What is the evidence thavvkx1 9 pdvzu)us3 l03t sound travels as a wave?

What is the evidence that sound is a form of energy k3656zanomgp ?

Children sometimes play with a homemade “tele5xt y)n.l 1kecphone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child sc)x1 tyen.lk5 peaks 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 other.

When a sound wave pavqc1otd6og5 pjr0m)k;x 8m d0 sses from air into water, do you expect the frequency or wavelength to cjoor v18x t0qcg65 )d0;mpdk mhange?

What evidence can you give that the speed of sound in air does not depend signifo gq j3ge*4wpo:ea8t4la6hn g5 a8 a9cicantlyagh*wg3 4856j:q4l 9eno 8teaao p agc on frequency?

The voice of a person who has inhaled helium sounds very high-pitched z3(trnp1zl68 by 2h.0ytddhq. Why?

How will the air temperatui:hf r*6-w lj3a) yz/z oq6dgxre in a room affect the pitch of organ pipes?

Explain how a tube m5n z)r :itl r6)g+xd tm(m+abwight be used as a filter to reduce the amplitude of sounds in various frequencybw(at :)tixlrmrg5d)+n z m6+ ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spj:y u 5bul+gaj71e;goaced closer together as you move up the fingerboard toward the brido 5gj;jl+y gue1au:7bge?

A noisy truck approaches you from behind a buildingla;..tfj 1;f-rt r css. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “jfc.sf1 ; tarr-l; st.brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whergoa0 b)b8 mjw-eas beats can be said to be due to “interference in time.” Explj-mg8 b)a ow0bain.

In Fig. 12–16, if the frequency klx6ce)zh2 8mof the speakers were lowered, would the points D and C (where destructive a6xzkh 8 mel)2cnd constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people zmt1z9ezl gzc;y1)/+o8r jcn who work in areas with very high noise levels havecz /ze11;+ t r)yon9zcg jzml8 consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Figz0g8 sl +iylj iqtoho s.v816+. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explav 0g6lj+8i+isoqh 1ylso. 8tz in.
(12-31)
(12-18)

Is there a Doppler shift if the source and ob u(sdhlnu:( cg2)5y 2u* tikw 2y7mofxmj5)oaserver move in the same direction, with the same2()i 5 a* wh2ydgust)ol7uojy:n(mfc5 xm2ku velocity? Explain.

If a wind is blowing, will this alter the frequency of the somjy*m)v h,de+;jvp22adle*3 ue9 auc und heard by a person at rest with respect to the source? Is the wavelength or velocityc *v am 93edd2aju,l up2mej+ye)h*v; changed?

