What is the evidence that sound zbqb9gd l c5++d,9nbvtravels as a wave?

What is the evidence that sound is a form of energy?be t10.ib,h 6bixuq nvl1 91lk

Children sometimes play witc4)0 zsah4z5vijf u4dnnf8al 5:,tq q h a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the soun da4,8fq5na5ul)4fnz: tz4jci hq0svd wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fw4b8 k: --c1dj qcpo-x djsct)requency or wavs)bcd-8 wjq4k dxcp-: t ojc1-elength to change?

What evidence can you give that the speed of sound in au(rk:g s j3:z o)h7rgx . q.9k9nf vso3dn:ktoir does not depend significantly onn9:o9uq(fjsv r o7rgoz3).kd:s 3k.:xnghkt frequency?

The voice of a person who has inhaleddpjc: f,l8( / na/ *qtn-ranuv helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch op ijh+x99tm dg)u)gx 2j9f4 j4fkkw9wf organ pipes?

Explain how a tube might y-dpj. k002g,,z qq pq 2trkyvbe used as a filter to reduce the amplitude of sounds in various frequency rangesyrkq ,pjv-tq,p g2 dz00.kqy2. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–m*axevf/vdh.e,mp2 + 30) spaced closer together as you move up the fingerboard toward the pdaef,v/m*+.2mx h vebridge?

A noisy truck approaches you from behind a building. Initially you hear it bu4v d,cg1m y)nksg-edb2esiv+1 9f) jtt cannot see it. When it emerges and you do see it, kvvbnge9t-1sg) ef2m4c1y,)+ isd j dits 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 space5 )(wrnul;tck(ql p+e,” whereas beats can be said to be rtw kle()+5pun; c(q ldue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were l s5 zicp*/art:z e9d)wowered, would the points D and C (where destructive and cons /aizwcd5 ts*:9 er)pztructive interference occur) move farther apart or closer together?

Traditional methods of protectin 3dj98ou8(wyw fo-hpa g 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 detectsp3do8y8ow- jw(h uf9a the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave*hxn/tvybs htw * ;,0ps:bdh- can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the wavb v n*;ydw ,h-/0:t*stphh bsxes, (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 move in the same +.sg sw2st w)bdirection, with th.+gs s) swbt2we same velocity? Explain.

If a wind is blowing, will thgljiw48(bh8aye7 kg 0 is alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength ob 7a8h4i0wg (8 yjkeglr velocity changed?

Figure 12–32 shows various vj n3 rk,/c0 l;cu5cempositions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which positi/vc0;km j,nrcul 3 ec5on, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening hq r i-xd:6onm/ih3 l2for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0i- or/mdlxn2h3 hq: i6 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterla mei,,pgdk bdqrw6;8c/ ,v.t ine. 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 ,;t. wk/ic8av rbgd,p6 medq, (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aimw;w5/ro ed2 pr 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 nk)e0a(j ujyy w,.9wwis drifting just above a school of tuna on a foggy day. Without warning, an engine backfire oaw u(kn,wej)wyyj9 0.ccurs 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 cliff. The splash itx/w,4 ,oph 8j etu*iio makes when striking the water below is heard 3.5 s later4ju/w et,ii8 o,xpho *. How high is the cliff?    m

  A person, with his ear to the ground, sees a h(b ahvg7jbo 6tenh;+ n4+ yp9luge stone strike the concrete pavement. A moment later two soundp ny vbbhgh j7(;+49+ 6alentos 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 occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over e(7ru64vhg fkcjb+is +8 / mxdone mile of distance by the “5-second rule” for estimating the distance fre kb8 + 7xhgc6sv4/f+(jmi urdom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sc6kgym9m ssur ;,kbo)0o)i 9round at the pain 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 le: xf e htd:jps/q4r,f9qz:e6bvel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB -rafiyol.k n)45rp, bcpygewgp /-6 8 when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Aigpgy. 48wra6e/,p)bf 5p - lr-o nkcydd intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jql.9xjl o jx26 n2 up0oi0h/jqet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this per x2oqx n060jl/jpuqio j .l9h2son 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 silft:hxhhs26u2 w:*hm gnal-to-noise ratio of 58 dB, whereas for a CD player it is 9522*x6 lfst:uh: hmhw h dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe q3ng l4bg+n4jr output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roqn +jng3lgb4 4ughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whos4: /ihuzq s4fae 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, whi dp-n,mq:).2oafuxds le the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would exp,-fn d.)xsmd2uo :apqect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dx2mjvr y/*: 7 k)xddrdB meter registered 130 dB when placed 2.8 m in front of a loudspea *y:r7kxvdxjrmdd2 )/ker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound leveb+geey,s e6 i8l of 2.0 dB. What is the ratio of the amplitudes of two sei ,yb6+se8egounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wa/izu hs1q 3tm-ve is tripled, (a) by what factor will the intensity increase? Increase by a factor of q ui-tm31h/sz   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice thxbh;i/b 4oa:ve frequency of the other. What is the ratio of theirhao:x;/4v bib intensities?   

