What is the evidence that sound travels as 8fzqi0hk py scs6op(,o y3ex0s1ej ;-a wave?

What is the evidence that sound is a form of energy?s 12q fsr, yt8 lc(:wui;h 0:gga;oqhk

Children sometimes play with a homemade “7d cyp1(pluxi2iq4g b+::p i,/dkn attelephone” 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 t :qd:yx ,g tdp(kb+aii/ 7n2lciup41phe other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the ,)j oio8p7;dx3e4t6c2veocw rp0o by d2yj3ifrequency or wavelength to 6oe0o4c8c7o;t dp2jyvxwb23 )p3 ierjyoi, dchange?

What evidence can you give that the speed of sound in air does not 9d oz09w5t r r 3jburvvjt10a4z.jnv0depend significantlydvo vb wv.9 103an 90j4z0t jrjzru5tr on frequency?

The voice of a person who has inho dvfogciag+tm73/(h13a65reb)q eg aled helium sounds very high-pitched. Why?

How will the air temperature in a roxrxk zn+uq3/3g*acuki; 9cv/om affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds s)z e+-ufncthzi 42 l0in varioust2 ne4c+-f0is u lhz)z frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) xeb *o sd,t7h7r3al 3gvop*(cspaced closer together as you move up the fingerboard toward the7s(rle 7bxa, o*3 cvhgdo 3t*p bridge?

A noisy truck approaches you from behind a building. Initially you hear it but j1*o-fp 9g sdlcannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the gpdjlf*o1-9s high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be 8e8 hab7m)3su 1aepwg due to “interference in space,” whereas beats can be said to be due to “interference in time.” Expla7e ew)u3pg8a 8ham bs1in.

In Fig. 12–16, if the frequency of the(bzl4-qm h rowxvh 8/.,vz/ uk speakers were lowered, would the points D and C (where destructive and constructive in4wvqoz/ x.-,k8l hr/v( zbuh mterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in arevzbgs)xu3 fr)) n .+flas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a rel+ lu)n )bvf fxr)z3g.satively 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 Fig. 12–31. Ead5(l jb , lfu0qimhh:5ch wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. q lbd 0(5l,jfhm5uh:i In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the samep)nny*sqm iry3+v /(8v5 tz(vzbyer0 direction, with the same velocity? Expmztr zv ns(0nqy+y) *(3 5i e8y/vrvbplain.

If a wind is blowing, will this alter the frequency of the sg9)k )( 9cffe, oaqnau7azxw; ound heard by a person at rest with respect to e9uxa;9z ocfgnaa)kq f7) (,w the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moneo ur3r 3c7qzsoic7 w5t( 2b5mitor 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 soou 5b37(rciw2 5s7t croe3qm zund of the whistle? Explain your reasoning.

