What is the evidence that soundzv2h7p- qar0so a ).vv travels as a wave?

What is the evidence 8a:0 khaj1zs nwkh:x;s/ rb z+that sound is a form of energy?

Children sometimes play with a homemade “telephone” by a ybmp4)fcoxd,go; /s.mte)s: ttaching a string to the bottoms oo/sto ) : b dmxp;,ce.yfs)m4gf two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency om;ys 6,-c+ rj ols-rf y qtf:2m,o1telr wavelength to chofemr2f-c+ t1qyo: ,s llr-ym 6j; st,ange?

What evidence can you give that the speed of sound kd/sak+vx/6eeyf ou :r a8j2ky +a,-lin air does not depend signif62+// kek 8 :fay x j-syeldak+ra,vouicantly on frequency?

The voice of a person who has inhaled helium sounds very hif)wl8la1s7-/zku gsx 4ms.co 9:b l+ukw- mt vgh-pitched. Why?

How will the air temperature in a room affect the pitch 8r5b5pma61g v iql57 zuvat-zof organ pipes?

Explain how a tube might be used as a filter to reduce the g85/zi+ykt-u bxiw )x p,ry9mamplitude of sounds in various frequency ranges. (An example is a car muffle98 g,ikmy+wiby) -ux5 p /xtrzr.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move gv6 /rst 6f+vwd,uep -up the fingerboard towatwe 6f v/6suv-d,rp+grd the bridge?

A noisy truck approaches you from behind a building. Initigg8eg *.qkrz 9ally 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. 8.*ggg9kzq erExplain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inte*izo(httlkb f)o ig 3pdz u5;9v,1-aqrference in space,” whereas beats can be said to be due to “interference in f3qv*tdp9thkz-,1 ;o5 a ugbl( zoii)time.” Explain.

In Fig. 12–16, if the frequency of the spea ewffpl2.yn yk*ik2j r*1u:u4kers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer toget:u*4 fk*pw k2jyryl f1i 2.enuher?

Traditional methods of protecting the+v/..eo jzo hy hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise r+..hyo vezoj/ educe the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–dgrt cre.hebx;be i4;jgw;3 p0k ,6 v:31. Each wave can be thought of as a superposi g0e :dv bj.4ete b;r3;iwk rp6cx,;hgtion of two sound 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 and observer mot5;+s6an+/fl 4j ghsx) 7qs sh7bqt hxve in the same direction, with the same velocity? E7sq n btlfg 4j/s qts+x+ 6ha;7h)x5shxplain.

If a wind is blowing, will this alter the frequency of the soundi8d+ xgyz/ ;w.-czrhq heard by a person at reshicgxrz/ z +;d y-.wq8t with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of atu;7pwv+;pw3h l.w i-she(we child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. ehe(wpsu+;tp. w ;3l-wviw 7hAt which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout pyd i)zfmw ,1ar e;9z*reflected by a cliff at the far ezwa*r9d)fy;p mie1, znd 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 sid, qre,b1id vs(0moz7i e of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12– 7dim e,sibzov,1r (q01) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng5rwmk ddpg( b: 44e4zgths 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 foggy day. W;6u s ca+cxywra:n ;r1ithout 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 f1n ;:rr+cs y;ua6c xawish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes who5x2jxu-g 1 ioyjgk7:en striking the water below is heard 3.5 s later. How high i 1oj:ogyk2j5x-gxui7 s the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the con8l5 y6r.xfohj crete 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 occur? See Ta5rlfox.68 hyj ble 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rulxr rsdv bf5c9y8qzy661o;/tve” for estimating the distance from a lightning strike6y5/c od tzv1r9 bfyr;6sq 8xv if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paiu6 ht11 ugrcp dn-tygm6:5xu(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 ow+( +lpawrdj 2f,uhm6 f a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pf.x-by fi1k*x;: w gt5(nghsyroduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dgb;*.- yixnwxh tyk:f(5s1fg B’s.]    dB

  A person standing a certain distance from an airplane with four equall)5,a kuka.zo fy 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 intensities, not dB’of).azkk 5a, us.]    dB

  A cassette player is said to have a signal-to-noise ratioa 2gc2 j7 a-grg decg698:l+vkc+niwu of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intekuc2 +g8c7+nal :6jg gg w2- arvecdi9nsities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pervhpzt1:dj0 fejd7w7 ++q9 jdl0rpw ,nson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uq,h d7+ p jdt 007 +vf:dnzwp1ejljwr9niformly 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 str- wifhdhmtr-5y0ocxz12+m 2 vy h/tl 8ikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated ik6 0 lwe(nce)f-j hy5at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound levely6i )felc e(50kjhw-n in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of a;a 7h6t74 rgvq gvv)0uyf+zge loudspeaker on the stage. vg4azg7f+vtqh;gvury0 e7)6
(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 2.0 dB.jb m/jkh3uf2d6pb5 cg, y 2.ig What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–dbf.h,c5 2jijgy /p6um3 gk2b9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor willf 5qqa. 6z0kxgt.an.u the intensity incre6qqgfn atz . .x5ua0.kase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equa3h2x btq,mb:*t 7n9equkxh 1vl displacement amplitudes, but one has twice the frequency of the other7:vqh21, b* 9ux te m3xhbtkqn. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that co0x)xh).y k on9pwj*rerresponds to a displacement amplitude of vibratingwox*9 )px .reknj0 yh) 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 tone th 4,c )v)m qpzmx4qqr,jat has a 50-dB sound level? (See vmq c) 4,rq,jq)xpm 4zFig. 12–6.)    dB