Figure 12–32 shows various positions of a child in motion on g,ll e um();hfa 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 el,( umgh)l;f the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listeqj*4hfe ml1+gz s r+q3ning for the echo of her shout reflected by a cliflfm +rs 31gzqe+h 4q*jf 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 belm4gnwtt n cs4k4ix9:yu(gu/( lgn :p -ow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly wit/x(94(itg :uw4-y4pug n:mknglncs th depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelen ng-wgqnrl qp* s37cjh3, uv;(gths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tunabzm)bl51-v4cpmwgw *s 3t ;kke* gq1h on a foggy day. Without wa)4 ekp hbzmwcts l531kw*vbg*g;-m1 qrning, an engine backfire occurs on 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 of a cl(na. s3:d*ug e/xryz jv,y1cyiff. The splash it makes when striking the water bex *d/j.azyvnseg 3cy1 ,ru(y: low 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 the conx+kfktsk/d5,5*e8rwlc/.he u s,vd2hb r5w t crete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occe2*k e.wrdfl/xs+bh,,kd5uw cv/ hk5rt 5t8 sur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-sl;lce:.y ck9 second rule” for estimating thlk;c9s c.y l:ee distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1203;nys :xzt( owb,9n0l kh,t x:tb q0c8f3pcvi 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 sounpsyq8w )t)mb x:eky-;n dc4sit j7*8+fl/ lj md whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95,wqzn1 -vngss1;l z l7 dB when fired simultaneously at 71gqsn wzlzls v n;1,-a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certai9g)j4 dx pkt0gn distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on x pjg9k4 )d0gtpain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas forl v8*zt pgpf,: a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? lpv, tp:g8*zf 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sos grb: 7fkzrk/k)ke-xqm)e3)qh 6b;kund from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the 3xkem kkkr:b);s) qr7-qhk)6bz fg/emouth. $\approx$    $ \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 ear a h5)tjt n:/rzcxk,d0drum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whileec53ailh y0 p5 /izrn8 the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loude0/n8cly 5ii rapzh 35speaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.0wug . 7x cgfk)a y:.jz;ql.fb8 m in front of a loudspeaker on the stage. ykfucw;.0fb7j.a. :qlxzg g)
(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. What 74.cbd* bbz eouqkf,0 is the ratio of the amplitudes of two sounds whose l.kz0b*dbefcb4 qu ,7oevels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fact(/ st.q+81ft vp sivnqor will the intensity increase? Increase by a factor of. /1+t qvpifq8sn (tsv    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacementi3w- jna,+ 5 boo2tbkd amplitudes, but one has twice the frequency of the other. What is the ratio of theirj ob 5-i2+tbw3a,k dno intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresq 7+zcv kf+m/3ebmp4a ponds to a displacement amplitude of vibrating air molecules of 0meq+m4b zpv3+/acfk 7.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lg6da es *r;n, ha)za1xoud as a 100-Hz tone that hasd* )sera za;gn6axh ,1 a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wm7 hy40a6vgq jt5aid-qs +y7rhen the sound level is 30 dB? (See ys547ad amr yjv-0+t7q 6 hgqiFig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What isjp05gc 3-)gqr l4xab c the ratio of highest to lowest5qgx3lr ajg 0pbc4c )- intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a vio *fajy1705pq, odg 0wdgy2pzwp:ybc: lin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, ygq2g, j fw 5zdo:ppw*00b7yy d:1acpand it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lr y:wn9bhro+uii. d6jy4*.xv ong. What are the fundamental and first three audible ovey*6o .uvnw 9rhji.xbr+ yd4i:rtones 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 expeltq.)2 0xa nko wct6b;v;y; gfct from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed i xnl; otq6k0cta; fbyg w)2;.vt 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 pnv hd2q( ae*xb:2/zqb6t f.xzipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range zh(.b6qqbf2xv:z txne2d/ *aof the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequdl z(o j, nvd8mb4 0f4/h)hko4jkeq(wency of 540 Hz as its third harmonic. What will be its fundame(k oq 4elkfn)44 hbmz dd/,vjj80who (ntal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned toi9/6qvole ( *ckd)p fr:w nz;i play E above middle C (330del6 ki)o/vn*(p:z;9fcrqw i 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 emits mwce 4t 7,7r8.9sngwlcx 5s hcziddle C (262 Hz) when the r9nsc5 z4wwh7,s87 gt .x eccltemperature 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 hx*v g5g4v2a ,hwbp*u$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpi0)jprgp9 mga0:bk 8 nlece of the flute in Example 12–10 should the hole be that must be uncovered to play D abg9)0lg pbp80njmk: arove middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz,0vn+ew0v vju( but not at any other frequencies in between. (a) Senu v (v+jv00whow 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 tubax o97tiyo pvl :2-hk7e 1.80 m long is open at both ends. It resonates at two successiv779o2i :hxlp tka-ov ye 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 dgb,p0h / pbi0$^{\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 pr7 cc2-qsc;lye abcm 9e92ad y,esent within the audible range for a 2.14-m-long organ pipe a2a7c-ccs9, a b;ydeqly2cm9 et 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2r. 9b-)uzo5ialw 1wkq .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) ab 59 1w)iqo ukrl-z.wof 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 adjustfa.00r2mjxg u two strings, one of which is sounding 440 Hz. How far off in frequencf jg.0x2rua0m y is the other string? ±    Hz

