What is the evidence that sound travels as a waveu 3h k;6pqeai4nens0:?

What is the evidence that sound is a form ozkno)t atp+.pjj j( yy*j;/y .k.;awjf energy?

Children sometimes play with a homemade “telephone” by attaching a strn7t,8 kwgvhe , 1ygb ld8ywo-(ing 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)vb(w8w8,gtoky,ly- 1enhgd 7. Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, doh:u4hpxmh6 knvd*ydw5 kl5 ,* you expect the frequency or wavele wd 645*m:dlh*uhp 5,nxhkkyvngth to change?

What evidence can you give that t skf.z(bl iwb2q/)v r3he speed of sound in air does not depend significantly on )sbvbi2 k rqw3 l/z(.ffrequency?

The voice of a person who has inhaled helium sounds very high-pfs:xh 9k, uap)wp;.yxitched. Why?

How will the air temperature in a room affect the pitc,0 1bp /iy(pm pasen,-jm6ih qh of organ pipes?

Explain how a tube might be used as a filter to reduce the a1twq;)3dw v5stl ol6 k cd.q5omplitude of sounds in various frequency ranges. (An example is a car mufflerw3two5)kov ;sdqt .1c56lldq .)

Why are the frets on a guitar (Fig. 12–30) spaced closer fcq72smzghjb +.9xw5(wm1 p6vqt h.htogether as you move up the fi+hchgtj7w .w9mp6xfb2qq.zh v m s5(1 ngerboard toward the bridge?

A noisy truck approaches you from behind a building. Iu nr; 4nwcm8y3n+9m h-l v2rmunitially you hear it but cannot see it. When it emerges and you do s2wlr9urnh +um m43nvc-y8 n ;mee it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in s6,r;r d y+qyy 7zuqpr9sygs,(pace,” whereas beats cays,qrr ,zyd7gyyrusp 6+;(q9 n be said to be due to “interference in time.” Explain.

In Fig. 12–16, if thesfw 24c,1pkme t/p+r6 v3 qahz frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occuz/+h rcm3,qa2swt ppf46vek1r) move farther apart or closer together?

Traditional methods of protecting the hearing of people who won8 4jo x ,yil,wk)jeg8rk 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 that4o yge nx8 jl)8ikw,,j 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. 12–3.8aagbr3 2 ovj1. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two compon.8gjarbo 32avent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directivd p)t/k r( f6 hkeqtmzsfz.29, )zfu6on, with the same velocity? E.v ,rdp/qfk(kte zm2 6fzh )utz9sf 6)xplain.

If a wind is blowing, will this alter the frequency of the sound heard b j/tq1(b 5mhcwh)jxg,y a person at rest with respect to the source? Is the wavelength or velocity chanwm5h qjjtg/h c,x) 1(bged?

Figure 12–32 shows various posity;68/c u mbk w. r06ssmxc-fvwions 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 for the sound of the whistle? Explain .cu r s/x-;bym 6wsfvwm6k c08your reasoning.

  A hiker determines the length of a lake bye/m )rk0)m-ijbg*1u mvr1vjivr qt (+ listening for the echo of her shout reflected by a cliff /tj1 *-qj1vr) mi+mv)iv bm grerku0(at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlinecnai7poa(jrzz w9 ( ulgc-.hd0*5 u;q. He hears the echo of the sound re c9qdl7(g oja0(nu* hazu5.cw-pr i;z flected 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 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in 3/qbph-pb 1/ f w:fekxair 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.j d xn0ayyr-byc,i20rr)e6 q is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) ) d2r6yyj0rba-q xce,0n r.yi by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of fxg )6j9e.la l -w 8vc2:kstuna cliff. The splash it makes when striking the water below is heard 3.5 s latervg2e uns9l ktwja.c)-x86 lf:. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stoned.2r:xnrzlh+ xc6k;mpf2 2u ucr0 k6m strike the concrete pavement. A moment l c u zhpdnml60kux2rrx:6+;.f2m rc2k ater 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 error madeoehlz2tp9 + 7a over one mile of distance by the “5-second rule” for estih ze7 l9+2oatpmating the distance from 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 pai 2ek+woc 8gb+fqql *au5lh0q *n level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intenpsa2g) li f54ksity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leve)4x+:t)h4pbtoo2 n +yidszl;5fd y rul of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensiti2ufdioy d :lp+ tzn4xsy4)o+ r;5) thbes, not dB’s.]    dB

  A person standing a certain distance from an airpl8,xttuyk(z j2*lv zm6ane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the vz,j68*ktz x t2u l(mycaptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have w,g(z/ z crn8iz-txb) a signal-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 back/r8it,gx z(nwbzz-) c ground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of soundinazw275cbz , from a person speaking in normal conversation. Use Table 12–2.2bz,5aw7zicn Assume the sound spreads roughly 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 whose a2q z52buy;1b3ow*kfk21b emykbp; g srea 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 25+0 hkx*7wr) pipo+34 bd qtclv0 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibeh40+kb+qlp w vi)73or c tpd*xls 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 when placed 2.8 m in frontr2iodp/*baf; a j;p lc3hb:;t of a loudspeaker on the sta* c:fltab; 2rophdpb3; a; ji/ge.
(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 differeu x5*a)g7ccqw nce in sound level of 2.0 dB. What is the ratio of the amplitudes of q x)ua*w7g5cctwo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled5wwj+x+ vkpitn,re, ,, (a) by what factor will the intensity increase? Increase by a f,xp ,rikwtvnw,++ ej 5actor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one4gn)9kui bwt 5 has twice the frequency of the other. What is the ratio ofn4wug9tb)5 ik their intensities?   

