What is the evidence that sound travels p)0mm8ty of ztj)uw;64wjpa x) 2ci a5as a wave?

What is the evidence that sound is b -ez cj9x;nd9xu:r /nj (sht:a form of energy?

Children sometimes play with a homemaf0wz*c+j)zhjk al8 -lo5:s l wde “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, zllh:5alowzf0kwj8 * +- cjs )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 frm). erei m7qxt;m/kj6om air into water, do you expect the frequency or wavelength to chae7krmq /xe j;6)m.it mnge?

What evidence can you give that tzrel k0 8w0(ea,sak3phe speed of sound in air does not depend signif(k3 przsk08 l a0ea,weicantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Wh rm8z+nrbu9 elay o9m,f3; fa7y?

How will the air temperature in a room affect the piv iwy)au(nrnm,+g7.x tch of organ pipes?

Explain how a tube might be used as a filt7hx 5tgps ev b)h*6l0aqu0-h,hpzqg5er to reduce the amplitude of sounds in various frequency ranges. (An example is a 5lu0v-7z65qghh )xepgq b*,s at0 hphcar muffler.)

Why are the frets on a guitar (Fig. bpq 5m:bnn:9 al cfa q*uqszdf8654d012–30) spaced closer together as you move up the fin5f0cdpsa :q bma8:qbq z49l5undnf 6*gerboard toward the bridge?

A noisy truck approaches you xr/,k1j9mt gdh6qrkv9x cx 49qlhw2 (from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Secth k1 rt/9qhx9xkwg46r l,92 xjc qmvd(ion 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherjc zk y4aumbsgv/f- ;5z8f2v se:1qq+eas beats can be said to be due to “interference in time.”b;8q+a qck ejzf 1sgmvz25-4: fsv /yu Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points D/m4j9m5 4cut:foj xpg and C (where destructive and c44c9ot5 xg mjjmf/p: uonstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work inx4,tjwvbff(6) kb9q y 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 electrob qk( wfbj9y4x6tv)f,nically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can bi*(8 hkrg2gqle thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In wh(h qk 82gri*glich of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if t3y9l o*qk u(w 8mpqg wp 8pwsbnf2e;5*he source and observer move in the same direction, with the same vp 2uq; s*5fwbq3e (ymo gpwkw8 8p*n9lelocity? Explain.

If a wind is blowing, will this alter the frevo5 9jfkbzt6i53i6 zq quency of the sound heard by a person at rest with respect to the sourc vkztq i6 ji53o69f5bze? Is the wavelength or velocity changed?

Figure 12–32 shows variousyomeq jn-u2ls,t9(hcfx /gly2* jv44 positions 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 c y(x2g jeq h4c-*lo9,yvf slu/n4 mtj2hild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengmuebi4v:v uqp1m 3 r/1th 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 lee11/vu:iv3um rqb p m4ngth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hk1) tl4p(rf upis ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s latrul)tfk pp41 (er. 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 wavgt,1p twv65ci gcqd96 elengths 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 ilqr d0 i-q7+x;l6 lt,me.dtw2t qgj5us drifting just above a school of tuna on a foggy day. Without warning, an engine backf5 -;+6ql,didjll7tg e2 .tqx wqrm0tuire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Thdl5fs0f4i-7ug3z pz ze splash it makes when striking the water below is heard 3.5 s later. How high 4sfzfzpduli7-5 03gz is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike mp 9d/5fazva8the concrete pavement. A moment later twoa9fm 5d/z8apv 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 mile of distance by 1a x ifxgo1(v*the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30 *af1 1x (ixvgo$^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lebi9uvknc7ku wtowh8x *6 815cvel 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 leve+vx z 20n3 dw:iz,retxl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producae g(v rso;va /xd73-ve a sound level of 95 dB when fired simultaneously at a certain place, what will be the soundaav/ ;7 v svgox(3r-ed level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance fro fh 8ry/t 597hhn;jtls5g,crk m 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 capttn,fk5j9lc/r 5h8 hs hr7y;g tain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for ;7p+p/dplh ihrkw 3o+ a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for ea+pl r;wikpop+h3h/d 7ch device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of 59m+x s a)0l4spfogamx1lt,jsound from a person speaking in normal conversation. Us+a1)gxft 40opmljs9xls,am 5 e Table 12–2. 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 whoseg 3 n,dpt2m um6zor4hc(i) oj- area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more (5 vl1w8vuib;h 02l6cglwk54n q aaqg modest amplifier B is rated at 40 W. (a) Esq40a 2k6l gl wq5wa8v5;gbu1 vil(cnhtimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 ddh)0vhjz:7u.iw, u hfvi 0 x)dB when placed 2.8 m in front of a loudspeaker on the stagew)uihvhj0dd0h ) ,7:uxiz.f v .
(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 2.85dfgalv m+b) 0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this 8gmf+5b d la)vamount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave ifwa67iz;qqkia;x 1ajk .t15js tripled, (a) by what factor will the intensity increase? Increase by a factor z t f.ikw;;jqaiq65 ak7j a1x1of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displa dw)2qjhpex3a3)t0f acement amplitudes, but one has twice the frequency of the other. What is the ra3q ) 3 fataew0pdj)hx2tio of their intensities?   

