.u j2cpb c7p1lends. It resonates at two successive harmonics of flpc ,2+j. dt7 bcfupj1requencies 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 ,ft +;j wzf+v,uti3p.el (z:o*he gp o$^{\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 presenhzsh rp:i. 3 2-deifdubg8vx;;.:b bot within the audible range for a 2.14-m-long organ pipe at : ibdpr.bg: 3-e;zfo;.hd hi8vx2ubs 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2. 49lm0 i0svqm:sjn/ mk5 cm long. It is open to the outside and isnj0:m4mlsm0 s/vk qi9 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 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 trying to adjust two striz ho;u 4h-2ns+,v5y; fpc)bgm 9fgaupngs, one of which is sounding 440 Hz. How far off i45;;p,+mh9ns hz)g pou -2gvffuc yban frequency is the other string? ±    Hz

  What is the beat frequency if mie hgx72nz9k;kddle 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, while another (b/r fy0oi.h jrtpw t)1+rand 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 op1ihtpjo)wr0 +y .tfr/ erating frequency of brand X.    kHz

  A guitar string produces 4 beats/s w i3a-ld//gcebe 43y xkhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational freq 3cl ed-4b3 /kgx/aieyuency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The ten fmu/f,92glmjqh4v.7hr td 4 )z.itlt sion in one string is then decreased by 2.0%. What wi mquj7tl/t2)zh fimlhv, d4 9grf..t4ll be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heardiae3tok-z( lmvl ,tiz0 qv 3;+ if two identical flutes each try to play middle C (262 Hz), but one i,kz miz e(vlt-o0 3+;tivl a3qs 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 441 Hz; wro4n(23 ipc4zo. y w)eb uds3ihen A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded tog3b iiz( py2u 4ow4)c sd.nore3ether, the 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 szy1p pfe9cz fb5 1+s4(tanl(from one speaker and 3.50 m from the o1p fp +9(4yltc( zbzn1afs5sether.
(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 supp)xyic32) rzz4a a)4ab;n 7tb0qxi (gtp,tml dosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are pl4a2t7xq )yt tma0n43a; bcp i)(dbx,zig)rl z ayed together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wa foym8,8 co.duvelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20moc y,.o8d8uf $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s s:sm:z0oj*il firen is 1550 Hz when at rest. What frequency do o:zj0*l: mfsiyou 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 do you detect if a ch1s/ eq6bxm72oq 5nf fire engine whose siren emits at 6mfn5cb/hqq2s1 o ex71550 Hz 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 towawjbcfas0l/+ /oay p84x/+w lard you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactlywflc 8sa+a//o /+l4y0xaj pwb 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 f 6xg gtj g(,afap8z:73z5qiknrequency 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 of 5.5 Hz. What is the frequency the hg nkf qj687g xag5p ,:tziza3(orns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out u*b 8hii0q)t mdtyal2+ltrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly a0ba2h mlq)i*y 8i t+dtway 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 5 m/s As it fliesp38xn 0ad; )y;c5geeyl vb-.d aclk0r , the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequeag-;dycxy5n38e0br. lce p lk) 0v;da ncy does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat t,p2r zmc(gj k*r9zpy0-p7-5g ixz tnsrain 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 frequency was heard ifty 7c ,xp g0k-z *mzspn-p9jrzgi5r( 2 the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves tok0tql .h-i;ll 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 bel0h -it;lkql. at 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 waves of frequency fokow t(0 ;7*k-uv d1zja/ sqc$2.25 \times10^{ 6}$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 570tkzjl m9n2yx1 c 4/ lqcim0/.y Hz. When the wind velocity is 12 m/s from the north, what frequency will1mjcit//lnmzc0 q9 lx4yy .2k observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spe89 jvv ft2pau2ut:)gned 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 wy ujn0q1 1vm;w ruh;.f wj05mqq ,/mhyhere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’ 1v ;q,nmjmq.j; /5yhwy1f0 mquhw0rus 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 atmosphm7e-3hr2 o vcgere of a planet where the speed of sound is only o7e-3hcv2gmrabout 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. De: )* woplmco1ttermine the shock wave angle it produces1m w)lopt:*oc
(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 b*syre -9eouz0 4ues03a9np h$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a p hk0q9n,k 7 jr1czpy3blane exactly 1.5 km above the ground flying fasteck 9yb0j 37 ,kpqrz1hnr than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device tm + ydt-o2,t/zw cvw78zd;m: jiwo p)ehat sends 20,000-Hz sound pulses downward from the bottom of the boat, andc7w wpvo/:jzite2-+t w8)m dm; od, zy 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)?    s