  What would be the sound level (in dB) of a sound wav erd,1 m5pmi1ze in air that corresponds to a displacement azp51e1immr, dmplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lowx jjmvzr5u5;42n p hd(5xg) bud as a 100-Hz tone that haswpj)gnb2hzdx55;x (um j5r4v a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when t*2*zj w2r:12wzh pmbrpf+rh a he sound level is 30 dB? (See a+fzmpr**hww b pz12h: j22rr Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Wha(k6zgd.n:ngy)( (d tirj5xp j t is the ratio of highest tjzdtygik:jx np5nd.()( 6r g( o lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violexn) kfv7umka3-m6 i0in has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under3m)7xe0a-nk im 6uvfk what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first n.b oyvpac. l86e655 twlnf .kthree audible overtones if the p 5 .6 nvk5bptl.8.awnlyeo6 cfipe 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 frequenc gi6bdjdf71 sjozny ,3l.(x 8cy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closeg87b njsd dj63x(z i1f.yloc,d 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 spanning the range of dbl;q5 22 ;fwvvw 0f e8;3 ggtadizae2human hearing (20 Hz to 20 kHz), what would be the range ow zeqab;vleg;t23ad ifgfd v20258;w f the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540i8 4jtlterkq 33rlj;7 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% l7jl 4tkrr t8je3q; i3of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to perd k(i 80hqx3f;vgp k b0t1w+lay E above middle C (330 Hz). rd;h8tfqexgpv 1i3kk b 0w+ 0(
(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 9; lidmq3 vkymp: st3 y:1+fwnC (262 Hz) when the temp ld:win:;fq33sm kvyt p19m+yerature 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 9lz n7h+q a0ibat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute inayrr33n /bs r: Example 12–10 should the hole be that m s/ray3:rr3 bnust be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz,o4u69 oy2yf q cuvz5+ hs3)oan:bkns. but not at any other frequencies in between. (a) Show why this is an open or a cl2s6.zc4nn 3yk:uoqof so5ahby v)+ u9 osed 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/kc dfy2 2eh27q l8rff ,x/xfv. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz2e8,xxh/ qd72f k yl2crv ff/f. 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 w, lvh a,;po)lk4 n. kkyvy1*fnjt4l0$^{\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 arexxjp9/ (ksie* present within the audible range for a 2.14-m-long organ xes9/kxipj *( pipe 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 fv)k/ly93eo5zw,q 3yq6o nilto 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 the informoqwvz i 65y,ye33)ko/9llnq fation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, oh3 tz mya; -10a 8gtxxcou2othm).d+sne of which is sounding 440 uz)2t3 d.a+ maxcstho- ot01xy hg8m;Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if 5:ze;pr k ;sjvmiddle 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,2c/lgtyxx-c) a.ggnb9s)9jt while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, esas9tcx ./)j-2ctxy)9nbl gggtimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hi; 6m-b 7or8cw5yab qrz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is trr a5q8;w7bb6 c io-myhe vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to themnp; 9sgh4 af*v-a *qn same frequency, 294 Hz. The tension in one string is then decreased byp fn*gna -9m;4q*hv sa 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 twosczr+7jv4 o w- identical flutes each try to play middle C (262 z j+7-v c4orswHz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A4d 5jc:n8ma vg, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C arjgnc:d 4a5mv 8e 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 are 1.80 m apart. A person stt4is+9mk7zopxkqf6r) tyo (- ands 3.00 m from one speaker and 3.50 m from th6z9tk ox mk-ti y+ 4pqf()s7ore 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 t)- 0qtoam0 2i*wl p z)vbe6a3rmjbh*vo be vibrating at 132 Hz, 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 mur0) a)6j-wvq i**bba m 3mpz0teo2h vlst 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 beats9afwcgawn e-p )f797 z per second will be hearfp 7cf99w- a7n)ae wzgd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaig6kwjr7+lx 5vxm .:t im )bm6v 2cyqn/n fire engine’s siren is 1550 Hz when at rest. What frequency do you detevg n vqb.m:)7t mi2j6lkyc6xxrw/ 5+mct if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stiq:*/2e sz1y z7hpoaw x6l tr2wll. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves a2 q/ 6z:a o* lrwh7yez2tsxpw1t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2)f*,3 i rs7)artvl msd000-Hz source is moving toward you at 15 m*t)ml 7 ,dasfirr3vs)/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same singleb0 .yt2ts. lld frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hellt2y0st.d b. ars 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 sound waves at 50.0 kHz and receives them ret2gj, c.po/o9wobc )fm0 lt .tiurned fjg9oto2cmcpw. .ti0f,b/o l )rom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a pzlsweq),* k, speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 )p*ek,lw q,sz kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba k/ ,p atusb.*jwas 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 stapjksbu,* . at/tion. 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 ultf+/w v*z)kh53 5vblbil +5q i .npnhcarasound waves to measure blood-flow speeds. Suppose the device e+)l vv pc/ik5i* b5nzqnf5hh3 la.+wbmits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wl:)ah uf+co)e* fx/dr/;wwi okps s( 8aves 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. W:y8; tnj a41vvy um-nzhen the wind velocity is 12 m/s from thv nn;vy4:t-8muja1 yz e north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on lanx-y/ku -zjeux;(a 94 mygjg 9nd 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) Wj2 qykk h533x+gn,z v*ef9wlqajg4/e hat is the angle the shock ,n*2/q 9vg h w4yf j+e3zejkxk53gqal 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 mnwox6;+-nv vspeed of sound is only about 35 m/s wo+v-n;6nv mx
(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 travelingm0x+q2 hyl+s u 8500 m/s strikes the ocean. Determine the shock wave angle it px+ m+lshu0 2yqroduces
(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 ydvuzc4-c wdq 6 ;4z *zs.g,x)sx5ljl$/theta$ 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 ground fiw-cpw)tq w 06lying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizonqwi -w) w6p0tctal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000- rp*agg vw+)6ynsrw5+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 a )6pww*+r5 nsggvry+the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible ra ;naqszo*l 0;umc4hpiw:5,lq vb q8h)nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Iqd7yk 2 ,kcfl06iv -wyt consists of many plastic pipes of various lengths, which are open on both endvq,0k6yyc 7i2-dlkfw s.
(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 febikcbau7w7r6hne qx4 3 .3b -)p uo8grom a person makes a sound close to the threshold of human hearing (0 dB). What ) e-8xuc3wp7eou4 .ibha bqr 36kb7ng will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and 9m 4 lyip l7c6dfyrcv.*l q44jan 87-dB sound are heard ydy f4ip4 q*jc.lrl47lm6vc 9simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in z1j/hg 8w l1pf0mk4 xcthe open, is 105 dB. What is the acoustic power output (Wfkxgw jz lp/h48mc110) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powerrqw 2 j:7zi4lw output drops bi4zw2w7:r lqjy 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typican m 02onpm/d /v(:cvuflly 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 airplav(02cf: md puvno/ m/nne engine?    W

