What is the evidence that sound travef6 t+61t j158tz ico:ko mdysels as a wave?

What is the evidence that soun.qjkdh:t/qfv5t s-etw9e w/ ; d is a form of energy?

Children sometimes play with a homemade “telephone” by attahzbrnd+*hih2 wg: tm h5/a8z k*pv(l9ching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). : hgl vhz/5bh8r+h9(damzpn* 2*wt ik 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 freq -6*p)ql3 oi( i1vvybaofwox5uency or waveoifx)- (*piv36v1wylqb 5ao olength to change?

What evidence can you give that the speed of sound in air does not depend fsy36 4b zffxg2, iqa0signifbqf2s,y63xfi zg4a 0ficantly on frequency?

The voice of a person who has inhaled helium sounds very high-7l irtt ru9.9 qtn qso;,f:h/gpitched. Why?

How will the air temperature in a roo6vs bw81-*wrdnfzsr;r . wy9xm affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the izucm+6 +a.rzwfc-b; amplitude of sounds in various frequency ranges.rz6 bczf+m.aw+-uc i; (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as youaop(t j p2 s2o8vzr09/b.ixpn move up the fingerboard toward th2p ztns( o9v 2xorj0pp/8ia b.e bridge?

A noisy truck approakh xattsm1+( xi-(m+2vb /xx5u;i esl ches you from behind a building. Initially you hear it but cannot see it. When it emerg /s(+xubmxt1i ts;xhva52-i + m(ekxles and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whby93781pwo8lfirs tcf (m 2ej ereas beats can be said 8ojel1pi3w2byf c9r(7m s 8tfto be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would to 1v hcx-cm;.fsbpr6oj ln64;he points D and C (where destructive and constructic. 6jon;x hr f-lc6bo1 ;4msvpve interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wip98z* ql 5qd0aa;/ko.vfrdir th 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 reduce the sound levels reaching thql/z.qri5a 9r8*pdfa0; vdkoe ears?

Consider the two waves shown in Fig. 12–31. Each 2xll.3vmh bttby* a((wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the la*l.hbvmtx( ty(32b waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourphem1u t++wa;o8 v8i r :f0qfece and observer move in the same direction, with the sa0u8ofa1; ph8q+e tf:i wv +rmeme velocity? Explain.

If a wind is blowing, will this alter the (kz5f;6dm2mr+m/ntrm b bak 7frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity c(m5/+rratbm7; mz mk26nbdkf hanged?

Figure 12–32 shows various positions of a child in motion on a swing:+)aj1zi y* :c ni7ax6yyaf la. A monitor is blowing a whistln*il ):7:c jaz a+xy61iya yafe in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fo wu h*-b )zp5(f8ezydcr the echo of her shout reflected by a cliff at the far end of t zdybf)ue(5-p 8z *hwche lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just be b7sa +ex22mlelow 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 12–1) and does nota+2e2 xelmbs7 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavkt(kn 1v;5vszlr en4 3elengths 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-q opxm uh:z*x17xoj)9y bkus*nhs9( just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How z1bmx*7(9ohj-nx husu) ox:qk9yp s* 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 2/gx zc*9,lblbx7jtcit makes when striking the water below is heard 3.5 s later. How high is the c9/b j7 l2xczbx,cg l*tliff?    m

  A person, with his ear to the ground, sees a huge stonsi,m0 c/;n.1fa xsz iie strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in theacf 1i0sx . i;n/zm,is 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 pa.asdr zpmr6wh 3+;uj n+3;ddistance by the “5-second rule” for estimating the distancnmu+w ad;+p3s6r;.a hdp z 3jre from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain o7 m)mfc2ql*s6nsi 7 olhc +qa:w2.gvlevel 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 ofh2ccr/ rbauehi11 t /w8,3i nn a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level ofj :u*hcczd1wc+t;)f )p+ zqhj 95 dB when fired simultaneously at a certain place, what will be p:qwcczh; d +j+c)z)1jt*ufhthe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance 8j+hbi74g.q2 u;k 1qgbtx sxbfrom 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 ebi17 .2gjkbhq4;u+q8tb s xxgngine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio o6/bk8zbvut 9;tsw9h* -dethcj95acp gta p12 f 58 dB, whereas for a CD player it is 95 d9ea65btw *vbdk8h tt/t9ca 1 szpp-cj9u h; 2gB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fro lt4rok+h719 /di*m +gqk m*evj7dcabm a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centv4m7/r 9+g tmlidadb c*+k*7 ejkhoq1ered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is j5l6)ckwy4w,p hi ( gs$5 \times10^{ -5} m^2$ (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 modest amplifier B is ro/*ios3)c+fax:k7 hb2x vam1llgd 2 wated at 40 W. (a) Estimate the sound level in decibels you would ex w+ lg17m2/ox hv2cla:)fo* ix3 dkbsapect 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 froz(6 e1 z/*zvi na-nclunt of a loudspeaker on the stanz in(c6alev/1 uz *z-ge.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a di j-zzngf(m0/d fference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sojm-d g0 n(z/fzunds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor-i ;g*s, f3fb7dz w.hco3ohci will the intensity increase? Increase by a factor oi7o,;3 wszcgi* 3bh -.cffhodf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampli(*vpyutp sv 8tfqle ;8o mogwn;,28h+tudes, but one has twice the frequency of the other. What is th ,whu( qptl;o 88gm os+*vt;2pnyev8 fe ratio of their intensities?   