What are the lowest and highest fcea(fq: jc6p a5 j/b2lzge:(v requencies that an ear can detect when the sound lec(jpf z: aj qgblae5:c/v6 (2evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the tbf:v:p2 m0on; rhwo9ratio of highest to lowest intensity atw;hf9 n:o tm2 0v:orbp
(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 441s+6 (vr wcilo8l rno:0 Hz. The length of the vibrating portion is 32 cm, and it halo+ wn v:i16so lcrr8(s 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 first three audyh7ua( 9 luav(fs3e3qible overtones i9l3ueaqs7uh a yv 3((ff 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 f ywd 0t)yv.mj*8wq7u oz)nsb2rom blowing across the top of an empty soda.wy8q)mb7 )2dsz w*vujy0t on 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 fsq2lz:xv66kaa -2vborgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be thea6q6xv a2lv:f 2skzb- 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 it 9u +cu663xct mjss9;kfor: bms third harmonic. What will be its fundamental frequency if it is fi6+9 9s rjufomk m3: ;6cxtusbcngered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is am 8jw nxw)2ti y0/j0btuned to play E above middle Cxiw ja 0/2ntb 0)wyjm8 (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 pipe that emiv)hc ))1u 4iqmp(u0osadc6i xts middle C (262 Hz) when the temperature is 2c 0(1 xdq)u)4im) vaschoiup61 $^{\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 2.2fu*uaadojmho3 5k$^{\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 shoulhn wjfb32ro16g w ho7*d the hole be that hr76h1fn *ojb3gw 2womust 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, anddrive :15f7kwz3qo- cbmp6 (k 616 Hz, but not at any other frequencies in betwe-65 7dkq:3fr1omwzi(k ecbvp en. (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 0e/bn vc -i-ziat both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whai-0 nvz-i ec/bt 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 (zuqwb,u f.j/yk0 4:nyz4n ou$^{\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-long orga phcj1eoa6.s8 n pipe aos1pa6. 8cjh et 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apprr)trmt/ml q c-6*tfe vrg )s(7oximately 2.5 cm long. It is open to the outside and is closed at the othetrmr6gmc*frt) (sl/ e ) v-qt7r 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 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 adjust two strings, o+lzw./hu i1 pg3;ky 58hfwu zone of which is sounding 440 Hz. How far off in frequency 3 5whglhu1yo8/fkzi .zw p+;uis the other string? ±    Hz

  What is the beat frequency bmw0 nc .ab/tzb (-ac3if 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 (brand X) operates b/r 1jn lrbb-h wg*7hqlgcw;a;a0 e)j)0eeb3at an unknown frequency. If neither whistle can be heard by humans when played separaawa;he h) 1b3-bjgb l) ne;7 jq0rc0* /gewbrltely, 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 beats5 ma up;ncvn*23u,dre/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a un,pcdrvm;aun5 3 *2e355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings adw09.nkg6n gwre tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when.ng9ng6 0wd wk the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eaij/kt7019/tp a*w n6z e ylioach try to play middle C (262 Hz), but one isztawy 9*i/eoil6 10pt ajn/ k7 at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bvvyph i g;a+q/x+h) :o 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)v/x;ih: oha++vgy pq are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from onmta7ih ib,:*c * vg q1e05nelve speaker and 3.50 m from the o: im1n5 ev g,0iqtv*albh*ec 7ther.
(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 hear g;fkcxf rv937kiy 1t:qjo )r7d;d8i os three beats evej;tkvxrod 7 i813fo idc )gy;k7rfq9:ry 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many bejrnb5:b(b,ow4 9s/far yh gv 8ats per second byfb sv/hrb5r4a w,jg(o:9n 8will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire *6iw tu zi.bs*vdo+y*engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with *btdiisv *.z+o*uwy 6a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire eo a4 i/mu5;lefngine whose siren emits at 1550 Hz moves at a speed oli /fu5; aem4of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz d mnmbp3/vcj j2;dtj/60d9h ysource is moving toward you at 15 m/s versus you ;/md3hjdj tmcb v n690jd/2yp 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 s/dw /p io1bw1iingle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest wbiw1p do//1i hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives themzkhl l08ejl36 retu0 jel 6l8lhk3zrned from 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 speed of 5 m/s Asv)ab i+0aax ud:4e/ oi it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear oiu vx +:4ie )b0/daaain the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentek8y, ew;f4y8;9juuzblj2re s, 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 statione 4, juyf9 e8w2el;ybjuz;8 rk. 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 ultra+l/u.7dn3f(tb ;so8qxk) gfgaa 1ykjsound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly a83aslnj gabkt fqox gd;1/k+.y( )u7fway from the sound source?   Hz