  What is the beat frequency if mnmr l5r5u v,z0iddle 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 operat 1:fm+j ownm)f ewx4/fes at 23.5 kHz, while another (brand 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 ocmof) mwwxfen 4j/:f+1curs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s wq)f*h ,xl6k - *yh(q h.r6exr 9ccbdeuhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of x.)xrlhy,e66*uk9qh* cdb e(hf- qrcthe string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. T)n fp2b-jadivu9 uy55- eqx4qhe tension in one string is then xfv -q5bi2up4najud ey95-)qdecreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eace rj.0y(p2v o:brns l.h try to play middle C (26es0r:bp(r y nl.vj2 .o2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of iz3o 4n.apvjx)fkxsz) h9s/qy .w5 :s 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 frequencies are possible when A and C are sounded together?ops4qn.ja59xysv h .w) fz3i)xk: s/z$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apar6+ znrvc xi lasqb9/*nj180 tst. A person stands 3.00 m from one speaker and 3./atj 08l6s19+sbzcxnriv *n q 50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supyix;2t; k fqrh(uk 7oy8qh7p 7posed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the f7 x;up(qoyt7 ihr y ;h78q2kkfrequency 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 2.6jybwaba;; y v chj8tibt0gn+ 1-6).hi qer6- j4 m and 2.76 m in air. How many beats per second will be heard? (Assume wqh y jebr+hgvaca;ytbn6 08j 6b- .j1t-) i;iT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 iol7,rstu9 7u 98) taynh y3a n+brv-.gbgv4 xHz when at rest. What frequency day-bur7t ,r.vy bstnuh4n+ i7g9l a3 )98g oxvo 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 ya dlmo svw07.gcvuhi1,ekoyw) 2w),,9 ctch, ou detect if a fire engine whose siren emits at 1550 Hz moves at a s,kctv0d ch.ew)y9 g,, l scv)o2,ouaw1 mw7hipeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift isrn oub2ph )2,n frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the twoh2po nu,srb )2 frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. el7en5m ye+:; bspb v4 ign7g.When one is at rest and the other is moving toward the first at 15 m/mg74; :n.pbveinl e5gb ye+7ss 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 at 50.0 kH zd0ee3cbj+5+o0 nar nz and receives them retrb+nencze0a30o+ 5jdurned from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it f3:lpwaxjqk: d2o +1pglies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does theqwjkg+ 2::plx 13a dpo bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuqnl q/x)zcc 9r-(eu 8k2us6 joba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while ajn) r(zq2o u8 6quc -lec9xk/st 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 us2f48mll o3fo3p z*enxyc a5 h9es ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood ezc l5 m ynx42of3oa3 p9h8*flis flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequenc pz2d 7--6m5ry+qncc5gorbtxy $2.25 \times10^{ 6}$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 f6jhk) 5da5djbz d; gp4wk5g+ ( w,ttnbrequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loc; w,n ktd5(a jdj)bd+zpwt5k gb4 5h6gated, 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 speed at ga)z dimj2p o8xg1n-)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 2.34ecoe4;zai hmn (,d4l where the speed of sound is 310 m/s (a) What is the angle the shock wave makes wit c44dm4;(,leai hzneoh the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the q0iak/my1 ow9tfk5 v6z 4m5q kspeed of sound is k mk4qw 5mk91i6tzaq yvf/ o05only 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:1fzip m ox6,j ocean. Determine the shock wave angle it producesjmf p :61,zixo
(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 4kdth 9qjdcpc5e:p. 6$/theta$ 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 1nsx1fxj/ m04q .5 km above the ground flying faster than the speed of sound. By the time you x1sfm/4 xjn0q 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 devich7)/xw ari)kpmo7 kdwat k+1,e that sends 20,000-Hz sound pulses downward from the bt kx/ikhorm p 77ka,wad)w 1+)ottom 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 fresh water)?    s

  Approximately how many octaves are the ,d:-tdq8snlwob 56fs re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonyp*h:4w(b4jbq h 2szqp . It consists of many plastic pipes of various lengths, which are open on : sh bh*pzbq q(44pwj2both 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 vx20-4x2 jjp+ feqn8r4kb/tia e ts 8xthe threshold of human hearing (0 dB). What will be the sound leve f8t ex0-2k2 4x qjp+ evrajb4/sti8nxl of 1000 such mosquitoes?    dB

