What is the evidence thn 2a3ont)*j 1:ay mtywat sound travels as a wave?

What is the evidence that souc(8d(cxdye c0nd is a form of energy?

Children sometimes play with a homemade “telephxy x)w2jby)ve0fs*82 z.+stweqar .kone” 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 hwb2k y wfe.vx) )s2zqtj a+e0x .sy*r8ow the sound wave travels from one cup to the other.

When a sound wave passes from ai l37ox dt jo0n6n)iw+er into water, do you expect the frequency or wavedw3 e0+t)x7n6olnj iolength to change?

What evidence can you give that the speed of sound in air lhwo3h: z 23j4 jfw8svdoes not depend significantly o3 hf j3vz: 28jww4oshln frequency?

The voice of a person who has inhaled helium sounds very high-pitchedx 2q v*4d.dlz6lkw yy:. Why?

How will the air temperature9t 2h9udrs2 no, v sz/pge15ym in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filtez-pcxu m. to2/(9gno e,bjy m;r to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufflercne9pz2,ub (/-.toy;x mojmg .)

Why are the frets on a gui.g8nqa+v85/ ak -tvy josd e-1sit9ct tar (Fig. 12–30) spaced closer together as you move up the 81aoavit ye/ q.jk sv-gd9tt8 sn-+5cfingerboard toward the bridge?

A noisy truck approaches you from behind a q7ibx9p9 dm7i5t yz(a building. Initially you hear it but cannot see it. When it emerges aqd7i9a 7 ibx5yt zm(9pnd you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said(/0dk z/ugqeq to be due to “interference in space,” whereas beats can be said to be due to “in(uk/ /dqz e0gqterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers we(y/l2e)c9qcou py ,y5ay(/c(jx6zp* m a sukyre lowered, would the points D and C (where d*uo(/, j(x(uaa yc)yyzsem c5yp29y q k6lpc/estructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectino.9 i;yu+ 8hkf+-iaekwpa/ ksg the hearing of people who work in areas with very high noise levels have consisted mainly of -8e p.k/u 9 akwkisoh+fa+y i;efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each acth2 gky)22 uwave can be thought of as a superposition of two sou )uat h222gcyknd waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the so r+ 7ag 0,xaj6jokllcu2 z/7veurce and observer move in the same direction, wk6 2j7,v /e alczg7jlu+axro0ith the same velocity? Explain.

If a wind is blowing, will this alter the ffbtp,2z shyq8a/).p* 1b diqr requency of the sound heard by a person at rest witrd/1qazh )t2 *p8bp.isb,q yfh respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child injo dldr7 (fz.7;vihbzk,c.-a motion on a swing. A monitor is blowing a whistle in front of the child on the ground.7zir7dfj . (; .adz,hlkv-boc 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 by listening for the echo of her slmf/ralwg: */ hout reflected by a cliff at the far end off ra:l//mw*lg 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 )jr ocxn )v;*w*2pzv6 ofpy0lof his ship just below the waterline. He hears the echo oowfx2zpv 6r0yo n pc**vjl));f the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in m4;taq+9;irn ew1dx z,( dwbr)dp)r tair 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 juse 2 /uu:lmo1- gsk:bfct above a school of tuna on a foggy day. Without warning, an engine backfire occurs on au k/- o2b1csge:ful:mnother 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 s2/iimha)c8* 82ylbetkbba3 when striking thkh2 mtyaab3il )i8 c bs8/b*2ee water 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 strik0c tjdwwl; 8c9e 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 s apart. How far away dlcj c;098twdw id the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percentt /;sqf gkvbv,k2uh f7 55u:td error made over one mile of distance by the “5-second rule” for estimating the distance from a hud qkf s:tkt2 u,vf7 g;/5bv5lightning 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 level of 12b6;h qns e+vo+0 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 sounm mj-odkgmsz r2p qax ,+6.g;3d whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simu/m 4ufrdksw1r ;h t.g9ltaneously at a certain place, what wil1tm;w.rughr4 sd / kf9l be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certainxf -mcotstc1q ;86h3ovdr4 /t distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if t4;8tds 1xvm/tof r6h-ocqc3the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-l *jr)y b4yh8i 0ooq-hnoise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the siy4)bhhy* 0rl- jio8o qgnal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal con.w /h c7 v,bv2 -6lkd/xcqqdq8t9kzqqversation. Use Table 12–2. Assume the sound spreads roughly 2./kk 97z/c ld6 xq,qc8-v wdtqbqqhv 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 eardrum7d a/-;dc 2jfhwd6 nc(ghsah / 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 25n4 a 6qh6z7wl-;/hor.d ogzoy0 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound rw ng h/hlz;oz.o -7q y66a4odlevel 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 pla 5psj kphore*8 )m9yo( u(9cblced 2.8 m in front of a loudspeaker o(koopsu8y9l(pr je ch 9m *)5bn 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 difference in sound level of 2.0 dB. Whaetr8l,cusi ze;.w(9 st is the ratio of the amplitudes of two sounds whosez.s9eus;ce (rw,lt 8i levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by zh9qy 6 5 vhm,.ncb.ufwhat factor will the intensity ic5y,hhq.fb zu9 6vm.nncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but oneh+kj/n8t ik5k has twice the frequency of t 8knthk5k /j+ihe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of9m3vdtcq3p t *8bn,xj a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules oftm*ptqcd 83 vxbj9 3n, 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a f5tn3*yr)ew *vrbdy2 100-Hz tone that has a *rfe*ynd 3w bytrv 25)50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tha( 0hdqnknk bkb, t9*26l oj*tb1)foast an ear can detect when the sound level is 30 dB? (See Fig. 12–6 o*ktn26 1ns,(tjf 0 *qlkb9bdh)abok.)

