What is the evidence that s l,; 2gjzg z x3d6b m/n eiahwu;vff5-jj38yi+ound travels as a wave?

What is the evidence that sound is a;wk)+ qt.e k; 7n94cshvorsem form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thegqivch4 p7os7f25.ks qa .ok 2 bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard ap5oh fiv2.24sq 7ka c7o qg.skt the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do youb-xq-.v ql*lw xld)3z expect the frequency or wavelenlxv*dz q.3-)-qblx lwgth to change?

What evidence can you give that the speed of sound in air does not zvy;f sz +7wbre1g5 +mlrbq54;:nurfdepend significantly ongl+r;bzs4w1unef5r7;b+ :qm r fy5 zv frequency?

The voice of a person who has inhaled helium sounds very high- ; mwyl153 hjthdde)6fpitched. Why?

How will the air temperature in a room affect the *-39ghx0m ikts-prakpitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude o:pwcpl5 )e.3nboz k8 kf sounds in various frequency ranges. (An ezon: . pe3ckw b8pk5)lxample is a car muffler.)

Why are the frets on b1.o3 r.hlaf0zlu 3vb;ea is:a guitar (Fig. 12–30) spaced closer together as you move up the fi3bsu e.: 3; 1vazh0laofb.lirngerboard toward the bridge?

A noisy truck approaches you zar5p:qf l/+y7vvh+j from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffra+ hva 7 z/lqypvj5:fr+ction.]

Standing waves can be said to be due to “interference in space,rvmd h*i;;h)o” whereas beats can be said to be due to “interv ih;oh ;)d*rmference in time.” Explain.

In Fig. 12–16, if the fxn,ym;yxkvs+)t04 x9ov5 fsvrequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togeth,x k+4nx mvsv9to sxv)5yy; 0fer?

Traditional methods ove1 ti/ q6hix5f 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 ambient noise. How c6 i5qt1/i hvexould adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sudb yaa(3nik g9qu/8d (ewbcfgw3; (m (perposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), a8 ((kdumg;caig febqw9y/wa ((3d b3nre the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observera3 yhu4co bymd-jj 34- move in the same direction, with the same velocity?yo34a- 4bchd 3uy-jjm Explain.

If a wind is blowing, will this altbjbwf5g(25hyo5 d7blb c sy,(er the frequency of the sound heard by a person at rest with respect to the source?ywdbolb2(5f, 5gb(h c jby57 s Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. Ai( typrlae 1*3van5.jzxc 67i 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 your reason yci6j.7(rt1x3 *lvanp a5 zieing.

  A hiker determines the length of a lake by listen sa..ou-i .61ctrsmqking for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after sh -q. iska6tcrs1m..uo outing. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the kq3ku g8jdst5 0wr.wae) s n2.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 spee ja8w5).kd0rk3tg s nq e2s.wud 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 air at 20 t.nn2q8 pjt.f$^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on m4y kib wq3b;3a foggy day. Without warning, 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 4bm; ywbi3 3kqfish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it (ddu ,w4y/ *abpz4rlcmakes when striking the water below is heard 3.5 s later. How highdbldzwu a*p,(cy/ 4 4r is the cliff?    m

