What is the evidence that sound tr+ 1 2gen( 6,wdwo1m yjoqr)s)fzhuu3uavels as a wave?

What is the evidence that sound is a form of energy?;/1 f(y8e6s+ ykx+rhhpco qzh

Children sometimes play with a homemade “telephone” by at excnpo3),kd; taching 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). Explainx3)ec ;pkno d, clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into watea/ jvugr r+ku02j-2km r, do you expect the frequency or wavelength to changej u2+kvgka /r02 ujmr-?

What evidence can you give that the speed85 t5l3nldipk 9ron 0m of sound in air does not depend significantly on frequenck 5m 85tn0pil3n l9droy?

The voice of a person who has inhaled hq0amo2 c/8s/ d6thxil6yl4+vtx6o u aelium sounds very high-pitched. Why?

How will the air tempera;wla / 5za pyit4 81-7joatgv7t e3gxeture in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitud7.kzoa aq 8kj8e of sounds in various frequency ranges. (An example is a carzkaj.7qo8k a8 muffler.)

Why are the frets on awtju4ucru4acj )2v y8f/ t 9tn(1ey z1 guitar (Fig. 12–30) spaced closer together as you move up the fingerboard towt t c(8yy41janz21wu4 uf v/r) jc9tueard the bridge?

A noisy truck approaches you from behind a building. Initially yn*am) e 6jnt/bu0-a1hdn1 o cfou 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-frequ11noh 6f n0*acbtan jued)/m- ency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spai94ffs k ulq* sl2cd8i1jw;s-ce,” whereas beats can be said to be due to “interference in qs iljk9*24 cfilu1-ds s8f;wtime.” Explain.

In Fig. 12–16, if the frequency of the speake;qe*,v a8r eu3/ +1hymif sfnkrs were lowered, would the points D and C (where destructive and constructive interfe 8inym,ef r*ke3f+v a;usq/h1rence occur) move farther apart or closer together?

Traditional methods of7sw5zb ;scr/a protecting 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 ambientrbz/ ;5sacs w7 noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can b8;9j+m7tzdf)h t 0ib( fxm-pp tpzlu+/u lyz;e thought 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 component frequencies farther apart? Explainj 9 z)m /t08l- zdp+itmu pff+ h7l;yx;utzbp(.
(12-31)
(12-18)

Is there a Doppler shift if the souu+(1/-g chu0ttg1gj o9cfpstrce and observer move in the same direction, with the same veo-ctujp(1 tgh0c/t9gu 1 + fgslocity? Explain.

If a wind is blowing, will this alter the frequenttqcv/0;unp/ cy of the sound heard by a person at rest with respec/c p/t; 0nvtuqt to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on nlfi54m6 r5af d+vt-n a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain f56na df-5+rm 4tivln your reasoning.