  Your auditory system can accommodate a huge range of sound legk gnrsjvlh0qr )sp-b3y .i *4kdqk+)rf 77e ,vels. What is the ratio of highest to 7 *nsfgvr7b4h rjk)eqkp+,l-s. i gr0 k3ydq)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 f9a h k **04 bkspkd3rfi,td(anhu1yi9 requency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be uf,ak t3rkii knd( 4yshd *91a*h p09bplaced?    N

  An organ pipe is 112 cm long. What are the fundamental and first threezi.l, -dn8e yk audible overtones if they 8ln-z.kde, i 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 tljvu n; jl5e+0op of an empty soda bottle that is 18 cm deep,;5elv0jj+ lun 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 kv)rvt ;v.n-g the range of human hearing (20 Hz to 20 kHz), wha ;nvrt)-k.vgvt 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 a frequency of 540 Hz as its thirdxq-b*2l) .i z8eouiu a harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origb8.uxui)2 qza-ile * oinal length?   Hz

  An unfingered guitar2qb6 qkuf4(aps 5 odx jwk+3h40hu 3,r h6ofon string is 0.73 m long and is tuned to play E above middle C (3300us q 5hkp o2f6h a 6,j3koh3u+ofnxbw4rq( d4 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 organ pipe zhk1law.v0 ee(.eqfc 2p w+ 9xpnk(a/that emits middle C (262 Hz) when the t /zka(wvpalew9 c+pkhfx 2e q01.e .n(emperature 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 20cqy2o e/n 2o+ka1 xx7b $^{\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 t mzsamy;ol )f5:ll1d/he hole be that must be uncovered to play D above middle C at 294 Hz? )d f y/;1s:zlo llmam5   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 Hz, 440 Hz, and 616 Hz, but not at d(c2qmqw- e(gaq x2i3 any other frequencies in between. (a) Show why this is an openw 32d 2qqxacq(-i(gme 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 h h 28xypvis(v:8q vl+* k d;nf)by*pjat both ends. It resonates at two successi:jvvpi(v ) f; bpklhdn8*8hx+yyq* s2ve harmonics of frequencies 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 eou7g*/ e4fxgjnt y4, $^{\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 tu;.z9i6w tax mhe audible range for a 2.14-m-long organ ;x9i.z m6atuw pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxima7wvo,x:iz,v-hungi*u z wdjl 6,p;s;tely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the grsxw6pgv,vwz ;j d-luo; :,i 7n zu*ih,aph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryiw:,2 rdj9ze*mkb1hugkl p,y bgh19/r ng to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is th99e l hg*yr1bmz1kk ,,w jgb2u:hpr/d e other string? ±    Hz