  A person, with his ear to the ground, seesb0.wqqqu pi32sn qervr+c 47 5t6iip 2 a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and t 3ni 2ctq.7p5i4 u qq0ve6i2rwbsqrp +he 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 rx kyeb3sdu,vln4*4;zfug; ;over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30 4ydek 3gn ,b4l;x*v;u ;zfsur $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dBz4gfsa5 ggx+k,empyve ;n*zy 6 dh/ lw960 f9s?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensitdm+bra,3 4 ekey is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simuj *k.60rpqb piltaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensiti 6qp*rkp j.ib0es, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noi)pp7a ;c4d onbhdm) n8y1 m4flsy jet engines is experiencing a sound level bordering on1d;8yp) md)4 4nnpf lomah bc7 pain, 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 signalk6 .axj y2tf 7drdx;+:p ln 8xudf/yb/-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? xn /8d j7+fkyr2d xt.u/bxy;fl :adp6 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speal 4 87*)x;rrlsm b-qbldgqpsznc,f1+king in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouts; qdf7xllsbr8 l+q)*-bc1prnm z 4,gh. $\approx$    $ \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 ebqyo 4)*cm-0kn xz -qkardrum 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, while the more m(lv09yf8 -tzt c xh+kwodest 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 loudspeaker connected inf90(cxth zv-w+l8 t ky 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 rtxz( shr;34t/2 v eptr)7nw isegistered 130 dB when placed 2.8 m in front of a loudspeaker on th4rw 372/rtpt e);ix(vh nzs tse 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 i zw q.pyb rus4e:s5g .ln:zqx i6/2-njn sound level of 2.0 dB. What is the rati6s n/yx2pbwzj. z::4neis u grqq-5l.o of the amplitudes of two 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 t( drfoj)4q9n the intensity increase? Incred94 f)nrt(qj oase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equalwwnr4xqt; sq; 7r jkty/02q+k)t s9 hu displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intenkt9;sqhtrs0 q+ 4x2)yw/;j tk7qr wn usities?   