  A hiker determines t n kla:t5hyl;y4w8w6p 8 ct0glhe length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lhl gpy580 tawkl6ln 8w;c:4t yake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below t,l: utq.0,u gso pv9puhe waterline. He hears the echo of the sound reflected from the ocean floor directly belotluq, gv sou,p0:p9. uw 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 wavelengthssg26a ky+plc 0 in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a fog6rf;xp yj ni*2v .jnd+s,w pi8gy day. Without warning, an engine backfire 8dfy;nri2 jn.jxvwisp ,*+6poccurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whwqlql,05s0 o+ x( x- s( o5oaryet+icaen striking the water below is heard 3.5 s laterw iq5-0oqt( ey0( ,ax+ola ss+xlroc 5. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone q+3cmts v6s) )aeg0cestrike the concrete pavement. A moment cm))c6q et+ 3v0egasslater 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 made over one min6qjthh97g k(n0 ;vp ule of distance by the “5-second rule” for esn (q7n;h u9tjgpv 06khtimating 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 sour z9 ujhr*(p fc0zu+w7nd at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensitq b35m :qua7vi2z8hv;gsqp3f k n3y) ,fc)ltvy is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired )irc7((notsd) zse6r simultaneously at a c)o ( i s(ntd7e)rrc6zsertain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certx cyhf;c29 2jpain distance from an airplane 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 captain shut down all but one engine? [Hint: Add intensi9fc2yjh 2px c;ties, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas +0na;bdgnt4 wfor a CD player it is 95 dB. What is the ratio of intensities of the signal and the ;at bg+ndw0n4background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpu g czect,*zg.vw48ow6t of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly 4eo6z8czg.c*wt w,v g 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 wh)bxx o 8cu.ysm*3qsg 7ose 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 ratede gzxj 0 r0.bghda7,9l at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would exd0 97 x e.bgjr,hlzag0pect 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 regi2 nnfrjx9.uk 1(w3c axvg0 :hgstered 130 dB when placed 2.8 m in front of a lo 20gav xcx91nf.uj kwgrn:(3hudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typicallyfwj,2qr kz / 2)dhrdu; detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whoserzu )22wq,rdfd ; /hjk levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intenr/qovp3f-p86f 9od zhsity8q6hdppf3 f/vor-o 9z increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice thldyzkipb n05+bls 2r(7s y +x-e frequenc y+iyps k bs-0+(x 7d2brznll5y of the other. What is the ratio of their intensities?   

  What would be the sound l u /t(,1ck+tvr /jxkfnevel (in dB) of a sound wave in air that corresponds to a displacement amp/+tfxut,jkk(1v r/c nlitude 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-Hz tou5ju3gea9e88 erl 2z qwg *pptex,0t6x;d5 aane that has d ;pl 5je3exup8azqwert ga9*x20u e6gta5,8a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest r m;v+ xw:g 2gn3j(oweand highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6meg(o:; gjw vwxrn+32 .)