  What is the beat freqddd.(sbu l;)4w-qtl : ycpx : 4sekl*uuency 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, while another (brand X) opbnyjhnzz92(4fby 8fl i:/-9 y dztj2gerates at an unknown frequency. If neither whistle can be heard by humans whebl-h fgiy 2d(9b z8 j t/j:429yfzynznn 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 bea r6k5rjl9m5wz ts/s when sounded with a 350-Hz tuning fork and 9 beats/z9m w65rkrjl5 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 samn 0o yqs8qy-vdk* en5m 8n7e5ee frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will -enyq88d s n07*oeme 5kvqy5nbe the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hey;r)h u9*a(kbv;jsjl7z jhrz l1 )ct1ard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and tc h)rjk 1(*j1u tv;r)z9hb;ay llz 7jshe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, l aes+pb x15ej4t i8m9 iu,te8and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3lui5189be4,xt+s ji8 etmea p Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one spd xg5gwdnu0+0a9c 3hc n5qu a)eaker and 3.50 m from the othndcw5na)ac3 uq+9u g d0x50g her.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano qver,/akxm,o jrv-f ,l 3 5)igtuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating atl3gfj,rk5o/ )m, vra,xi- qe v 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 2.6/;1yd/kzn +)acre p7r: juvpb 55xltos; g 1nj4 m and 2.76 m in air. How many beats perz y7;pkr 1ov:;bju/xe/js1c5agn5n+pdr t) l second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of zr kev12 v7uqs -ey75ua certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a sp2 e 7v75qr y-suvk1ezueed 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 8uhn56fmon-r yr/* hf 2+pmi jwhose siren emits + h5y*m2ro-6fhn iu rj/fn8pmat 1550 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 toward you a 7xdu)uzv /-a26cthj a7j-bmtt 15 m/s versus you ada- tvhmuczj6 -7xt)j2bu/7 moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped witl3 o6;ye5bdnxy1qn. tzl q x)0h the same single frequency horn. When one is at rest and the other is moving toward t.lexy) txnz0yq36 b dnl 5o1q;he 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 o ymr4 hhrx3kq ghewuu2(i 2/ v:(t7u,jut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequencyu ghx72,m 2quvh (ut(4w r3e/h rikj:y?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the g(-,lij pns.*o5pqsb bat emits an ultrasonic souljo pg . nbs,pis*-q5(nd wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimqtn**tju6tyo 4 6d+w gents, 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 frequency was heard if the train car approached the station at a spee*yd*t4 tqon w6+6ujgt d of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound qt 5cw(h2ja+z30yzny 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 dire( wqhzy3+02c5jtnya z ctly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofxte1gyj/wsd9u/( + v pmm4bgk98f8ac 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 frequwy9ho q7ubk62gr k0s7ency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who u 9wos720 7kqkygh6brare 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 mo ;y.l ek)p)tn 1inr.qmving 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 2crhb3m+w9r. tdk7ig c ; j2jaMach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction ora g t7jm2di rchkw.;b 23cj9+f 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 at0 8r 8nqv*z.sg1i) sf(quv4wsd8 nuvbmosphere of a planet where the speed of sound is on b ( s8 *.ngvsqu0wqv)8 4urvis1df8znly about 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 gtb udo+3k9-av lh3 n:shock wave anglekb9-o g+nadlu 3tvh3 : it produces
(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 z-/f bk 7gk8)jjd2lmv$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead4-c+fzy2. fiiq 4+mybtysw(v and see a plane exactly 1.5 km above the ground flying faster than the speed24ifqzyf-c.bvsm4+yi (w y+t 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 that sends 20,000-Hz sound pulseu;d3h (,wyw/oygyz p9 s downward from the bottom of the boat, and then detects echoes. If the ,w;yhpzydy3wg(9 /uomaximum 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 th mtk88 ay:afb *qx*c;kere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symp or59g c9x8xeb8pqt5ahony. It consists of many plastic pipes of varpxt gbq9o5re9c88 x a5ious lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshol-sh2j- 7w g qie:n4a;op)t xqtd of human hearing (0 dB). What will be the sound level of 1000 such mosquitoeenaq-tgi2 x:p tq4-; w )s7jhos?    dB