  A hiker determines the length of a lake by listening for the echo of her s);lb8avm53zr lax * kpvuwu.0 hout reflected b*rub 5z uka v8lvpx w;03a)m.ly a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears bdw0 :3u)epkoe 0eh(vthe echo of the ) :dpe3e0bkhv(weuo 0sound 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 indezt; keqy5 u o-k*5yik5 jsy m7y4-pek:6r-p 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 abo0o ./ro2i m ,j dw)opk6vhckw3ve a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 k.)hd/ocwv, ji6kk r02oow3pm m 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 striking tho9mymfb.bn3lg*. h c:e water belo bbo*3hf. .9m:l nygmcw is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike tjc0.3:n outwghe concrete pavement. A moment later two sounds are heard from the impact: onw. t3 0jcgo:nue travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secozpvqoo p 7ys.7 7;oea/nd rule” for estimating the distance from a lightning strike if the o z;q sepo/7vao77 yp.temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levelb( *1dglarevh (6.fej 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 sounda gf;fg ybm3p 4xnpmt)5uk 925 whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultan o *)z00nvcz.g wfy4mr,y)vsjeously at a certain place, what will be the sound level if on))v0wzs*fyvo,j n y. 0mz 4crgly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distanckhidcx - elj(9,i62zhe 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 the captain shut down allz9ix,k 2-6 dheij(chl but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have0 y/ y/kenkulf.z3 .lw a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio .knwe3 l/.z 0kfyul/y of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fr-43ijdn2o-icqc+ p md om a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a s2-q i3m-d 4con d+cpijphere 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 area i -hka*gd7l;z*nqp2 3e+c cdbxs $5 \times10^{ -5} m^2$ (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 ratedfc.e5 ,b6xvhom.09rsk w 7 p2wqec yo- at 250 W, while the more modest amplifier B is rated a7p 5qcrv 9fs.oky2.x, w-m b e60hoewct 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 regi, /lri )4zsy3 sw,mbqxstered 130 dB when placed 2.8 m in front of a loudspeaker on the iz rml/)b xssq3y4,,w stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a dif z(qpaw yk5g1pq*t 5j*ference in sound level of 2.0 dB. What is the ratio of the amplitudes of tpyp1jzag *w5*tk( q q5wo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will t5aqk82w zr69j h- x3k7ihz yxnhe intensity increase? zxyj7hzh w qnxk 2589r-a36ki Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampfeuxl, wage ((b9mw/2 litudes, but one has twice the frequency of the othbu/a(mle,xg 2w( wef9er. What is the ratio of their intensities?   

  What would be the sound lev+ ua-+zob u/bg dg7dtpaut/0+el (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 d t+7 gbut a0-oup/u+bd+gza/ Hz?    dB

  A 6000-Hz tone must have whaucwi)lfb c2 0+t sound level to seem as loud as a 100-Hz tone that has a 50-dB sound leve+l f2i wc0)cubl? (See Fig. 12–6.)    dB

What are the lowest and high;4 s 1l1kohelmest frequencies that an ear can detect when the sound level is 30 dB? (Seemske1h l14;lo Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thslk,s;)k 1d-q hbw 6uye ratio of highest to lowest intk ,sh6k 1ls)u;-dqyb wensity 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. The letp 4zpca/ -x,wngth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must wx,a/ pzc-p4t the string be placed?    N

  An organ pipe is 112 cm lif7*xx/bhf4d +mcn. yong. What are the fundamental and first three audible overtones if the pipe n*ixy+b h4f.mcdx/7f 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 rlol(,79z6ifnxe li 1h y6 yu)across the top of an empty soda bottle that is 18 cm deep, if you assumed it was 16l(irix7yfuon zh) yl9l 6,ea 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 pipeo :ummf abn+9.ms/cxk0*+4 bhhm6s xas spanning the range of human hearing (20 Hz to muns+xh+9b :6k0 s*m.x/4 o acfmambh20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strin1be 3;u odt0* 7jnmasfg has a frequency 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 oro7n3 aum bj*; ed1f0tsiginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p w(5+alyrce7i lay E above middle C (33 cy5(wi 7+alre0 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 that)xb9mx d(twpd8m g8w( emits middle C (262 Hz) when the temperature is 28)gmw xb8tm ddx( p9(w1 $^{\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 atqbv qe5b1h : 8nufi8*m 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 the hole be tha8px.2ibtxv 5s d bvmm:5sm,mivi ,*:dt must be unc*m ., :8m,2 ipxv:5idm 5bdvsvtsbixm overed 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 usj .s5jb7so 3resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any so s.j 3suj7b5other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonoij9;4 m a- hpzb-uk2nates at two successive harmm-2 -z hoaj4inpk;b9u onics 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 gdt5qfu90*3xqkwb3da 2ctk6$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.1ca -i)5,rl,q*-bd z ueup dvl94-m-long organ pipe lldcba 9uvr-d)i*zu,p 5e,q -at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to theqv0b g1i ,mh;-,pq hxk 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. Whihh10;bg q xqk- ,p,mvat 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 adjg9b/ sk:cys ybd w m-;7(iyy+lust two strings, one of which is sounding 440 Hz. How far off in frequency is the oyd ywy l/c( :k m7sy9+gbsb-;ither string? ±    Hz

