What is the evidence thatk o:( bz jwsi2yg)0d9o sound travels as a wave?

What is the evidencejo +vf; 26sz+a kyhg.dfxh(7i that sound is a form of energy?

Children sometimes planelz2/1c50qm81it cj mpkzk2 y with 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 howkjmq 0k 1zme n1i5c2tz/p2 8cl the sound wave travels from one cup to the other.

When a sound wave passes from air i (.oya;usy;tr nto water, do you expect the frequency or wavelength to csryu ty;a ;o.(hange?

What evidence can you give that the speed of sound in air dobero,swv ;++scm i(wog+ w j34es not depend significantly on frequenvw;m so+jsb,oe cw 4(3rw+g+ icy?

The voice of a person whol7d9 ja f:rnk6:w ydu; has inhaled helium sounds very high-pitched. Why?

How will the air temf9*lhm;na d ;vperature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a fi ys3v0gsb 4w* )pl wlvgj3k2*tlter to reduce the amplitude of sounds in v30skv ty3s4* *blg wpgl)wj2various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer to ggote ko2:h(5gether as you move up the fet kog5 (h:go2ingerboard toward the bridge?

A noisy truck approaches you from behind a building. Ihxbumb- (zv a*5b2fn-nitially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sectbh-m2f5 nz* u-bxa(bvion 11–15 on diffraction.]

Standing waves can be said to wrsynt9:/ny+ onk26b be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explainkb n 6tyy+wn s/o2r:9n.

In Fig. 12–16, if the frequencel 7p zd1od pxzxh:/m5 v/gd+3y of the speakers were lowered, would the points D and C (where destructive and constructive interfxd dmex po+:l5 d/1zzvgp3 /7herence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with r x8ctm8 jqhjmt09t *0very high noise levels have consisted mainly of effo009*hxrt8q tc8jjt mm rts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in dpz cg006ivtsu4x/b)Fig. 12–31. Each wave can be thought of as a superposition of two s0 60sp/ gxt4cdzbiv u)ound 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 asmx1tzfe - ;e+;ox, cmnd observer move in the same direction, with the samezm ;,s1 +mxexf o;ct-e velocity? Explain.

If a wind is blowing, will this altw ryf q40wms5zbx+bax229t. l er the frequency of the sound heard by a person at rest with respect to the source? Is the wavele xr2a9qx 4zy+ bwbw20mtlf. s5ngth or velocity changed?

Figure 12–32 shows various poswhkbzb:akh1t;e0, t*itions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency forw*t k:e;1 bbkha h0zt, the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake:-rca 1c g+eph by listening for the echo of her shout reflected by a cliff ac1a-grch e :p+t 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 6jeba (mz-b91f kzzgl.upk)t ,4x5hzbelow 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? Assumeg1j zzetlkb. h5 -6zp,z) fk(bm49au x the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelxzh,x d;cm j,8engths 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 schoieb ecsjr -5;:ol of tuna on a foggy day. Withou;b- :i5sjeecrt warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the mbrok 7jw;f .a 41e5qptop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff? wfek ;.7r5ao4b mq1jp    m

  A person, with his ear to the ground, s3n ci2m tl1c6vees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact o2t cc13vimln6ccur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one m (k6*x kse9 4uke+iaatile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature aukxat 6sk 9e4ki+( *eis (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 d,hbhya4 m 0g9 ucs*q(mB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leua4n5i.c r al9vel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously0/r(a;p:eqr p 6p*plq fbiu0a at a certain place, what will be the sound level if only one is explodedeq/l pfi0 b up(r a0r;*a:qp6p? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equalr5l st 50 ch7vy(eqh: nb1gj0vly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut b:g0r e5h nv(1ly5jcths0qv7down 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 dcu,mgr,m7e +v0cy i 8x l3kpf.B, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgrmec fr0i g7ly8kp,c3 +uvx .m,ound noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conveqkc/k9zc5)kcg f :8lzrsation. Use Table 12–2. Assume the sound spreads roughly uniformly over a spher/k: cgkcz85kfcz) lq9e 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 whi+qd()r y w36pxggqv7ir v ywy*;u9o,ose 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 dn47rsg+fk p(f6 rs,v-q8 y wqA is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from 4dsfr7+,v(fnq -kwy86g sqrp 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 when placed 2.8 m in b 3b1f2+(4blwvezmm m front of a loudspeaker on the stage. mb+em1lb m234(wvfzb
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of:heb6 36thwmf 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: S: e6m3wbt6fhh ee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intg wh0r+2v 8t3fmxye (sensity increase? Increase by a factor of 8y+wt 0eg fs2rv3mx(h    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplituz3vu+dmm.emxt;i9i+nk) 8 dvdes, but one has twice the frequency of the other. What is the ratio of u3.8ediz;)m m+tdx9+ mnvivk their intensities?   