  Your auditory system can accommodate a huge range of sound levels. What is 81 u)v4ga )ycfya9ru tthe ratio of highest to lowest intensity at 4 yyf))t ru1v9ca agu8
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a cjk*f dhjul/zl;86 j 2fg .x:rfundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, gcu;jlzx j*kf.:6jlf/8r d 2hand 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 fundpyl g(l+jd;8mil4 p2qyw;v* camental and first three audible overtones if the pipe is lygm* ;d wcl2jp( 4v8l pqi;+y
(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 p75 yq;i7v1r: k/ana;dy5co b0b( uijh; mvqvwould you expect from blowing across the top of an empty sod1vqv;b; y70ira;h n :vab jpkiq5 7/5y(mduco a bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube p 1d*uykn e6r43- 4kband o0ojxipes spanning the range of human hearingdk1ua4n n0k-rbeo3 yod j4*6 x (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third .-/ vm83fbqse,vbf( *ndz/zzrw. o dkharmonic. What will be its fundamental frequency if it is fingered at a len/z( ed k/vm8dobsvfq,.wr*. n-3 zf zbgth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7dyq9a rod,fe k;b 6/9e3 m long and is tuned to play E above middle C (d96q9k,o/bef e a r;dy330 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 leng,2q; qw-.llth s p6ndbk)q)orth of an open organ pipe that emits middle C (262 Hz) when the temp2-q lsbknrh.6 )p dlqt,w)q; oerature 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 ati4i d:,(-:g3eu kfkgvzbkzh.s 6q1oo 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be ) ;a v vd7xr*rg(g:dflthat must be uncovered to play D above middle C 7 xd d(ag:*)vlrgrvf ;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 Hffc7 s. +hz; lop6xk.sbzxk4s. ef 57nz, 440 Hz, and 616 Hz, but not at any other frequencis sfe+.fosp7 h xb.7.6k;zlkz4xcnf5 es in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both h42 9uhzxr m,fqs+ i ed3/ig0yends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wha z2gs9uqy4,/ f+himx0 e3rdh it 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 r*l h1/x;cs e5cmwm3s$^{\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 5nb9: j bi9yqn2fkeiml.3hy0iab( ytlp.f;/ 2.14-m-long organ pipe blf:bi9hf 3 9/lb(0 nim.. npeq5ai;kyt 2yjyat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximapdgzawfse1 g,4)0 91 vdpv(vi tely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate t9fvi 14 gs p0v1,veza(d pwg)dhe frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to a*pj hexsh r)k//k5o8emn *b i(.y /xitdjust two strings, one of which is sounding 440 Hsmyrk*ike./ /o 8x 5htpne/bj h)(i*x z. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if m- 47dc csclz8jiddle 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 (brand X) opera-+x2 h gdpbz+ptes at an unknown frequency. If neither whistle can be heard by humans when played separately, but a s+dph- 2gpb+zx hrill 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 withr3 mhzru4 1o/q a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork.o1r3 hu/mrqz 4 What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hzbw qx;dwbb47+o6r q+.ir9oqt . The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when6;4+ bqwqowx9bor dqr i b+.7t the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try tofn6cgv3yz1 bpn ak37/ play middle C (262 Hz), but on n/ 37fgcz6vank1b3pye is 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 frequency of 441 Hz;r)dtg8+ .ai ok when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded.i+ agrok)8td 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 ax0rt xg9 om-u-part. A person stands 3.00 m from one speaker and 3.50 m from the other. uog09-mx-x r t
(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 Hz, but a piano tuner m/uj ehz*bkx+ qapqp; (t7n-)hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, j*p-hn+q z7t ampu(/ q;b )kexwhat 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 p.*)nafy6v*vj imb9qp1p nk 0 of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assumepm9n yb.k*0pv n1i q)*6v pfja T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginvrh c0 / *p1rxiwshn80e’s siren is 1550 Hz when at rest. What frequency do you dete18rv hic0wns*r/ x0h pct 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 y3odzxbp db61 ;zh 0s5x iq:lz41o/xwaou detect if a fire engine whose siren emits at 1550 Hz moves at a speed o0 shlxozbb:5qw 4x1xa p3i;dd 16z/ozf 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-6z;hg b)6 ; ijjijnlh 7y(cs,,:qvldr Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are thyr: l( sc;jjvl,ih6 zng);7h d,6ji qbey 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 a (mhw45c4h 3zrn uulbehy5;6kt rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. Whath6;4yhu(e l4chk3 b5w 5 mruzn 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 a,/iby qyib + apod+;f3nd receives them returned from an object moving diib 3/b+q+apo,iy;y dfrectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a souxfa) o9;tbg w*k *iqf39k; tpeed of 5 m/s As it flies, the bat emits an ultrasonic sound wavex;3fi9qafuk)g*twtk b9* o o; with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originale;0,uxtqrji ) 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 was hear)xq;ruje,i0t d if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to meax l 7qlqj ege2wt;.y+odkt+bp, 2g9i7sure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is tjdx tqlqpo,; +w l2gyt7bie g+9k2.7 eaken 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 usingz0 s9dai*36ec g*vch y7gj6f u ultrasonic waves 