What is the evidence that sound travels asr2jx.c o t.w +.d cbqrtg*2(ep a wave?

What is the evidence that s) 4 viqqks8uk nq9h2h0ound is a form of energy?

Children sometimes play with a homemade “telephon9gg ) a e.lofa30b.sd t-vgqp7e” by attaching a string to the bottoms of two paper cups. When the string is strbaa .3f .7gv-dtqg l09oesp)g etched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect tz 3(ukgjaj gx az7p;i24pw/+phe frequency or wavelength toxuijpgp/ 2zwgz3;(+7ajk4ap change?

What evidence can you give that the speed of sound in airqn2q ;(k3krs:1qq8ak vu9 boy does not depend significantly onkkyoqrv 1qns9: 23u( q;8bqa k frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?t.w;9o i 4zq ml (y9kh5r7jwio

How will the air temperature in a roo/yb53aqk jun 9w) n+8dw:dt w8a0 bghim affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce3bx( r+tgmka(dtk f(e 74uc.m the amplitude of sounds in various frequency range7kdcrm b x3 (tga4mek(tu(. f+s. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1 :7;bxm8myeg v2–30) spaced closer together as you move up the fingerboard towa;87 gyxbm m:evrd the bridge?

A noisy truck approaches you from behind v29ix8f ,qaaq a building. Initially you hear it but cannot s8x9 aiavf,qq2 ee 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 diffraction.]

Standing waves can be said to be due to “interference in space+8p fyvl 8gta6/nh . s hi1yseiggb919,” whereas beats can be sah v.sgb+tya18n9 yggh/8 liispfe16 9 id to be due to “interference in time.” Explain.

In Fig. 12–16, if the freq dudfqs.h9-,orrxq 2s+ 4j u2buency of the speakers were lowered, would the points D and C (where destructive and constructi uso.rs,j bd2qur94f+ 2h dqx-ve interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in q3isk:d z 82ol 9,cbfnareas 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, thb3 f:sc,9iqn8dlk 2z oen 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 s: 1mdyjxft+c-p7un)y hown in Fig. 12–31. Each wave can be thought of as a superposition- 7)updc 1mftx+n:jy y 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? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer movzi0/xfr*d5;ym 3e -ezg -3n iy)bwbwtl)sht ;e in the same direction, with t lwti33ni)t bd rwy yzef; egz-mhb/)*x5s; -0he same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hearhxry,pv,rt )( 8sqkk : wil;w+7xqm t,v,h7czd by a person )8; t:, w7 kpyiqr tcl,zmqr+h7,vkv, xhswx(at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swin)0mj (hj im0dsg. A monitor is blowing a whistle in f md m0j0(j)hisront 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 reasoning.

  A hiker determines the length of a lake 0e )ht;m6rpms by listening for the echo of her shout refle;p 0 t)hs6mrmected by 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 belowzbdyw 5+bgti2s9j)*c 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 soubw 5 2jy+)cgs9t*izdbnd in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths/nnwqrubl, k++ t-b)g 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 tuna on a foab uv*/f1 q,scggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). ubs* v /f,cqa1How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frm::r46/u opex ,hl znhom the top of a cliff. The splash it makes when striking the waterz6hxm:e/u,phro 4 l:n below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ep3 eyvh0tt - tm70nf 6og8fh,qwpi a4p7s-(hground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from fh0, (v ne7pt0i8th3yomwgfe 4a- 6 p-thqp7s the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent er9clw+ui64p wjror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) plwj64 icuw9+ 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the ptj( se m:,0n uzy*i,fn y7h q9cdxk;ny.8fjl*ain level 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 sound whose in,bzrxre v(vo-m7 ph4)tensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producesrsc5qxz k ln:p15: 5x a sound level of 95 dB when fired simultaneously at a certain pl:qx:x5ss51k 5 pn rczlace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain di2 hghq5c:+lfkm4 ( e/jzn7 jgwstance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wqge 7mjcg+5w : 2 zlj/4kh(fnhould 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, (v(b:qbmbv -mwhereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the bvbm:b-((vm b qackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outputmm6uc, 9vmh (q of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centcuq9vm ,m6h m(ered 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 strike2den0 tj8 m6 b0cpzl8es an eardrum 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 v/+gg9b +q6 jfqv( , ksi4tisamodest 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 connectbvi,( a9/q 4fg+tv6 gk+i ssqjed 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 rr0iv4 gtae*n8egistered 130 dB when placed 2.8 m in front of a loudspeaker on 08ing4 are v*tthe 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 dedo/9*js8f z - sf:nddjtect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ9/8dn dfdjz sf-* soj: by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wvi n 2szq5dtef9 vx(x(8 fya0.ill the intensity increase? Increase by a facti8(ex(.sz5 dvq v ax2ffn09ty or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice tyq;x uyj6 ojk/p+5n (bhe frequency of the j xqny /buj+;6po5k y(other. What is the ratio of their intensities?   

