What is the evidence that sound travelsyf; *nwk3ld.wzvz *o : as a wave?

What is the evidence that sound g1j3hhhyp(.4kt f7 ym is a form of energy?

Children sometimes play with a hom:0n 7v3 ov2(vukbnbk.n: diuoemade “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 tu(v v.20 n uboibkn7vkd:3on:he sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect yrog70x (nw 3mthe frequency or wavelength to change?7n wr(3mxg0 oy

What evidence can you give that the speed of sound in airk4o8 1mn1gpoj does not depend signific1 8o o4jkngp1mantly on frequency?

The voice of a person who has inhaled he,sbj e0;z.x mllium sounds very high-pitched. Why?

How will the air temperature in a room affect the7wjj 2d.cv up(eqq)c5 pitch of organ pipes?

Explain how a tube might be usq7lcu8-b6l* cci af 2ued as a filter to reduce the amplitude of sounds in various flq u*2cl68a7cc fb iu-requency ranges. (An example is a car muffler.)

Why are the frets on a gu8d) qn5n k(x 8s8jex vprt7,r)svvj6litar (Fig. 12–30) spaced closer together as you move up the fi jr6sn,8n vdx)(7le5vqv jsp trk)88 xngerboard toward the bridge?

A noisy truck approaches you from behind a building. In ig:x( scsig(05ct 4preo r5)witially 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. [H5 igwrso4e )grscc0x t(i :5p(int: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beecb--tchb xvh4,/hejh;wn/6 ats can be said to be due to “int4h- hn6jevxwh,;bceb-h/tc / erference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers we g o)j.gg5pfdqbd9h9 j8p0i *nre lowered, would the points D and C (where destructive and constructive interference occur) move farther apart gd8pj *9g5do 0 j9np hfg.qib)or closer together?

Traditional methods of protecting the hearing of people who work in areas with v*ilahn 0t2j,u 5 +nzmgmg5.ldery high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technog* g5lu,hm.2 znlj d5 im0na+tlogy, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought,-- -rdc e:oslpoals+ of as a superposition of two sound d e+ a-c:-op,lr-s slowaves 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 sourera zqp so(e 15mbu 195j10ortce and observer move in the same direction, with the same velocity? qo(s5110etupz9ob rm1a jre 5 Explain.

If a wind is blowing, will this alter the n2g; f/y x(kkpy :q2twej k5e*frequency of the sound heard by a person; j*nw px:y qkgt2kkyef5e /(2 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 swing. Ao x(+w*rp:z xx monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the(x*wzr xp x+o: child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lv,9 km82cqjtcistening for the echo of her shout reflected by a cliff at the far end of the lake. She hears 8 tk9c2,mcj qvthe 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 b1er5+ msw7jtn7+t junelow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not +57t jtnums7n+rw e1j vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airn:lw4 13itto c 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 foggy dayvo2.c m gz8+) +znyetu. Without warning, an engine backfire occurs on another boat 1.0 km28 tuvz +g.)oyze+ mnc 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 ofjnkd4t0x5sms c47c; e a cliff. The splash it makes when striking the water below4 snt4ke c07j5 xds;mc is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to theajy2u*m*fw/h d7 uby. g(5- vf iex(lk ground, sees a huge stone strike the concrete pavement. A moment(h 7 uk- b.*/vufwi e*mjad(52xfyly g later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent err;naym-9 +ydmior made over one mile of distance by the “5-second rule” for estimating the distance fro+ aiymdy-9n; mm a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lev9sew519typ 0 v:neqom el 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 intenb7cly i0 sh 6odhcc)ipq;4 x0(sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soun y)pyoj9) wn ikg+zyir0 nye56:72t ped level of 95 dB when fired simultaneously at a) yy)p96 ryeepngz n k7+oitiw52:0j y certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an au+3 926, kflafhh vxhyirplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What ax lfy,9 6hhv2 uk+hf3sound 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 sign,6gya.a)jz90 gj jy wlal-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? 6yzjj0awyj a.,l9 )gg 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spmq;9ezxcf +6uosiz4 .eaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on tfz4 czmo6sq+u ix. 9;ehe 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 strik ( .;:oxk,- nfxkhwa+ntb *qmses 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 modest amplifier lkhbok)ya(8 aq7 c eg38k (l xaoa 9f*c/q,e1vB is rated at 40 W. (a) Estimate t oo ak8l,1((g*hay) 8ec3c fvaqx7/eba k9klqhe sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB wv/gua *s0ou(h hen placed 2.8 m in front of a loudspeaker v u*guo(/sh0aon 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 level ofgl3/y wn.ub:q 2.0 dB. What is the ratio of the amplitudes of two sounds wgb w.y:3ln/q uhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whatfgvhl b:js- :yy*6d v8 6onys- factor will the intensity increase? Increase by ad -v:l sf*h8 v 6bgnsyj6y-y:o factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tkh b*uew tp.55wice the frequency of the other. What is the ratio of their intenkhptb*.ew5 u5sities?   