  What would be the sound level (in (1i3v+b qeus i05c;hzazd.rv dB) of a sound wave in air that corresponds to a disp 3z(51qi+ 0vhcsd uebzr.ia; vlacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as louib fno9ife 7/;.s- otid as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6/f.s ; oo9-fb inii7et.)    dB

What are the lowest and highest frequencies that an ear n kpv47 x2v)dz4pbi/ qcan detect when the sound level is 30 dB? (Sep 42zp7nq) xb4vd ivk/e Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is t.+h () z7iqoaxri*j mju;h;pdhe rati7.ij pqj*)u m+;ro;z( hahidx o of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengtk1ymkf ):ryv ndr) t *k:ux38eh of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the sk13u))y mk*8:k v tn:f rrdxeytring be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first hkmbj :owwizt:)j m/b:p22t 7nm 7sr) three audible overtones if the p7njji t272rwbhomz:m/w kt m)pb:s ):ipe 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 fr9wo m6fyw b:;vequency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed io w9wbm vy6f;:t 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 orytl584qu lr4 1z;jhbxnjluu)0c *5 gfgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? 8uq t rf5b4zl*14njygllc5u x)j0;hu$L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thiit968bkmc h )z ajy1(ljay3r2rd harmonic. What will be its fundamenta )l(3tjy brma 2 y6ajhck9iz81l frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunop+qpn 01bp 9ped to play E above middle C bp+9 onp1p0q p(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 ley+gcq-7 i3 55tf6szhtebz8v9;dq hy rngth of an open organ pipe that emits middle C (262 Hz) when t6q9q 5-c7zty;rs5 tbh g 8iey d3hf+vzhe temperature 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 at 2n8u v 1b1mbj6e0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exam56rd o76xjr kwdynqr z8:g0 y+ple 12–10 should the hole be that mu6y5oygqj0dzn+rr7k dr 8wx6 :st 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 ca 3ef-w.) 1a 9b rhj(6cjokpslcn resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is k ar) eh.j-psc6bj (lf3cwo19an 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 ) 5mhi7 bious*c8c) jr ul4k:iopen at both ends. It resonates at two successive harmonics of frequencies 275isi) 7 )uc :h 54l8bm*iockjru Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 jot pec 3zy:4 sf8,d9r$^{\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 ouol bi)trgl;)s4 m47grgan pi7urt;b m )g4 g4ll)soipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximsyvj b) g8iiz90rsshdt 8tajlmu7 2)2rx1k1 9ately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the grap)yzjji xgs7t29md1vhril a rsks)09b 1288 u th of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tt pin fsn3q;pd4j :1a2rying to adjust two strings, one of which ; n2314q:jftsppidna is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if midh. c*flbu)i8z)9ee iz4 .kiyjx1u7 addle 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 a15kbbs )d*oest 23.5 kHz, 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, estimate the )b1koss* bd5 eoperating frequency of brand X.    kHz