  In audio and communications systemlhqja rcb7hmw. - 8t2 /b*oln2s, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tun5kjhl/ c6b:s t8oaus 9ed to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points witjgu41zy/r+eqc9. j my5-z q roh a fundamental fre+z1 q9zqgej4 rcm-yj y/or5.u quency 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 vibr;pbu 9b9/-as w fee7uh78fzrfation above 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 water87 7 f;-f bfewbpu 9haue9szr/ 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 open a- p-r ockuxn2+t one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundameu+-pcnox k r2-ntal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as kq8cn+vu snnq-i b:7 a 2vi/g9one 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.kl- j zomz5d9–1000-Hz range 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 and finds-d m.k z5olzj9 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 statio oi/h l4vgytqc,5p30r dci..enary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approacheh.qoegcdcpy40rli 3. v 5ti ,/s. What is the speed of the moving train?   m/s

  The frequency of a steam n jv5lc1m,y-he,5j8b h. oq uwtrain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fastqo 5n e5,.lhvbjh,jymuwc 1-8 was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeniq2qh5 baw8ktjt7e*9 ing to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain9w jak2e 8tqhq57*ibt 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, soun l/;9hgu *hcjcding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 mguj;hclc/ h *9 long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad 81o fv 0urrsfj y8wx62car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hes 8y82jx 1v06wforfruars the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 u.jdozpwg5;n+w3 i4 q m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood d;43g+ 5oqwj.uiwznpcells? 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 motuo g4 a:/l9ysxotukb7. 2wk3zh is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the fkk :b9 w/3oyug2at x.7o4lzsurequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of pyzi 6; 0p4mbf*;hq/y )fzi e;2licu bhigh frequency 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 next chirp 4)ui*f;h z;pp ibiyzy mlfc/0e;q6b 2is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send-1 p2oe g6zx4o8cnicg 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 gp -xn26occoze i4g8 112–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of standip8t7kb79i sl/e t1mur ng waves, which can cause7b/ l8ttips1kum9 er7 acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” iiwm.3a)zxrei t4hpw *n90bt3nvolves 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,” )b*pnw.4w 9x trht mz3 3i0eiaor 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 vakyna6gya0*d2w j/)0v+x ds hearing for the human ear at a frequency of about 10djdvyk 6*w) yg+n0/axs0 v aa200 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observerba,vs( n ::( gvzk1ysf on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alzvgbkfs:yvn: s( (,a1 titude?    $ \times10^{4 }$ m

  The wake of a speedboat kq kld5r- :i-mis 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