  What would be the sound level (in dB) of a sound wave in 3s; qt8m-*r9ywpnaage 7 f lt* *ojsdh1)uux1air that corresponds to a displacement amplitude of vibrat3a*d *hmtqt9ef; w ygu18p* )us rnjs-xo l1a7ing air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to srx zzht1o -w9r-rw2 :ului*-keem as loud as a 100-Hz tone that has a 50-dB w u--1itowuzk:rz-l xr2 h9r* sound level? (See Fig. 12–6.)    dB

What are the lowest and highest .pzz6s ic. 7-nnm76 :gpapo3rjb p4xsfrequencies that an ear can detect when the sound level is 30 dB? (See 4 7i 3mjz sp-p.pparnz6bs: xo.c67ngFig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. de3g*)b;fxsn( :cpm+ /8tc3tpy vphj What is the ratio of highest to lowest te/t:s+ j(mc 3);vcnp3g xbpdy f8h *pintensity 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 fund;p d (r10mwsdgamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a ma;w rsg 1p(0ddmss of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. -lweh5k 8y uqha1emnv8 k 47*sWhat are the fundamental and first three audible overtones 88vk7-ml q4hy5ew 1s u*nakheif 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 frequenctm+qmc. 8oh;)qx.m gsy would you expect from blowing across the top of an empty soda bottle th;8omghtxscqq m m)+. .at 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 spannidhk6 b*:/wetcng the range of human hearing (20 Hz to 20 kHz), what would be the range of t k* hecwb/6d:the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wj)tfl, ; a iflox,/xy/hat will be its fundamental frequency if it is fingered at a lei x/ fx)ot,fj,/a;yl lngth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plsxkgs(1h z* o.7d7i rkay E above middle C (33r7i hdgs(*1xz k 7.oks0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz4el5wwa 3 ie7hzp* lf-) when the temperature is 21 7e plw543ea- lzwifh* $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20cdf* q(n2j9uv $^{\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 holeu*ui9(ez72is g gc w6p be that must be uncovered 2gzs ip(cuuw 6 gi9*7eto 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, but not at rq43cp5 j kyua mc8o,.any other frequencies in between. (a) Show why this is an open or a cloqoy ,3 5km4j8ur ca.pcsed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. Ixjc8cvf, hq3g qs1;ub-r-5 odt resonates at two successive harmonics of frequencies 275 Hz and 330 Hzodg;hs -5f,3c q bjru8vq1c-x. 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 uc 1jtq rs;*1756+yyee emcpw09qbb o$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for g)nc3/fpd)l/lpl dflk;7/b xaz 7)du a 2.14-m-long organ pipepa;x)n3cpd7df)/kul gzb l dfl7) /l/ at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open 0t0 b )g9yt 95zbgvtusto 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 eb9t )00 ugg9v5t bsytzar 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 z9yxp 4mud vsjsz5. l5+t/sdv v(94 haadjust two strings, one of which is sounding 440 Hz. How far off in fre(9u 95dlv pzxjs zv45.sydv amhs4t+ /quency is the other string? ±    Hz