  What would be the sound level (in dB) of a sound wave in ai. ,q tas7u y5qz+p,aier that corresponds to a displacement amplitude of vibrating air meuaqzq.7 5ptysia +,, olecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as e:/iq cxo;qmxhr(,wp p 2y c-;loud as a 100-Hz tone that has a 50-dB soucq;ix,ep- ry ho/ (p:c;2mxq wnd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an efy(ci s.cc)eb) wj50lar can detect when the sound l 5sbc (e.cjy)cfiw0)level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levxpj9ttd3/+i7+i k li;+htj r wels. What is the ratio of highest to lowest iptj ;/lj+dwrxi3i9t+ +i h7ktntensity 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 b39d4a a(opyzy )d,ep+l9 w kpegm(;olength of the vibrating portion is 32 cm, and it has a poy p94k)m+lwgoade(3ez d y p9b ,(a;mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible;y5 hp pqa3 s7vmb:it1 overtonsqpm1;b: 75ah pivty3 es if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from )8yt xsj7- t6cd9bt b;hvnbk)blowing across the top of an empty soda bottle that is 8n b6-xdys;k )t) 7cvbtbjth918 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe+z7rnbm*mw+-j7 qp1 jf isdo( organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes +j +qs7j1wzo* idp(mm- fr7b nrequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has agk3e; bn;: 7qj,atgri w5i +-a vrnyb5 frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length r; q ngrgni5k5bi +v:a3j;w,t- eby7a of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above midw:gku)sdq h(cq2y +b 4k +q2rrdle C (33d2:qy+)r2 k( 4sukhq bgc+ qrw0 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 len (4)p kt*f/i tsip9r iz,tl0vngth of an open organ pipe that emits middle C (262 Hz) when the temperature rf4s(0zikpn tt*ipi9 v)/t,l 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 ats tbwy:z5brg *6 2 pcf;/k7ekc 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiec3a-7 ;jqk co yqtgc,,pe of the flute in Example 12–10 should the hole be that must be uncovereag73k jc,qtop, yq c-;d 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 tbx ;s k7d kmj v+l:u6i)*6kjjao(ws,resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequenciejvat)6;bk j,+:i xs mjdu7wl6*(ok kss 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 gj kbm;kq7-y: m long is open at both ends. It resonates at two successiv-7gkyqbkj: m ;e 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 *r-bd0ig5 0vd6qau0p m e*krx$^{\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 f.cngo4l,pd4e/0 lstms*d c* dor a 2.14-m-long organ pipsl ds 4.*0dntc meodpc,*/4 lge at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm :a 2a-qtzvir))j x+3a8rhki blong. 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 z+:aihtr 2ax8iarb -) qk vj3)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 c yxb6d4(who(one beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 (o cb4 (dxwyh6Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and 45xzr;p 3sslfpv(vo )crh2*f 9 6ocvq$C^＃$ (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 kh79b h q-hv8muHz, 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 occurs when they are mvhu8b-q7 h 9hplayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whhjz ;att tu1a(6w6na9o0d) d3.kd. y jhf7uem en sounded with a 350-Hz tuning fork and 9 beat16am k.ut973a d.nw;h h(tuj 6fjdy0a ode )zts/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. 6 w8rlfo2i:)sjn ze(dThe tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are rd6 wsn8zel):i(fj2oplayed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identica w*g; bb/0mswvugbo4/)naw4 pl flutes each try to play middle C (2gspou;w m nb4a g /wb0*v4wb/)62 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forqci6qja t;-h.q3gh,ivi; 3vw pu9 ew- k 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 bea-vhqh a,- qe ; 6i.;qtjvwcp 9g3iwu3it 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 areq)b+ yt; cz2lh 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 mc l;h +2y)btzq from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 13xia,i/hx8f 36 p f*e ajwg.j7k2 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratinggwfx ,i8p. aa6kj *7 xj3eifh/ 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 and 2.76 h29 m+zq:obi4qlctl y o0j h4(1zshw6m in air. How many beats per second will bs lh:4yoqowh(6 imt+z29h4b j 0czq1le heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certk gs1kh/.g; ei 9avjks;(wi 2uain fire engine’s siren is 1550 Hz when at rest. What frequency do yoas(9hgiwkj eu;kv;s / 2i1g .ku detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose rkf5rmm(3 vjl.y; 8y ssiren 8jlm53;frr .kyv( yms 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 tl ,veh3sq*2 xfrequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it aqv 23s *tel,xht 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 with the same single frequekg:5 uq3 eqlx07,)mvfzv-hu+ c1ywthncy horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hztvlfeyuq:g1h-mw zx +c 7v0h3k, u5q). 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 kg; 3zk+p 4vancHz and receives them returned from aakgzpn +3;c4v n 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 speem:w j,,kw.b ppd of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in thjwmb:wp., pk,e reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, amwlzk//e2bip6 . svzvsk;g7 s) voz;; tuba was played on a moving flat train car a6;i ;os7)gk pwb/s lvz./ vm2kz;szev t 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spee1*mse f ) :qznkyi+i2eds. Suppose the device emits sound at 3.5 MHz, and the speed o:ee* zq)+miiysk n21ff 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 ultrvph:9 1un f5ylasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz ;:r 08mu sf4 ytn8fmserexe 2t6;bu+v. When the wind velocity is 12 m/s from the nrv6 e:;0 eyxbft4esfs+mnruut;8 2 m8orth, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object cv*w1yvmnk xs67: o,xyga41jmoving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What3g* yx+hchf4 r is the angle the shock wave makes wi*c3hf+gy h 4rxth 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 thv 3p+ o( c5aubzdw3hwid7c6 k;n:vnx 0e thin atmosphere of a planet where the speed of sound is only about 3uxiw+ad0ochnpz73v5 :dw;cvn 6b k(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. Ded77 a.+czdamaqgtcj*6 s 3rh-termine the shock wave angle it prd7czg6t 3d+-ar.aqj7sm a*hcoduces
(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 s)o+o ;zkh+fw-7bykj $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and s5on gl+n: 8brwxxrj d;*u:2dbee a plane exactly 1.5 km above the ground flying faster than tdxg; xdr+wnubj o2lnb*5r 8: :he 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 that sends 20,000-Hz sound pulses dow+ek 8olt4h,cm nward from the bottom of the boat, and then detects echoes. If the maximum depth fot,o me+8clhk4r which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the 8/k3 rdyq4fs7s fml5lhuman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cg2 u9bcj:.uz:6n xuadb5-o ,brz j pl6onsists of many plastic pipes of various lengths, which are open on both en2 -z96xg,jpu.:j5 cubban blz6 r:douds.
(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 sou(gh*a)lcruqgmj 20j v);uj .x nd close to the threshold of human hearing (0 dB).jc(0jh*)j2 g) x.mlguq rvu ;a What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when anzotexa9p4 ,z7m t7v0g 82-dB sound and an 87-dB sound are heard simultaneousaz7pg0vx4z, emto t97 ly?    dB