  What is the beat frequency if midd y,8pf9f9a;yxz u6 2wrwn.evx v2p7+5l qaps ile 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, whil fmfcjn*o++vw .j wv76)zwy9x9s pa 4fe another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when cv 9 . 6xf4j wjowayvs*n9f+)w7z+fpmplayed 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 beat3s+ ,aqtn. q+b g8xazzs/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibtq +sn3a q8g+zzx.ba,rational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the s br: 4 gk cpqja7l62)c/ma.x4osaol5same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eqs4b6po rmgox./7a2s ca:al )ql4 j ck5. 11–13.]    Hz

  How many beats will be heard if two i2-vp /u0o vxee)giz6qdentical flutes each try to play middle C (gq6e0epu2o /x z-viv)262 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. Fobxxh4j 09:ohbrk 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 frequenjbh9xx4o0h: bcies 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 g(j y/od )9dphperson stands 3.00 m from one speaker and 3.50 m from t9 )dp(djyg /ohhe other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, buthn.i55/ 3s0q -mjlc7 pjv jley a piano tuner hears three beats every 2.0 s when they are played together. (a) If ojcjl5. l y/-m7e ivnhs5j q03pne is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m a ye1 *u kt2e*xa)mrsr)vdn0w6nd 2.76 m in air. How many beats per second will be heard? (Assm)1k6ae ny exr*dr20w )utv*sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fi po6mb ;xhqcr,/1k1 f5l cn7fnre engine’s siren is 1550 Hz when at rest. What frequency 7 on,61cmr1cfkf5x /bhl p qn;do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if jc (yqwak:uuf,).e8 1mczp2 k a fire engine whose siren k:apq8c ekjc m. )uu1y(z2,wf emits at 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 isayu(0xcas5 8, ,ehsj90 w8ivpln)efd moving toward you at 15 m/s versus you moving toward it 0s8n0xj,vaifs(9 8ewuyldep5)h, a c 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 withf8eou8bc2bjaf zw .v t+(-pk+ the same single frequency horn. When one is at rest and the other i8+jk cpzo2w fv faetb8b (u+.-s moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves alseg(5 ;ej,.fhov o2a5- oqnwt 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is5l owoj,sv5a2 ogeh-;f .( nqe the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 nlhz ( z9on p;-4w.) ygvjyykcmt/o1/m/s As it flies, the bat emits an ultrasonic sound wave with frequenojozc hyk)t1ynl-ym/vp .z;9nwg 4 (/cy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppl;g:tq9/xn9 cb dqvj /ser experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second tq9/: /jd;gvsbnxqc9 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blosa1xk5hssgk2hzb k)r+ /l5 qg ;l4c+bod-flow speeds. Suppose the device emits sound at 3.5 MHz, and 5kqgh+ c5 k4sx ;a)2zbrhl1/ kbg+s lsthe speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wave h7y+ 3pg u( a u:dz*dnqs)-0lmewxn)os of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind vcb6 b vtcqdbx 56883grelocity is 12 m/s from the north, what frequency will observers hear who are located, at rx56cbv6c388gr tq dbbest,
(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 s n6)8xdv(jhi7s 7 zldipeed 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 whhbio* 4e2+d 9h+t4,nre3ubif z,d umr ere the speed of sound is 310 m/s (a) What is the angle the shock wavfr2bt 4m4hen,d d,uzo+u* 3 b9i+ierhe 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 wher 83b.r4 oczjvw jj0xe:e the speed of sound is only about bj0cv xe:wj8. jzro4335 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 c wf4n3 ham0/k3mjtm* 8500 m/s strikes the ocean. Determine the shock wave angle it wnmakth4m*3 0 fm 3/jcproduces
(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 sw3supa4m5 lgzwsxc-7,gt.( hjw*6h $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 cw yx:0e2:daewlx+-cj00 ir8q lv)r t km above the ground flying faster than t y0:d ixw+)cl8 -2 xtweel:0rr0jca qvhe 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 th1) cottntm,f) :dimy ;at sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in frony)if ttdm1t); ,mc:esh water)?    s