  What would be the sound level (in o;rhx tx)7vt/ f ma qix/5vr9 g8 1l3+ut8upzhdB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air moleculesg ti;ovm)atf rxh l9t v3x87r1 qxu8/5 +/zhpu of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lvhn9 +imu )sl9oud as a 100-Hz tone that has a 50-dB sound level9m)+vsh lniu9 ? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear zp, j; tt9 vovnbbyjo.l 4geit4* /w 95urwe/3can detect when the sound levewzw p/ lt9io outv/yj5ervgb;bt4 e3 *jn,9.4l is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wh7uv2 6gizzby 1at is the ratio of hibiug27v zz6y 1ghest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has 1z)c -o)jgcgzbj0( e na fundamental frequency of 440 Hz. The length of the vibrating portion is 3(z)gb- cjnj oe1)0zgc2 cm, and it has 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 thd ocm-rqt0//rree audible ovrmo/qctdr 0-/ertones 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 eerf8z faln) x.iv 2g qig9,*t8xpect from blowing across the top of an empty soda 92.igq*tgareif)lxn 8fv8 z ,bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes sp s(+uu 6rw ln+ 9kq1hbdq;9litanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes r9 ql w+ql1rti+;duh su6b9(nkequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freque6pkieo9zeg ,5q8b y4wncy of 540 Hz as its third harmonic. What will be its yoe4g6 ek5 bq9wp,iz8 fundamental 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 toypo7oj(xzr*y -t a dbpp.1:o1 play E above middle C (33jorbdpzpa7x.-oo y yt1(p 1*: 0 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 lengts -4ef/b/x y/xxyji)v z 7eo)rh of an open organ pipe that emits middle C (262 Hz) when the temperature )vxif)x/br ye z/x7o/ yes- 4jis 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 uqilhu e3w6*1vp;nxh j 4t/ c33-fxda at 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 Examp9u7- g*l wvavnle 12–10 should the hole be that must-lva*g 9u7nvw be uncovered 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 resonate at 264 Hz, 440 Hz, and 616 Hz, b,:n 9z6 i5xf3a0 agzw,eghdzjut not at any other frequencies in between. (a) Show why this isfz gaih,9 j zzg0,wane:35x6d 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 openqq9vyh90mw*3 ) kakkb at both ends. It resonates at two successive harmonqb hk*q 3 ay)9kk09mvwics 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 -bijn)fj r s93 ymsao b-k12o2$^{\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 audiblej gmu,f ofimd(a -j09. range for a 2.14-m-long organ pipe, a f9m-f( ujmg0ij.od at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 23l/o(vaxb136 xl drwi .5 cm long. It is open to the outside and is closed at the o3w(6 xa/3lolrdbx 1vither end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two stri te4wolk q1l*9ngs, one of which is sounding 440 Hz. How far o l*k9e 1tl4owqff in frequency is the other string? ±    Hz

  What is the beat frequency if middle C vby6zi9:ps*r (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, jufn;kmg6qb649 aon, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans 9bnma4jguq;6,fk o6n when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beaa15xom +dpl)rts/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuninal 5or) pm+1dxg fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, :er* u) xdann kc( psvqf.))1k294 Hz. The tension in one string is then decru ):)f( kea )d*c r.nxkn1psqveased 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 each try to play am4;qd.*yju x9 p8/ 0wf2q lt bg0qsysmiddle C (262 Hz), but one is at qs.8tdy smup0 ;bal*/x2qg90y fwq4 j5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequen zpullp4n5o 7l nfa-mhdn6n78 w -pr/(tw 0,vycy 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 Hzz 7n tlp8l(5 r7doa6lnfpp h n4nwmv-y-0,uw/. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stmmv/m /e/ zy *fmf-pg,v/x - 7vpqs u5(ggw-vjands 3.00 m from one speaker and 3.50 m from the ot 5vgw7vy,v/mm-p-x/vf pmm q*gje -/ fzs/u g(her.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be xifc,8*rb;mq (3gzou vibrating at 132 Hz, but a piano tuner hears three beatcfr8 ,(mg3x *io;qzbu s every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats/ (.mq igz(zeq27od ot per second will be heard? (Ass go(qtmqizde (. z7o/2ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engi d ,wg/we 5oj0qcc*kd0ne’s siren is 1550 Hz when at rest. What frequency do y w0,o/*wc0gj5ecddkq ou 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. Whaasvm77 mw(8 hlcwe6 f7t frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s vwh7emas6 7fw87lm(c
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequeh hj;8,bw3i0, ajc ilzgi4t7mncy if a 2000-Hz source is moving toward you at 15 a iljbc,43z0hj;8,m gh7 iiw tm/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequencyc5ej xg. k.an rrr/44vvw 4ac) 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 a. c/v4g4r wk4xnjrer5 a.v) cof 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wave sesngs 7j:a6 ur8, /0icrsryfbp,h-4s at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is t8,pu-j:06 4,eshs7rcass/n igb yr rf he received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall a dvw6-f.i m7kzt a speed 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 the reff idk.w 6-m7vzlected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler o:90wm/qm n 77vcbvx1v-gt uyexperiments, a tuba was played on a moving flat train car at a frequencmqwc7:t/7-vv9xnvom0 ubg y1y 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 ultrasoundry(o di hw vl,/edp09*1hte 6y waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s dih0 dp/*1,ov l 6wyeryt(e9id hrectly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency xcw/ c) k6xcd. gow 9xy 0*ubf*;)fhjxjhp7o ; $2.25 \times10^{ 6}$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 velocitl);nmjk)du:m pak + m 53y)khcy is 12 m/s from the n p)3;)uy)ljh 5m:dkmkm kcna +orth, 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 moving on land if its qz)l32y, 4engpwzgq pm.z2cq/ +d j5 pspeed 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/sfz s 6v0htdbvi0kxcc7; +9f-m (a) What is the angle the shock wave makes wi+m-zfi 0;df07t96cc bkvhxsvth 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 speed z5d .um 7yon/6 fcfmerd q2r70of sound is onlyrem2y.u76mzodq fn 7/0cr5df 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 ocea li0/3tpg(gz dn. Determine the shock wave angle g(d lz t03ip/git produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle l,.- ,uyrslpz$/theta$ 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 j oohia:s)s3/exactly 1.5 km above the ground flying faster tha)ias:3hj /oson the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulfktc;k/ futwkv,7oks c (0 j7/ses 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 (i0(ok7 tukj;c7fw c, kvk/s/tf n fresh water)?    s