  What is the resultant sound level when an 82-dl);ro9 wh1tazB sound and an 87-dB sound are heard simultaneously?)lzahr 19;owt    dB

  The sound level 12.0 m from a loudspeakerh+6 hg4j 9l2.kk wcp5ybqlo*p, placed in the open, is 105 dB. What is the acous4*2ko5 lcgh pqwkb.jy +ph9l6tic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Th90+ 6bp 4dbvinga-hlk e power output drops by 10 dB at 15 kHz. What is the power output in watts ad -l4+g khn abvp609bit 15 kHz?    dB

  Workers around jet aircraft typically wear / 3uw vz4h3yirprotective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance o/3hr i4vz y3wuf 30 m from a jet airplane engine?    W

  In audio and communications syst1brwhoc4s45 b zd /6gcems, 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 violinz+yd6a8c;is0e ahw7g d;g 2yz 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 betw+b+w2:r01vznoyo:uw .tar3bjda n g3een fixed points with a fundamental frequency of 440 Hz and a mass per unit lengthb32zg+j vw+:b.tr woroaud:1y ann 30 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 water 3byed:yi.+-dvxkc8 (s 7eu uk (Fig. 12–35). The water(yxi7-: 8syekvuke.3 c+db du 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is nearz8ff+po i ,pk1 a tube that is open at one end and also 75 cm long. How much tensi k,popz f+i1f8on should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was om:9 pt6idbj ( ss rrqf7e0g:l1zxj y3:bserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1f:ek no3sbbt8da k9p vn0:+ s.000-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 the sound level is minimal at a point 0.34 m farther from one sn9+n8:sto3kd f: .kps ebva0bource than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-3j wns+,9uuwto / :fylks,,uu Hz whistles. One train is stationary. The conductor on the stationary train hea wujwf3tuuu: ,+os/ln,ys9 k,rs a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a s cbaomw, ym5: l*r28tvie ,z x1a.y5rhteam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constat,yeax a5* c18w2 zrl,bvh5:yi mm. ornt velocity)?    m/s

  At a race track, you can estimate the speed of ca5+flo +isdf*wi*v e4nrs just by listening to the difference in pitch of the engii*df+* w5osf v+lin4 ene noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togeq6a n af *;j;gv9th/m33h tgqnpp1fr.ther, produce a beat frequency of 11 Hz. The sgvg1 9*phnjaa/ .fq6h33t pq;tnm ;rfhorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s -lh; pqi /67xipcz+pxtationary observer at 10 m/s as shown in Fig. 12–37. Iz/ lxp6;qc p7h ii+p-xf the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow inh -;b2g jeo1 egxl ob9s4zly6 q-lg+,n 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 travel with -;lzb b,4xynghgol29+ 6-e1o lqgs jea 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 towartt/2yw wu 6urwt ;c)y*d the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat afteu;ww26w/)*uty r tcy tr that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approache1ud( 5bbhyvqud66n 3gh+ k2 evs 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 detec dk6ubv bh2q(uv1nh 6ye+3gd5ted 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 tuy2z80d8ed ; i2i szzko 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 which overtone is close to F shari2zedik y0s8u2d8 z;zp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the prmn:7 ;foap fw*,8lgy uesence 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. Camafgyf ,oln;*:p87 uwlculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calledoc2; dvt5ru0y jp :c,s “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-cdr; tjs02pv5 y,ucco:m-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 thr kat, i-42buphu)ydz pd,9xy2eshold of hearing for the human ear at a frequency of about 1000 pytu9, -duki)zxy,4d 22ah bpHz 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 p-xx l0apq8 knor+( j pc+84jxMach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Wh p(4lop pc8xjn0-+kxxar8+ jqat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is oxrpf5i-6fne(nk aw . b0l-2p 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