  A guitar string produces 4 beathmcgs 73s1waq7;(y.a fx 9uvgs/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning. ys(s faac1 ;u3xmvgwh g.97q 7   Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension i.u taqu8 v wtq5.d)uc,g*box+n one string is then decreased by 2.0%. What will be the beat f) tu..gdb5o + uvau qqctw*x8,requency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if twos5nxh.b :vbtv ;,k5tert0 1 lp identical flutes each try to play middle C (10ebp;vlt:tkn5, 5 r. xthbvs262 Hz), but one 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 .7n8 rptq:c+a lp.pj9-tp qlyof 441 Hz; when A and B are sounded together, a beat fq acnyrj pp7.pt :+t.8p9-lql requency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A persoe;dy2 c* ogeab1 z5zx(n stands 3.00 m from one speaker and 3.50 m frdg; b(a1z c2*5xyeeozom the 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 suppihq;ijez, p8e2z s7 h-osed to 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 must be the frequency of the other i -2jezps 7h,zeh 8iq;?   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 (ybz f:g,)ezzhixzzuky -lo+ j1.+c(wavelengths 2.64 m and 2.76 m in air. How many beats per secobioj: z ) kz-+gfy.zx(ucez1 +y(hzl, nd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15 /, zge1u5 *dd5l1 pdy4lilyd0 e(xdpn50 Hz when at rest. What frequency do you d ll dpz1dd40d n *g1dyep5l,/x(5uiey etect 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,:8efwa w+ns3 xnnmb3w9 prp(. What frequency do you detect if a fire engine whose siren :3ab8p pn9 ,+n fwmxwn3se(rwemits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mjq/v2 e cljox5xnq zf; cn51;3oving toward you at 15 m/s versus you moving toward it at 15 m/s Arnc jj/f n;q2x 1c;oevlz 5x5q3e 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 single frequency horn. When one is abb:rwzz / 3fqj9m, ahsr;b 98wt rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hf9zq;z wa39b j:8r,bwshbr / mz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends oky 6 yf9y7h+veut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s Wha7h+yy 9eky6v ft is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, thecp ;km4d5+ dts55)cx(c huhih bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear +h 5ms k(chd45tchcu5;ix) pd in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plat 2 v/resgxomp1.b1f .yed on a moving flat train car at a frequency of 75 Hz, 2. epb/1xm1otv.sgfr and a second identical tuba played the same tone while at rest in the railway station. 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 ultrasound waves to measure blood-flxqpea s0tajvz;/--ko q50do4a 1 fa9pow speeds. Suppose the devfv1o4stk 0;ap0axj-dqzo pe9- 5/ aqaice 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 away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofr m8pw*qh;2vc 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 ajq 9x5b0f8dn Hz. When the wind velocity is 12 m/s from the no0adb 9q8jxf5 nrth, 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 objectijv+;mqn (+l u moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sous;+sk.jz yl3 jnd is 310 m/s (a) What is the angle the shock wave m;y j lsz+.ksj3akes 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 thinsg:ye mb ,7bm, atmosphere of a planet where the speed of sound is only about :gmb7mye s, ,b35 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. Determine the szrov9e 2 aw+ j),shsq-hock wave angle it producers o9ha-j,) v2wq+esz s
(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 :jkftfona b2fe:+ m)v 7 9ow8j$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhew iitgh3lb23 5cmu:4r n22gvta 9h8 vfad and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. w 2gl4ahhi58 rtv n23c u:g9bti32vfmDetermine
(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-Hhqo:,r fx.9 zkx+j0eqz sound pulses downward from the bottom of the boat, azxq0o,9re q: +kj x.hfnd 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 human audible range23d l.+j;ppvwlbmh( w? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sbyt itag o-2(+ewer pipe symphony. It consists of many plastic pipes of various lengths, which are open ont( i+t2 gboa-y 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 sola ibbf(js) 04und close to the threshold of human hearing (0 dB). What will be the sound 0fs)(bai4 jlblevel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB m ;8gkavx shti g/sj79m3+sb 7sound and an 87-dB sound are hea i;3tjs+xsm97g8gv s/mkab7h rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wha5a0 aksozxja ,7 )e.yat is the acoustic poweky07aa eaozs.5)a,xj r output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops si ako*m7efc3/a1bx;v v x*1eby 10 dB at 15 kHz. What is the power oumocx aex3e7vks*1 /i af v;*1btput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over ovhxuu23o/y9rmu3 m2 their ears. Assumeh/uu9mmv u x332o2 ryo 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 airplane engine?    W