  What would be the sound level (in dB) of a sound wave isxvgt;:f4 c z2n air that corresponds to a displacegt: 2vxc 4s;zfment amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100- fr3+ ir(9r h 3xmp2hple01;w)g mdtjyHz tone that has a pm r+lr;9i32t hh(mp30wfyj )1drxge50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when t- ye y4il*h/zkhe sound levelh /zkei*yl-y 4 is 30 dB? (See Fig. 12–6.)

  Your auditory system can accomgy7c3noe*iyi9 75 ycs modate a huge range of sound levels. What is the ratio of highest to lowest intensity at 7nyic5yogi 9c3 7s*e y
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length p2bxjtb msuhmfv. y1;a- o43 2of the vibrating portion mpjs2u fm2h4-xoa vyb3. b;t1 is 32 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 firs:im.26 6zpoz6ll:l 2seafz bxt three audible overtones ilz2il 6f26sbp o mz:el.x6:a zf the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect u pzh;f3i fl)rwow x+hz,) 9.yfrom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clos,+)i rz.p z;wf h9x3) flhuwoyed 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 spannii8)nf:f3cjvz1z )g e nng the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes ren8f):)3v gzzf1jeic nquired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonicq.u,z8oad nl -. What will be its fundamental frequency if it is fingered at a length of only 60% of its original a.u- 8oqndz,l length?   Hz

  An unfingered guitar, p+zyohot dkao by828;1n:spjb8nu0 string is 0.73 m long and is tuned to play E above middle Cynn,8uo 1h:a8pp8 bd2tk;o +jybzo 0s (330 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 pipre; wdtv 0m* typk:6(x/tt5mde that emits middle C (262 Hz) when the temperature is wr*:0ym 5(v/d ;6xkt tett mdp21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 v -n cwjp):a9alwt olwq4-+.s $^{\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 +nx8aw45p )k1bi.)y owgtlj kthe hole be that must be uncovered to play D g4k op)liwt85.j+k 1wyn x) ababove 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 resoazgtm+n 8g a:vy l(0d6um1/n*bm 4evnnate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why t84z *lv vbmudmaeant/ nng0(+m: 1gy6his 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:)t vjdvw6.ff)sk m*zr: kk2 l at both ends. It resonates at two successive harmo jw)vkd6s*m f2lt.kk:f) zv:rnics 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 g6-zl6tz 5w mr$^{\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 a 2.14-m-lqt xt2h-gln e 2+t;c-iong organ pipe at 20 e2; c2t-x+tgtl nih-q$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is .d q0sc6cn2 ,0 1l9unqjdrk ywapproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to.rj29n w1qlk ,dc cuqdn600sy 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 ( l;8qn*yvpb8w c*dmpua6b*i s when trying to adjust two strings, one of which l8ydap8bu *cv qwpb*mn6*i ;( is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency ifgv9topwy25jwl ;52 h u 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 23.5 kHz, while another (bryy zggp)b/b a1m0oe-1 3nod 1hand X) operates at an unknown nea0gobbh-y1 p 131/)g ozmdyfrequency. If neither whistle can be heard by humans 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 beats/s when sounded with a 350-Hz tuning fork q)e5 llqk n8kzo)v)9 sand 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stri)vlqk9kozn )e)sq85 lng? Explain your reasoning.    Hz

  Two violin strings are tu85ybg,uh f d;ia8yu 5fned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat5g8auh fudyy8i5,fb ; frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard e/t(/fmsfege7ak/o d/o+ka2 if two identical flutes each try to play middle C (262 Hz), but one isf/ ao+ fk dto/7eskm /2e/ea(g at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freqjt bzfc 3hyef xbi,5 l47c-.1muency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sohb. bcc3m7 fe541y xzf,lj ti-unded 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 persoe d6ib() s53fl3wm -y fa;k.kck1oefdsx( ,i on stands 3.00 m from one speaker and 3.50 m from the i56(eo 1c3emfw.s3;dbla()off ikys ,x kd k- other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hzhk gt8wp gf5:iq 4.ttr;l)r5 e, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the fe 4itth5rp 5.;lgwgk q)r:8tother ?   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 mgr 3u5wbnpc-t2.io 6rg78whn and 2.76 m in air. How many beats per second will be heard? (Assumwpb5 rn3.r8n 7 o-62 cwggiuthe T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency mk0u/c* rlqieto8n pt/:: * sjof a certain fire engine’s siren is 1550 Hz when at rest. What freq 8lt0 :uc:n*qk jpmt erio*//suency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you dq(uh6 y-3kto cetect if a fire engine whose siren emits at 1550 Hz yc ko63q- h(utmoves 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-Hz source is moving toward lk(dxg*jrwu+l3 a tshz .q5 yha18m +:you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly8 y l5hkz3qa1+w(tmrx d*u+.gh slja: the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is uk0x .p/(0pc hx ghqo4z)8zyf at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat freo.hxu(8gxhzq) p zc/k 4py0f 0quency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ults )pls n-ha6v7 1n)bydrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received s61vlps snnbad h -y)7)ound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies,mt 68x2,p* mgnhwdy5q the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the ,* td8 h562nq pmgyxwmreflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playedm izmr4,c6-am6r ve2-v hio m8 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 was heard if thezem2 -r6 8ohmiaivvrm,mc- 64 train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. h 2jfqeh0hy/ l348f3:jzzbrvSuppose 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 arv0rlhj 2338fbf h :yje/4zqhzteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic 57ikvr:/ t)ht1hn u iejafdl7(*9 wpuwaves 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. When th-;a)m d +chcbbe wind velocity is 12 m/s from the north, what freq )+bh;mac db-cuency 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 movinpx7 g7u q6hcj8g 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 en qpk0y ngmo 1g1:.5hsound is 310 m/s (a) What is the angle the shock wa hngk0:mqpe .15y1gonve 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 of p4;eczn/7x 8s3aniq rsound is only about 35 s4x8i 7znp3a/ n; recqm/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 jwobns/6,jyn gz f6s 56.4sjdocean. Determine the shock wave angle 6.,j noyfdzb/w g n ss564sjj6it 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 nh 99-ug ta+kvurv( x.$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overh2 da;-/ molgo2z;qy7k frgx /dead and see a plane 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 distancgx/ qdd;o;l7of- k22 /magyzre 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 22ms72gkd.e, j +sm .boil+q jikp8sr6 0,000-Hz sound pulses 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 betwe.bg q8dri+jsjmk,. o e2 i +k7m2lps6sen pulses (in fresh water)?    s