  What would be the sound level (in dB) of a sound wavk )wu sanx0vgbt1r.. g3p(d)le in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm)0vt(3sga grd u.1k.)b xpnwl at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that qkk3)xv*qm y,h ,k vqy3m*xqk)as a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear*z3tvqb xlu6i1: vhkg k a2x20 can detect when the sound level0k2guh2v tx 13 iakq*zlvxb 6: is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levelszl tq697duvo75:(e fx2)fcys jcfng* . What is the ratio of hi 2s9*7 njq6fco: fctly e) v5gu7z(xfdghest 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 a fundamental6ekvm *n8g z93to*juzgo3 ;uk frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass 6j ;u 98v3k*teumkz o3 ogz*ngof 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 audiblef0 35 bttj1i zwwd,3px overtones if the tpfj,w1i0 bx3tz 5d3wpipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of jug(5cf*:liban empty soda bottle that is 18 cm deep,u:j g*(bfcl5 i 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-tubeg7b zhjsmd4uq47 1y nzz dyiv jh(39nn4h)t37 pipes spanning the range of human hea)h1izj7j3hy(n7 b 3ydu4g n4t7 d n zhqmz9sv4ring (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string haz iga:s f/yro k- i-7)pbr-ql,s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of i- lrkr7p-i,qfsy zoa): -/ igbts original length?   Hz

  An unfingered guitar string is 0.73 8/ou+jcpxj g7;atw tf*v9(z fm long and is tuned to play E above middle C (330 Hz( cj9+o 8u; f/ wvfpt7jta*gxz).
(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 th ou8,(jw/3srpv5 amjgat emits middle C (262 Hz) when the temperavo,r 8j/wsa(mg ju3p 5ture 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 at8a 3 a0xdnso.6sf br9t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the;w,d*la4coln2s6 8phqi v; rg hole be that must be uncovered to play D ablro,wqg46n*cli va;h8;ds 2p ove 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 x vcg:dx9 nxr,og:0i)264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in ,ivor gx9 ::gdx cnx)0between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at b6ox d-okw09mgl0jxe ,oth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What isl o-6o k0e9m0gxw,xdj
(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 dfb -we5s zy e8/i (udezg(x:4$^{\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 forsu:nbwi-k-f 4 a 2.14-m-long organ pipe at 2-wfbiu4k:-s n 0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outk y3f 4bn+tjh:side and is closed at the other end by the eardrum. Estimate the frequencies (in the audiblhb :tnjyfk+ 43e 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 beatts d 55iyzj+,i every 2.0 s when trying to adjust two strings, one o ,+jdzyi si5t5f which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequencpdel1k3cb,yo . z*9tj y if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at +24)u nk ff fd4b/5 slylj4djjfwjt-*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 shrilbkdsu-2 f*f4jl5ld) f +f4jy/4tw jj nl whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning f84wt lb4yt3fjl*d7fc ork and 9 beatwlct3d8fjt47 lby *4fs/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 ti pf2zj.q(ju-he same frequency, 294 Hz. The tension in one string is then decreasedzuiqf p2(jj-. 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 hhk (jk1d826 c2l;h oyw8pa yttwo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other y8wh2; 2h1k6(ktol 8jahpydcat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4w6zb2/anb.fna+ 8u bf41 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the bea2nafbbn6w+.8fb uz a /t frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 t3q10 oq 54jka abuy4qm from one speaker and 3.50 m fq 4q3t40j1 ao5 qbykaurom 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 vibnw0cy5p f-:uzrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are play5-:fzcuy np0w ed 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 md344 .rqk+br. kxx -ec.ny qlfany beats per second will nfcxbdqk .-34r. ky4r+q.xle be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Heieymmtw h9h 6dd-yy - fwb0ob*nb;/xum -. )3z when at rest. What frequency do you detect if you move b3m6 )d0-mh nw-fxtio9ym* - yd/ .w;ehbyeub with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What;9pbm9g6d b7 ds,nofr frequency do you detect if a fire engine whose siren emits at 1550 Hz mov9op6m ,sbd7bg9rnf;d es at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift bexcqc8zmq f -q :601zin 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 two frequencies exabqc -ecm 68q z01xf:zqctly 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 equipp wcz./na .vpka +j r4par+s4n:ed with the same single frequency 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 Hz. What is the frequency thn.awz pr v :+.saarp4k4 j+nc/e horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives t,:xlvlbnhbn5pp1 y 4*y ,1sqm hem returned from an object moving directly away from it at 25 m/s What 1n4 b,q yhlsmnl5vp* :1y,px bis the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, p h ,bj75c s2ndu8u+mul4xng2the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in th2,2 slc7jgxb4h unud8u5 mp+ne reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on ahiotkio1j iwf 78,; n8 moving flat train car at a frequency of 75 Hz, k,8tfi;71n8wh jiioo 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 speedsvsa2igo c 15g9. 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 1as c2v9o igg5leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wa .xi(*f mtpwb2aqlr)( ves 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. Whe4 3m5,i eqt6p bp.hjsan the wind velocity is 12 m/s from the north, what frequency will obserq634patm.i,sb p5 hjevers 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 objectw2waj jptm9*kb0(et c(s: y8 w moving 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) Wh s-x(.o:sgk x296/5xqjxlzus6fcvvdat is the angle thv/s6x29qj v( us dgcx5k6ox:zlx -s f.e shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed ofe:ood*j nv o log4/7ehwrp8-/ sound is only aode/ *v/ ner4 gjow- :7lo8ophbout 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. Dewvauvt)x 75m1 4oqnvl1w (rb 3termine the shock wave angle it producemao7(v5w4l31qv xbt uw1 nv r)s
(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 rgz xbqdxffk; h72i2:rz)k,4 q(2rpf $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grou(i( dnx4qm r1lx6v ben;wn8q4sbw2 c8nd flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See8n44swd6i (ml 1b qr(8w;2qxvncnex b 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 tx97 ac/bzy2dd vi: :dthat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is des: /7 cda:dixbzv ty29digned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how manadi, l i;mh 56ovj y1qpi)c,h,y octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a diw l lr2kn68jx+dfls(7nfh0 7ssplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both end lhk7r s( nns+fxd8j2w76ll0fs.
(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 3w.a8n .iv ajf8*w nqt4m2y+zi(l ci cmakes a sound close to the threshold of human hearing (0 dB).m.zciy a8+qiwcifv l n4( 8t.2w3a*jn What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sou35b2q dmp8pwynd are heard simultaneouslb5 3qd w8yppm2y?    dB