  Approximately how many *;.d q1vc,vmk6,ghlr8 pxe baoctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a*bkpic (e+z2w3tbs (n display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both t3n (cs ip( wzb+ke2b*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 3hey ra38wj5 wu5mtr6person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosry5wuh t6a3er35 jwm8 quitoes?    dB

  What is the resultant sound level when an 82-dB sv/x.h3iet id4ound and an 87-dB sound are heard 3i4 e i/vhtx.dsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in nbvv5s 5 n8tj0the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiaten8s v5vnb05jts equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 , vk2jlvw*hf- Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kj*fv w-,vhk l2Hz?    dB

  Workers around jet aircraft typically wear protective devices ovc6ok-ck4xt1k dyy p8 q6 ld1f1er their ears. Assume that the sound level of a jet airplane engine, at a distance of 30k4lqytdcfc -1 6yk18dk 1ox6p 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 communic:xvh gp+j.q v(si.4 ww-hwfd*ations 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 freqw11p**j byu jxa ,ej+ouru -)nuency 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 between fixed points with a funda. (fxfs c8 pk)gsm/fd8mental frequency of 440 Hz a.)ssfck(f8 /fgm d px8nd 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 open tube filled with waterc*any m(3anhnd ) p9a7 (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the 3 7anam (pyn9*cadnh) tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tubm2ii tz*1b -u4mrf8rpe that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube t upb4 81mm*2i-zfrir?    $ \times10^{ 2}$ N

A highway overpass was observed to resonat vo seev5u*)6ve as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 5(/31, )oy rhurw mvzvp5 naoe/00–1000-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 pervw1rayp/m)3 , n(oz5hov/ eurson moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor +w4+vj7er lxue2i 7ooon the stationary train hears a 3.7w4ej2uvx r+o le7 o+i0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approayfopwdbu0+3 p2s 7 *zy88nsu kches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (ask b f2upuo3p0*+s zwn7y8ys d8sume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the diov zt5*cja 9f;fference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halotjf*ca 9; z5vved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, producezo+pn3+)tm kavi 2m6m a beat frequency of 11 Hz. The shorter one is 2.40 m long. Ho)3mapm imv 2t+nz+k6o w long is the other?    m

Two loudspeakers are at opposite ends of a railroq7avuid9-cx * ;z8fr uad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is betwf9ix rq-*8d7vc;az u ueen the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow ihdl3e. +tf*f de38gy an the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travetal+de.gh ef d83 *y3fl 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 flyin8e9lm*(zba (oqpy51 vosb( jd g toward the bat at speed 5 m/s The batzpe( ym9v8qj(15oobs lab*d ( emits a sound wave 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 i9 ih-a dh49guax,xhbgo :0)bct 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 be detected by the bat so that the echo from one chirp returns before the next chirp hh49, gxacbx)9oau:0hd - big is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sizftq ew6lz +3fti2o6y2o m5o:gnals 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 which overtone is close to F sharp? e2yzz6+ t2qifwlomf63 oot: 5(See Table 12–3.) Model as an open tube.

  Room acoustics for soj tcndf,z 7 l5xt) tad4fj,5:tereo listening can be compromised 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 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standint c)7dxfttafln,4d 5 j:j5zo,g waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a rzbw5*q (j-ry long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a littl zrryj(5*w-qb e practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a f6 4g0 j +jxh6jtv7;btju cc2u 1,pqhpjrequency of about 1000 Hz jhjxh4 b62 juu 71ttcc06pp g,qj;+jvis $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic bo9pt/tt)xykq ((dig5 d om 1.5 min after the plane passes directly ovid5qx(( tg y/td )kpt9erhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatc0+ sky*b:r it-9kvfz 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