  In audio and communicac+ lh47u p6tzbtions 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 frequency(+t,c d9 wd9dr(jyft vi 9zk3j )dtct;4hiix 7 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 with a fundamentd36ryun)qq:v47foavu w/ 9 ycal frequency of 44 u4 9)ydw/q3rfqcu ya v6vn7o:0 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 vi9)epj(b1ibya bration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, iey1bj9 ap)(bthe air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is neari39 ,wg6d q6cd)bsmoup5d(kn7 l4a ac a tube that is open at one end and also 75 cm long. How much tension should be in thes69lbckwnu63a)d5 7 o gdc,4di(pm a q string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to re8 )ntvk,/s zfxsonate 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 p1m v;loino:e- w+r(knu7e8e* *lbm- pzqy;a500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two source7*k i-upl1y(q+lb;e ; aepmznr :wnov8 -m*eos. 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 source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductbow7mo,jc4o gt 8),b-* mk fibor on the stationary train hears a 3.0-Hz beat frequency whekm7omfitbbj 8, o*oc-)4b wg,n 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. cnf4z7 s )rjqktc- 0w;After it passes you, its fre;)ckw4rqz j 7nfcs0t-quency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estima qtmnpt)b4*+mx kc/ d9te the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certainbtdtkm49q+c*x m p/)n 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, so6* m)a7j gyriuunding together, produce a beat frequency of 11 Hz. The shorter one m7i*y6r ja)gu is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a+7f;6qi. dio nm xjszmq* u 2/nqy1zg1 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 hears the speakers after they have passe*dzq/7fm.u nqg msx2+qzi n y;6 ij1o1d him, at C?

  If the velocity of blood flow in the aorta is normally about 0.pg8rzkvgcp898 9nm8:l6 cgof32 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 cells? Assume that the waven989 mv6grfogp8g8 :kcp 8 zlcs travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flyin1uch4.rvc3g wih;- cag 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 o1-4ih.3 ;grccuhcvawff the moth?    kHz

  A bat emits a series of hi9boyqs *ij+t1gh 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 nsbqy+1oi t* 9jext chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send s nm 3 snml0pbr.-0 2fo2aqsqs1ignals 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 r02q.lss-ma pnom n3q b2 1fs0flat) 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 c vau 6vfnd4u;el/4fp jtz/. -uan be compromised by the presence of standing waves, which can caus4nt/z6;d/. vae 4fup -ljufv ue 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,” involves a long,u2a1-ugj3y nk slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a littl1ua jk-n2y u3ge 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 tedh:9o/e yxy) hreshold of hearing for the human ear at a frequency of about 1000 Heehy x:)oy 9d/z is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An ob94whw4c8d y 3mfnq q8bserver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude?dn4cyfwhq m8q 4398bw    $ \times10^{4 }$ m

  The wake of a speedboz e st5n+3jh7;g bp nyo*4yj0hat is 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