  Approximately how many octaves are there in the human audible rang5nj*c06 h9tbg4 zxo8f 1pjvfwe? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consiq.7a, 5eb e wlnzi-p(rj 2 fl:.9bdarusts of many plaq. d 2rarb(lzpl5u:e9ien -.baj w7 ,fstic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from8i*l7d .fphsx a person makes a sound close to the threshold of human l*p8h7.isd xf hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when a0eq403vsfg j6b+y/i our hrs7n 82-dB sound and an 87-dB sound are heard simultaneously? g/e0 4uh0+vy i7r qfj6os r3bs   dB

  The sound level 12.0 m from a+0 /bkxdq6s hb loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, x b0dh b/+qsk6assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pxr9m;go/qti 2f,8p bsower output drops by 10 dBftm9g xs2b8; oi/,prq at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically weaocjq( f :pr:b3l/e/ cm-;h,v d vdodi/r protective devices over their ears. Assume that th: oepoihv m fd3,/(;vlc:j -//d dbcrqe 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 airplane engine?    W

  In audio and communications systems, the gain,4ht*o1hom;ah c*9wqi $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fre 9:l(5jisybv9)b qv r2ipspw,/9dkuiquency 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 b vsvcag k2n wvh )n*d2n..f51vuyp0t-etween fixed points with a fundamental freq gs2n vnvk-)1fa uph*t5.dc.0yvn2wvuency 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 filledr2ae1w7 ):j-onvy/gydxr x2c with water (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 openic2ax2dr yvyg/r: 71 jwnx-)o eng 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 2y5p4brg l lnu;d+rq5 +.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 (inyn lurg b5q+rd+l5;p 4 its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonfz2 sus,: -eacate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone immw vkfjw vv9m w72:.5n the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. T jkw w75mv fmw9.2:mvvo 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 2p yj( e7pe2wh9xub6p conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approa2bpu67 ppy(e whx9e2j ches. What is the speed of the moving train?   m/s

  The frequency of a steam train0zky4tsq ; lf2 whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume t0 ;qlzk sf4y2constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by bwc,uip/i 121pnnf*u 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 straightaway. How fast isu u w112pi*i c/nfb,pn it going?    m/s

  Two open organ pipes, sounding together,3v pd b:awxv-3 produce a beat frequency of 11 Hz. The shorter one is 2.40 3v:wax dp3-v bm long. How long is the other?    m

Two loudspeakers are at opposite ends of a rac )wfgu, dc8l,erh u.xwu ;w3: -8kstyilroad 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 passed him, af cr,cu: 8gd8txe.3-s ,)wwwh;klyu ut C?

  If the velocity of blood flow in the aorta iwehu- r uzw7(xe h8 u;n0r(rs0s normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wa-euszurw((0rwu 087n;rehxh ves 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 8egq v 8tq-5jkat speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s58- vq8ketq jg The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sounxy zo snaycjq3 l*/38;d 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 ty3x; ql /8oc*3janyz she echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to se1,mgg1qqq ;k+ yqc- lhnd 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 overy l q1k;m-qgqh,1g+cqtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be coju6x ic4wfh;icep*o( zyshn gu(,14 *mpromised by the presence of standi1gc;p(ohs4u*wi(6xe yj, nh4c* zuifng 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 standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singiyj .os 96gveb5ng rods,” involves a long, slender aluminum rod held in t ob96.y s5jgevhe hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-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 hearinnh rxdyv/6hte 1z7 iw6:wa9+ tg for the human ear at a frequency of about 1000 Hz is wdnvw6i/az:y 9h+xt7 1te 6hr$I_0$ = $1 \times10^{12 } W / m^2$ 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 M s a041p53egw4xieezyt3c/ca ach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is 45saa zc0y43ee3wtpe gx/c1ithe plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa-ezol: ooxfo9gr;cuf)-, s,;mflp l; t is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h