  What is the beat frequency if middlqdjfjiib).9 rpz ;/o *e C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 s e3vw g;0jb/hl1wrf1kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans wheg1r1be 0svj3;wf hwl/n 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 beats/s when sounder xkuv55hbm 2jx+o-ek0w 1c4xd with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is e-w c4u xr5o0 2mvjxbkxhk+15the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the4qv p+xteh9v6v3g gc2 same frequency, 294 Hz. The tension in one string is then decreased by 2.gg3vxvht2cp 9qe6+v40%. 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 middle C (n nf+t5 q/s1ao262 Hz), but one is a a +1qsftnon5/t 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hasptm5ffap04 + vp/pmmn); i1p s a frequency of 441 Hz; when A and B are sounded together, a beat fretnp m smmif1 ppp5)vfp4+ /0a;quency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers arearoxzv jk; t0) y2274iv7ccn.9r veiv 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the oth77a22vitcrv ic)x.ey0kov4;zv j rn9er.
(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 ( mlkauo7,5sxbe vibrating at 132 Hz, but a piano tuner hears three beats ksx(7 u,oma5 levery 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 per xbkgk ;cbdnhv2lu (:1od96-i dxz p8* sec z: dx9n(x k8vbk-;o* g216hdlbp ucdiond will 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 Hzz/pp r,bxim /9p ig-36/vpn cs when at rest. What frequency do you detect if pgn-csp3/m v/ibxpr6z,9 /p i 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 zh -kd7/5t(vdvqczx7mokk 4 ,you detect if a fire engine whose siren emits at 1550 Hz kk(odm-k7qz / c5 t hv,zdxv47moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-iymqe6d0 (l lg;2rt3c Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies ex m(6li2r3y ;dqe 0ltgcactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn0f3q13zag bhl. When one is at rest and the other is moving toward the first at 15 m/s the dr0g f3zabhq3l1 iver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic so5p s y2 )dz8uz0kccp*qund waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the recey)dp s qk5u*z8 ccz0p2ived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s 8wkt2(y brb .f+ 0nx0e 2)/mvwqyoke lAs it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave? kxk0v 2r.8eenyw+/o2)f m w0(lqtb yb   $ \times10^{4}$ Hz

  In one of the originapxc9czqz 07x3l Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency waz0xxc c7p3 z9qs heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves d 0t/dfs*6ht 5jjpj,ty+)yi :ybqqd8to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz *f/sy:j, 0qit8q h6+jdt)t5dpjb yyd, 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 directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of tkl+ ps.uc-t5 xocd7 .frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the winyft8vw;u )+dbe0 *w w.q 0aoyvd velocity is 12 m/s from the north, what w*w 8ty;de0+uvbf.vwo)0 aqyfrequency 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 5cvwz:m6 5v)vim) h0q7 wzqhbon 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 s.wi05 xm40f ez,wq q+pj2faxo gdk7 4(a) What is the angle the shock wave makes with the dix7 s0afz0 eqw42i. jd,5fk+pxm q 4ogwrection 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 of soul3 +) wmljmrvsf+q ;k/:oxbcb1 f*/zp0 x gg3wnd is only about 35 m/ pb3ljkv3zw/0 lqfxs*bo/+grx:gm;cm +w1 )fs
(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. Dete6zdi1c r5 y9ciq/y7vhrmine the shock wave angle it ic/z7vy iqd5cy 1hr 69produces
(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 vsa w85u yc8tx-zn( f5$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plat2tt6pt q/qvfce, o1;iz q7 fs*bcc xr77,)ty ne exactly 1.5 km above the ground 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 kmx)q6csiq 1brt/7tt fcq; cz7*y p vef2tot7,,. 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 devicdvf*3r14j2 qwpggu5wl n .u;ge that 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 d2jw .gq*; pnwug51dg3fu v4lr esigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the /b1t:* r9*ng 2+or wsb.pjdsxbv l+n bhuman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display c.nz d:n56h85je +lsheyk1.w hgttw 0 s,qy;aualled a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. h;ez h ,sy kgqd n0wws: 5thy8.ae5+jun6.lt1
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresq d)u6o :amrt9gd4nf c/:7 7equzzo7ohold of human hearing (0 dB). What will be the sound levmq uc7z) dfag:u/do6rt oen7o4:z97q el of 1000 such mosquitoes?    dB