  Approximately how many octaves are there in the g ri8myxj;1m7human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe shuxf8uergi8g--isy 2u+ z2/nymphony. It consists of many plastic pipes of variou-s +g2i euu-u2 h8i/nxy 8zfgrs 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 from a person makes a sound close gomtj m)di,3z 7 li :bf,iswg2 9ly-x.,hb5zpto the threshold of human hearing (0 dB). What will be the sound level of 1000 such z.d5zmmy3i t,: xlif)i,hp-g9s g2obwb ,jl7 mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-b/k:t e 5fctk*dB sound are heard simultaneously? bf/te : ckkt*5   dB

  The sound level 12.0 m y 8gq7yhx1zi5)pyu7m from a loudspeaker, placed in the open, is 105 dB. What is the ph 5yyi8q7z7mxuyg )1acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output ohjb: 2:b )kxidrops by 10 dB at 1i jo:b) 2khb:x5 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prom nac319du6mffw:0n ntective 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 fundm wnm96310n:f caairplane engine?    W

  In audio and communications systems, the gaad 7dxty:n a :y1wpwqo)2 s.k/in, $\beta$ 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 viol8x wknh wg,o0p6c hh0r7 nt9-kin 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 betw- nh zlia+m( a/98qomdeen fixed points with a fundamental frequency of 440 Hz andm+a/ziqh 8ol( da9n m- 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 filledcarpo9jju-6c. u3f, l 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 tur3ccl f 6o,p-.juj9auning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near - ,rj23yvi,+fub1xsgbkof8 ba tube that is open at one end and also 75 cm long. How much tensi bs,,f j32+bg-byvu x8r1 ifkoon should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop .bcu2c5ky y9l ($\frac{1}{2}\lambda$) 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 ra+ 9 qj+zhlijzm*rd6 9bnge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and96jljq +br9 *zdi zm+h 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 conduct0)/m oxud,n ud8hjjj- or on the stationary train hears a 3.0-Hz beat frequency wj )uho-jdm/0u,n8 jdx hen 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 a9v jl,(ujox0 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? ox( ,lavj9uj0   m/s

  At a race track, you can estimate the speed of cars just by liste) uv29afk +ww-gdiy0ening to the difference in pitch of tvw dkify029e+u)ga - whe 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 is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The 3g6lgs z*4 gxu7hq dfgm2*-mtshorter one is 2.40 m long. How long is xgd7mlgt4 ms gq6 z*f-*hg23uthe other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pake s.f9g:n e4r(cl 7mest 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 m 4ee lf7:kgsre.9(c nof 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 norz1hc 1ljuj a:)w..jmemally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along tz:)aj wj.lc hu1j.me1 he 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 is flying toward the almb1)(rzjc 5bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the f5m ) (crljaz1brequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequensxs)ei2cez. : cy sound 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 the echo from one chirp returns before the nexts.e ):2ce xizs chirp is emitted?    m

The “alpenhorn” (Fig. 121bzibhdrooa6/6qp/f s d,o- 2–38) 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 overto dfsoh, 6a zdi-or1bp2b/6/oq ne is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo lis:j)npddf y)r- kprw*(0(5sk2na gy vi tening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies fo )kap:-i5jpd0( *vyf nr)ksry(w 2dgnr the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involve0k,itkst. u m,s a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, lukski,m .tt0, oud, 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 thr0. zv-nwahrk pu8u1evd ( 0qa,eshold of hearing for the human ear at a frequency of about 1000 H,kur.ph (eq 80avdw0 za1unv-z is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boomy8le;;f l0a:p mq7zko 1.5 min after the pmfl lz ky0 ;78e;qp:aolane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isaoo :evti5o/) 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