  Approximately how many octaves are ther9hh9,2p cmqrkhq7 6sve in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of many1/sw5xg o f/zh plastic pipes of various lengths, which are 5o/gz /fh1wsxopen 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 fr.sbl).,f p3 is*sq wbwf:ls1 xom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 suf3llw.fssi x.q 1)*ps :ws,bbch mosquitoes?    dB

  What is the resultant sound level when an 82-dB so70 syn jjyy12jt /viy71 w,c2hiq+ybgund and an 87-dB sound are heard simultan 1 g,bsyw7 jv2yyj+2iyncy01jit 7qh/eously?    dB

  The sound level 12.0 m from a loudspeaker,m ,qto;) d ;1au8ud3x(qqqvkv placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in u;vv ,d3qox1;) ( 8k qautmqdqall directions?    W

  A stereo amplifier is rated at )5 ywzn7jp.ij150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powe7jp5 yniwz.j)r output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their efv fc59ej;wj 8ars. 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 of 30 m from a jet aiwjfv9c j8 5f;erplane engine?    W

  In audio and communicatio z+ )k4wh o:tl9p*ytkcfguys23 l b59vns 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 tunipbir fx(1px6 j186msed 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 35pyr: npkz/ .z2 cm long between fixed points with a fundamental frequ.k y 5rzp:pzn/ency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertzl vyjyd :h 8g9;pzarfxg)30cd:p67 wical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the wate:8 dg7py a) j:r03dzhc lgp9zvwyxf; 6r 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 near a tube that is openqa24ir,)alb x 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 tub2 aail)r,q4 xbe?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fut4jou0* 4q9+ey4gvqk )a4 j viyn 8gqnll loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from twz9 k)ko)q gonc/ wk. tx/(g0iyo 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 s ktxnq9k/ )iyo.z/ko c)gwg0 (ound 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 station+2p yvs p-dxiu ;lb19pt(gc;81nadb zary. The conductor on the stationary train hears ad; +9n ;1p 8ibz(l1pds y2c abvupxgt- 3.0-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 appqx4r+(ot+ iycq*xo 7rroaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movin4 oc*xq+t +r7yqi rx(og (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to zqce i c 1hz44u7 vztj+e*,1futhe difference in pitch of the engine noise between approaching and receding cars. Suppose u fq7e , *itcve1c+zh44z1zjuthe sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequencya(z(goy86 b5avc *e;vacd 4d yw6mut , of 11 Hz. The shorter one is 2.40 m long. How long is thezgac ,m6cdy 6e;ov(w4 aty*b a v8ud5( other?    m

Two loudspeakers are at opposite ends of a railro /v6*c r(kzz09s ngkwwad 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 frequen0 vz6kz wc /*ng(kws9rcy 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 bloex z13h4ty6zu od flow in the aorta is normally about 0.32 m/s what beat frequency would you expeux1zte 43yz6 hct if 5.50-MHz ultrasound 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 t f*3-f tdf-c-it*klh zhe bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of thekt**h-3ftf --l idzfc wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series okcl0og ag0gz/7:b a k-f high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the n-0z7gkk/ :agog0blcaext chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was onckf d8zn;h1 gisw; s.2qyce9p3e used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this h;d ;esi9381fqspg czw2.khn yorn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be co82o9d nd.tsevd3ix v*mpromised 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 standingsxen29ovt38v i .d* dd waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumi5cw) ;b1wjcnhnum 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, louwc jb5w)c1;nh d, 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 frequenccn,v-3y mvno * :b8ztjy of about 100 n 8nyvboj:tmzc-3 v,*0 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hearcq8 5gdvk 9ltm;1(gtw s the sonic boom 1.5 min afd(w ql8;g1 tmv9 t5ckgter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is wg- hk.x g4aodd1b.qu kpq0y5;rf2d 6 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