  What is the resultant sound levnp;d*q oxr5e) el when an 82-dB sound and an 87-dB sound are heard simult;pdqo)*e rnx 5aneously?    dB

  The sound level 12.0 m from a louds0*;p et5d14j:d/kyv9c2iwda qg mg l vpeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the sp20g ce t/ladq;9idyk1 pm 4j vdw5*v:geaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is raten) ue ,tad3 v*fl 1w5oipuh20.outr,o d at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 21,tirlf) oo*0ew35 andvo.p huu ,tukHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protef h. (8dlr*cjoctive 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 oclj8hf* d .r(a jet airplane engine?    W

  In audio and communications systems, the gain - q/ddxew:oc 9v6g5pq, $\beta$ 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 frct+; e3cziyh gq ..7tsequency 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 points wvg *z/04dx mfmith a fundamental frequency of 440 Hz and a mass per unitm fgz4v/*m 0xd 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 tugbz-q vyqo- o4go 5ml1yh3*s.be 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 gq .3loos-yh*q -vo yz1g4mb5level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is opwthha61d q2 ne33 o+xpen 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 moded 23ox h63nt1we +aqph) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as oy2 c9: nz* tdlg.9o ioiwwb1-yne 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. e tvyylcvwrfc**vr z,l,9 n /3-m :+vwThe 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 c* 3vl y+wc,-wv:yrzfv *m/vnt r9l,e 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 statwm2in 7j:b2x xionary. The conductor on the stationary train hears a 3.0-Hz beat frequencyxnx bm 2:jiw27 when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After6s gys+ xof7,a it passes you, its frequency isxags67y ,f s+o measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lo(t- g--k u1mr q 6khw2yg83t 0rppyolistening to the difference in pitch of the engine noise between approaching and receding cars. Supposeyr02wk-p lhq8oo-rtmgg yu 1( k-tp63 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, sf 3h;xi:3 gufo :o y()fkahd5,,pva3rcbr o e.ounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m longrbf:uhoria 3f,:y ) (p oek3 h;5c,.o3fvxadg. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pasp- qb a9gwvq3)k ,r6(g;knklbt 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);kvw)k gb ,3kanbgrqpl- q6(9 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 beat up(oy)auwy 0 6u po(+mfrequency would you expe)o+p(( yoyuuu6m wap 0ct if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s w*quhw- xl+bd 5hile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What i*dhqux+ lbw-5 s 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 sound pulses as it approaches (ik62fbk(+nxintaf0 6rk wp-a moth. The pulses are p0ki k+(n (66baf2tkiwf-nr xapproximately 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)-7: bssct qzp*eq 9/+mnvhe8u was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular 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 87nq+qe/pbtm *9z :uhes -scvtube.

  Room acoustics for stereo listening can be compromised by the presence of / ;*-o0ln;bwkmdxp a fstanding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room xn0pam/d* w k;-lof;b5.0 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, slender bz a4dj1z h7;taluminum rod held in the handh bj4z;1atz7d 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 hearing for the human ear at a frequency os bnb40 ;+qi rc,eoo/of about 1000 Hz i, 4/0bobri qo o+ne;scs $I_0$ = $1 \times10^{12 } W / m^2$ 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 slx -rj4,lmi..agj b.ng+y r c-onic boom 1.5 min after the plane passes directly overhead. What+j4, gly xa.n lm gri.cj-.-rb is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is )(( f n3yfahyv15 $^{\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