  The sound level 12.0 m from a loudspe goh1:1ghho s/itb:lmr + +ix.aker, placed in the open, is 105 dB. What is the acoustic power output (W) of the sphbm1g+i+l1s xr/: g.o:o ithheaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output9hz, )ps/zaz b at 1000 Hz. The power output drops by 10 dB at 15 kHz.9bz/z hsaz)p, What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earsg( : v,nojulu9. 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 vj(g,uo:9n u lairplane engine?    W

  In audio and communic n x /y.o)fpnjtdg, ccp0/1:ykations 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 id lodp7.r3(o7z i tuc*s 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 poing5wbkqd6q8 ,4 -c ja:skub p-zts with a fundamental frequency, b6zac:8kqb wj4pdk- qs-u5g 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 vertical open tube filled with wat *2vlt j ;yq:rbju)o3mer (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of t; u)*3jjmb:qr2 vytol he tuning fork?   Hz

  A 75-cm-long guitar 7i;l)wm 1nxzogj); 9jcg r,exstring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental m ;)gx rmw1; 9noxi z,7ce)jlgjode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ful1s9feucia ix2 qm,rwo5 i,.3x l 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 two sourceg/1xpw y u469/cj3h sf/.jra +b0d gm9cnxryns. 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 source than the other. What is the frequency of6sc3 rdg a/rj1n04g9jmx+w/ u y9c.x /fbnp hy the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condu epz6*-b1akr qy4z-v zctor on the stationary train hears a 3.0-Hz beat frequency when the other train approachp -ye6bzz a*k r-4qz1ves. What is the speed of the moving train?   m/s

  The frequency of a steam train whis0ge)hwi8,-zcm c3zkr8yji b 1 tle 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 constant vec8k 8z ihjr103 mce,bw-g)yiz locity)?    m/s

  At a race track, you can esti)gdpb2v*e 5b )w- huh2xy 7frik4nn7ymate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the st2 ybp) 2 wd-r7ub*7hn5xekng vi)hf4yraightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat freq2,5 u1hrocwl- wdbbd9dlz ( -4xut0qu uency of 11 Hz. The shorter one is 2.40 m long. How lonz5l d dw-x-9d 4u w2rt,bc hlob1(qu0ug is the other?    m

Two loudspeakers are at opposite ends of a railro,d3 wuol gurd i-l/j(7r(,zwq ad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have pa-(lwgu/w 3ur(,r dzi,jol 7qd ssed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/jzp( k*bg p28u hp9:hos 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 with2zj h9*koh:g 8ub(ppp a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whiled*k 7:o (aypx08tfle-luhj6w 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 frequ7oyeafpx80j-(utd *:k 6 wlhlency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses ad39,;wouij kvs it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abo 3iv9ok wu,d;jut 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 onc j2xebc0a:b4 5-- uc) o)*y pspqxhf89o kpweae 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. ppy *04cs b2 5we9 :x cojq)8eafpobu-)hakx- The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can bzqxo y3,e;5 (uis1tzmrbe :e -e compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies fo1 bm eex5 -rzeoyiu(sq3,t;z :r the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invo3*n8 d 5g dbqv)rwn)zklves 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.d5)ndbr*n w zvgq )8k3 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 frequency o0t/fw; d 9cjzff about 1000zf; cft0dw/9j 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 bo* djf:zmgc mu6(wn i)td,c*5qom 1.5 min after the mcfn) * twcud:i,( dqg6z5*mjplane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i,1i evdabfyx5n x *3b4s 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