  The Doppler effect using ultrasont( bsp8xmm1,qmaoj q:x.c 33lic 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 sound of frequency 570 Hz. When the x .ci0csgb s0)wind velocity is 12 m/s from the north, what frequency will observers hear who are located, asb .icsx)c 0g0t 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 l doh3t8 t5,hzgand 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 Machwm x i*/zl bflpd*(10l 2.3 where the speed of sound is 310 m/s (a) What is the angle the wdm*i(p0f *z1xl/bllshock 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 abem- lyt o6 61s0w3wy5ton9c speed of sound is only about 35 m/s to 60waocy t3m9 e-bwl51 nsy6
(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. De w:65l*lo1st4xk dmidtermine the shock wave angle it produces :sl *dowk1 6xli54m dt
(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 rl3 3r8l)u ggm$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and+t x :(jf5bb3jl3z xz.mu d*ab 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 mj .3b3* la5(x dbtubzj+:f zxhorizontal 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-Hz sound pulses dowk q0z5;v )5)) uk;yjfo hghw8 dauss4znward from the bottom of vks j))z;4s hoz55;fqwduk8u ya)g0hthe boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the huuob w h+to)g51man audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a fuo5,ict :r9 n87 defydisplay called a sewer pipe symphony. It consists of many plastic pipes of variou ,c7yi:unofdtf985r es 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 to the threshold v. plq(k3zu 7r(njq a*wj7g h1of human hearing (0 dB). What will be z wnp(q1.vjl 7(jg*7ka3hr quthe sound level of 1000 such mosquitoes?    dB

  What is the resultant swg +1datd3zg 8ound level when an 82-dB sound and an 87-dB sound are heard simu3t+gwd dga1 z8ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 d81n)emnmn 9.h(rxha dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?mnha x 98)h1 .enrnd(m    W

  A stereo amplifier is rated at 150 W outputm4+r 9*xi+3zlizo/8rha hs c j at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outpum+ 9+8 3hlz ziohrij/4xac*rst in watts at 15 kHz?    dB

  Workers around jet aircraftkmf + n1rlfb9s8n24al typically 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 jl4rsbf 9 + a12nnflmk8et airplane engine?    W

  In audio and communications systems, the m g:urh/oujy8b46.gxz3wjq 7 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 frequencoqgne08hm 4)j 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 viol5 e7 9l)hwpa;z3 bakbmin is 32 cm long between fixed points with a fundamental frequency of 440 Hz ea;z 75k)b bl9hwpam3and 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 aeju 3.e bltdzr-6rwqvu859 c 5bove 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 td8r l6u vbqjwe59cet. z5u3r-ube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that i 5i4y)e /demzbeeu//5w pxlp8s open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the thieem 45byuee w //8d5xpz)l/iprd harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as onetx6e 659 pqo scnsq-z0 full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Thet6rb fw;b-l+ m 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 fa6tbm;f -+lrbwrther 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 conductor on the 2s h my9v+nbt 6,wgfr9stationary train hears a 3.0-Hz beat freqr2m99bvg f n+ws,hy t6uency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. dh8gp,e*:rrjbyfu/- 9 oedv* After it passes you, its frequency is measured as 486 Hz. How fast wd,bfe8 v-od9grj y/*hpr *:u eas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeninxz e7hm6d jj8*g to the difference in pitch of the engine noise between approaching and receding ca687 d*jxzehjm rs. 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 z *wu70 0,t+yt0 fq) kjnbxvwvof 11 Hz. The shorter one is 2.40 m l0+v70y)nxv wwt qjbz,tu*0k f ong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pi.-b6rr 7+aa9qastzj ast 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 fr9ts+76zri -b.aqa aj ront 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 fpguj+ /koq 5:+zb1 a b2yevgz1low in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound ku +oeb1+gp2vg51j zz b :/yqawaves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth 9v t7 (o*mibps0g+dd zn (.ijris flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off tbrm+s*i( d t dv.iznp9(gj70ohe moth?    kHz

  A bat emits a series of high frequency sound pulses as it approacoj zx,,vj 58oshes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far awayxojs jz5v ,o8, can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once 1,zl,4qczhrd71su aq 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 dz 4dlsu,7q1hz,a1rc q eep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presetf1 5 y/uy yy kdjr/kkr+;+4qnnce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 5yunrq+4dk r+ kj;/ f yt/kyy14.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender 8.ptbof)q ewu5:: lcx6u4uqh aluminum rod54lf xe8 uu:)w o: bqc6thpqu. 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, 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 hear( vx)n5zzv: qxing for the human ear at a frequency of about 1000( )x:vzxn 5zqv 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 m 7np x 1u l0hzg*uj7magh15i1ground hears the sonic boom 1.5 min after the pla hmzx p7i05a*g1nh 1jgluum71 ne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iq:v zmjl4:v )ks 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