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 sonr 9m n3:e7pdpund of frequency 570 Hz. When the wind velocity is 12 m/s from the north,re:p7mn3p9 nd what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land m13 .e*jx0e,tnt c iqwif 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 iss4hhajz1*dbv- 3d o 7i 310 m/s (a) What is the ad7bos3dahijh* v1 -z4ngle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosi98mdw x p 7c38tqji5pl5(oxi phere of a planet where the speed of sound is only about 35it pw9l8p(i cxm5x5 i o7qd8j3 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Dethre0kk./h qrxy ouby9)wj-, (ermine the shock wave angle kwy kxhrj0y/r9 ob,.h (q- )euit 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 3a+ 4k i4b wixe g-kajjlt:,+v$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a )o iz-.ti qq+gus)d :,q(ylpar: 3qn qplane 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 km. See Fig. 12–3an s,i:t qoi:yr gl+)zqq3pdqu(q ).- 4. 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 20,000ai(vf7-fs2 t,;gehz 4rz ; gdg-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is f,4gvz- tr zs(fi 2;;gda7gehdesigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rangmgz x9w( */rzrf 6z5mj2:asq ee? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer p20jt.*zr0t 4ovn lq wn5oxj rk1:qq3ripe symphony. It consists of many plastic pipes of various lenqzqw:xko4 1 rj0rqo.0*5nj n t32vrtlgths, 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 ffd(0ku rf m)am;9x7+drvru6 from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound d d6rfmuru)rav9 ;fx+m0f7k( level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-jl;yzk4hny;t g7v k:6 dB sound are heard simut;yzy6kkn j47:lvh; gltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dBg u bt+v2djp;6*mknnf/m3j czfe y *-). What is the acoustic power output (W) of the speaker, assuming it radi+k ct*;ej3mpynu/2g *d -b ) zfmfvjn6ates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thn4u2b*a cq; vgtyt /i;e power output drops by 10 dB at 15 kc*t;i; vg42abyqu/ tnHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices od5/ri6q 5e,ef7h wgdi7yp1 ktver 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 effe /5f1dd tg ep6 ,r7yewih75iqkctive radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatn4gc2c g ia7lgc)qi7(gkc.b ,ions systems, 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 tuned to a frequenc-.0 vp9pse r 1y yn9izrzbmm3,y 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 longbxm5 kpx d,55ykq8f .i between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of pd8.5my5xkf b,q5kx i$6.1 \times10^{-4 }$ 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 abovmv a2dm;x*cc + rs9-wfe a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and a ac-9svf mw ;2c+dx*mrgain 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 iuup+: 2g0 crjvs open at one end and also 75 cm long. How much tension should be in the string if it is to pr r+gp20u: jvcuoduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass w-dxwng:c++ ass0hic( zt9 75c/m yyacas observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 5:f -kxseutg v,wo1 53xk5kpk700–1000-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 that the sound level is minimal at a point 0.34 m farther from one so31k- k,se :gfv7tk o5ukxxw5purce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The coniyp7, 6:7dxi +z tc5ipbglg3uductor on the stationary train hears a 3.0-H6ulp7bxi,g7pdtg yz+:ci i 35z beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train 9*nwv2hpk pt9 whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movinp9wn2 h t9vp*kg (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thew7lbam3er* az 7du00h difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goe* dh7wl030a zb7meu ars by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding to4nxhx4d6a pgxw/ok+fk 4 i, 7av78zqngether, produce a beat frequency of 11 Hz. The shorter one is 2.4pkvh4/afg8oaq+nw 6inx4 z 47dx7,k x 0 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as ipr+pf-qnjj;d*f+ p cj :ki6a.t moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identica rj+p-i:jqk afp6pf;d+nj.*cl sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flqy **qsv2t jcgf,am 9(ow in the aorta is normally about 0.32 m/s what beat frequency would yoc(tq q ,j9sy**fga 2vmu expect 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 while r o:)htx ,xmn3the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wn m:xrotx3 h,)ave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pug7z *-xgl 8)9m dp8z4 d8zyxwrhed ue5lses 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 9xz )l5z 7e*- xdezu8h dmg88 4yprwdgone chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to senmkdc8 2q6-wj t8ngui-d 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 8n- qc2du8miwkj g6-tclose to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromisedsfc-vo,76 j zu by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure node z7 c6uov-s,fjs. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, s l+ :yfz (w*f0dpv)w4+kowdaglender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hady:4) *gw+ df0fpw voklw+(az nd. 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 of7e7ij;r pywc me/c-p 9 about 1ew;cprcyip 79e-7 / mj000 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 observer on the ground; ke4 2rda ;hvux0,gat hears the sonic boom 1.5 min after the pl4ar2 tgu he; ;vd,axk0ane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i *wt(u8 yxgbrp72 8rw ,bzq1rws 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