  The sound level 12.0 m from a loudspeaker, placedqph 8:/eae wi amiccs:1g87;j in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it mc:p 87 hi:eeig1q s jaac;w8/radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W,i; k.dtdm pq 2ai193qd n3kkn output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is inp,3;kdqk 13tadi qmd .2n9k the power output in watts at 15 kHz?    dB

  Workers around jet aircraft t.l8/irxl-v sa/qq jp5 m,swsl g6+ 9dgypically 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. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane e, m-/ rwg5/sl 9dx86qipl +s alqs.gjvngine?    W

  In audio and communications systems, the)ifzzd6 q,cc9 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 4tm-qv8f +2vv*y texv 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 fixfz q6cd08 pue el5kb6;ed points with a fundamental frequu8e;0 k6c5fpldq b6ezency 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 abo/-oz igfvyiq8u08c m.ve a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the 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. - iomyz8qi ufc/80gv?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one aw07oy9z1q cb/gd szm0dst0f9 /-svn end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) ds- qw09ct osma/fvs y /g7009bnzz d1with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obseu3+lu s /8yqwurved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Thf:.au95ywm gtkdm8/yp(w zhz*5om2s e sound is loudest at points equidistant from the two z 5m spm9d:ho.t8wum25y(fya /k*zwgsources. 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 conducad dc5x9.fuw0 tor on the stationary train hears a 3.0-Hz beat frequency when the other train app9axd u5d fcw0.roaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches g7isyv.l s-q of,.cm azm 8-4tyou is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)4 a c-gy, fsm.o-mtq8is7lz .v?    m/s

  At a race track, you can esl-d -m8:xffnbb(+ap5xz 6 paetimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cxmpzfl6( pfab8- e-xb:+adn5 ars. 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 ayjz xjmgj.81ng m,6,rxfz5/ o beat frequency of 11 Hz. The shorter one is 2.40 m long. How x,5jjzm8/ y 6zr1 mn jx.ggo,flong is the other?    m

Two loudspeakers are at opposite:t19+trae(ro.o o qll ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in r:+e(o ot9l 1t .laqorFig. 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, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beatshe 7etqwe q95 *l(8ty frequency would you expect if 5.50-MHz ultrasount85 (e*e wt7l9 yhsqqed waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth b7(8hul 7eem3nam d/s 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 detected by the bat after that wave reflects off thamub7hd(e e38/ smnl7e moth?    kHz

  A bat emits a series of high frequency sound pulses +w9q9aweldz 8,t6d ejnuxtkz 8)jq0 5as it approaches a moth. The pu 58dtqj)nzdul8w6 exzw 99, j0e+aqktlses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was on )f5;d +jrui: wx2lbpmce 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 blo ib)wfuxpl r 5;:j2d+mwn in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listeky*z1go u-4 opning can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the press4*py go-z uk1oure 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 “singing rods,” involves a long, sle8d)jeg v quf51nder aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With u8vfqg1 edj5)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 thef f0b5 sv4mw , tg2zjgzr3x9y+ threshold of hearing for the human ear at a frequency of about 1000 Hz isgzvs9 t23wgzf+5 m0x fy 4b,jr $I_0$ = $1 \times10^{12 } W / m^2$ 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 obha.k7 z1 aw(m 9c(vczhserver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What ca7va9 ( zz1mh.(cwk his the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isl: bc3+zsb2ey .+etczw: p -an 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