  What is the resultant sound le8te2js krdkof8 t,7h sel+5r+x;yw+mvel when an 82-dB sound and an 87-dB sound are heard simult7sx8d w2ls t5 o+,;yertfh++krjkm8eaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whad*pf3c6 ghe u -t0p,vot is the acoustic power output (W) of the oc0-u pvt,3*dhf6ep g speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at fxu-h uw vh9/c+n /s.d1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts a-hcuw// v.hndus9 x+ ft 15 kHz?    dB

  Workers around jet aircraft typicallyis 6,7zx +g8x2lasghy wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. Wha+zs6x ,lxay hg8i7s 2gt would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications syst- m pdwt1nm4d3a,yq- mw)v s7wems, 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 violg3x* -vo i0runin 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 between fixed poinsmzh 2gyp6h ny h0nueoe766:2 ts with a fundamental frequency of 440 Hz and a mass per unit lengn huepo2sng60 z:2y7hyemh6 6 th of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a verticukp x1t-f/mc*xchf v s(0m 7w:al open tube filled with water (Fig. 12–35). Thsfx*t f:0pmch-cx v1/( wmuk7 e 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is3 w9*vw)qnbruvg -) md open at one end and also 75 cm long. How mg)r- 9*w3w )qndvuvb much tension 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 observed to resonate as one full loop (j5cjaf5ei6ed/a v5m4$\frac{1}{2}\lambda$) 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 th*k d) 2m ko64nrz:pwx(o wd5ume 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant fmpm:x zo 6kn5d(k 2ruwwod4*) rom the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on thel 6ipduf 8af(*f jnaegjt+,7krv( /r,4 4f mny stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed offt/ mi4 ,j,4*nday +frlj7p((f8uraken6g vf the moving train?   m/s

  The frequency of a steam train whistle as it approaches you isfdizv9kvq8v wo(45cz )5na s 4 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume cons(z ov459z4v5a8wqn ifk c)dsvtant velocity)?    m/s

  At a race track, you can estimate the speed of cars just0.vwo os, .+ 8itlgcdf by listening to the difference in pitch of the eniovsc.8 wgd. f +0otl,gine 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 together, produce a beat frequency of 11 Hz. Thieil(1 ; ujvv7cc0s3de shorter one is 2.40 m long. How long is the othjdi c7(v;v i1eclu0s3 er?    m

Two loudspeakers are at opposite ends of a railroad car as it mo(v::f8 ubglr 0vjpz (e jezb5w(6trz,ves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have 8bj(:jrw(l pe f bu:z05v ,t(ez6g vrzpassed him, at C?

  If the velocity of blood flow in, 5d9s7kiupuc ; v6wh ;oocp)m the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directedo6wh 7i5pusvcp)ok;9d, ;um c 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/do* jp6,ih5 9ddo+uoys while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected956opo*y ddj,+diu oh by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. T7oh(v pgz z1-xhe pulses are apz zg7 x-ovh(1pproximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was) xlr8qtz(v/)xjcnts2 s/dk8e )- udf once 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 alp)j2 qk d)cd zx(xtev8-/8f)rnu/s tlsenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stej0d(t, )2v3xlzw.sn k qr 7muereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressu rk,nj)etz0w( 2 m3s.uq7xv ldre nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singg nj ug)yc5i 8t-;b3t qq17tnstr *2lving rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hvl)2 t3tt-rb u7;c ng g51yq*jsn8 iqtand. With a little 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 fr9 fr y.,ezul/ s*4qozi7atppop+r, 3sequency of abouty,to,s 4ez9 7poz+.lq*rfups/ri 3 a p 1000 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 hears the sonic boo m29c oy*:vclomlv: y oco2m9*c 1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isq3yt9yxqeykee)u+gx kr;3 +v4.r fs0 /ny q8x 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