  What would be the sound lc 6dwk50s(+gv(pf5ux x8e mpdxsur6:evel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecule8(( +cpm pu65drxvsk fe0ux5s gx w:d6s 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 t-sa2 ap1gi n p+*vgd/what has a 50-dB sound level? (See Fig. p np 2ga asgw1i/v+-*d12–6.)    dB

What are the lowest and highest frequencies that an ear can det if/rx ac.:wm;jkm1yro8.,jd ect when the sound level is 30 dB? (See F:ryiamf.ox jr8cmkj /d,1;w . ig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What i c mg-d.-lvy6q:aei x7s the ra6emxa-.q cdy lv:ig7 -tio 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 fun*j jul)54 /:xfbmntihdamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stri)mi:bx tjlj/nuh *f 54ng be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thr,crr;dn5 +9f qs f2 ke7wq,vjnee audible overtones if the pipe is je9krvnqw 2ff+rc 7,; s5 ,qdn
(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 from blowing across the top r +x*dnvafxoabwnsp.8x9 z r) ;pw;(,of an empty soda bottle that is 18 cm deep,xan;*8p9owf,.vax( ;+)xdn r z bpswr 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 pipes spanning the ranga- h90e rotev+ftx,d0ur d54ee of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requihex 4fd vdt5ro+,-0t9euer0a red? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a .abrc t co*z3)qx -tor:iw(+i :dxe1sfrequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is finge d)tra:twe 3izsb -+(ic.o*1o xrqc:x red at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long,(i g md)oteq8;x7o bp and is tuned to play E above middle C ieto q ,o) bmp87x(;dg(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 ofjb) okxds5k,c.0rt l( an open organ pipe that emits middle C (262 Hz) when the temperat5d j rb0.,xcstl) kk(oure 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 7 :o(ksjpe0p mat 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 th1 wk4lsz k p::zpo(fm:on ;cd:e hole be tha z ;(:k:oklmfw4os:pdzpcn 1:t must be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but n74 ,fkl1kxqzm8lw9m pi mrn 5,ot at any other frequencies in bki l1, 94ml,qkmx 5 rw78fmnzpetween. (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 ends. It resonates at twr)+dj0oi 7 a-l vn-ujho successive harmonics of frequencies vu) 0 a+-ji-rno 7jldh275 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 ;6c 5h)3x ragkw0pal5n) jcv e$^{\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 or55xbtum m: vtb0 r/amw;(n )wggan pipe at 20 a( g5mw5rtnbv /b: 0wmum x)t;$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsivaz/c*dtj*o1 vzp m)1 zl fx a1pn-6m6de and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) p1zf x a6dv)o/6l-nmmjpza1*cz*1tv 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 tryinnic8 u:i3f +jqk+ 8kd d-wtsf(tbj;k9g to adjust two strings, one of which is sounding 440 +f8in: kjs9 b(-ifk 8qwt3tj+kduc; d Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mi c+g )b6o5 6xjxi.ita-*iqtczk w50pjddle 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 ty (qfe l(wx5n+yl(kg)x- l;u(brand X) operates at an unknown frequency. If neither whisegf5w()qylull(yk+-n tx; x (tle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9;x/:v jols e0o beats/s when sounded with a 35s xolvoj:/ ;e05-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 ldouix 50 : llrw(hz2(qj(u w-Hz. The tension in one string is then decreased by 2.0%. What will be the x: lz5rldj2(iuhq l0(o(-w wubeat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play :3ytttsl8dseg vw3 d64e;cl .middle C (262 Hz), but one is at 5.0°C and tt etyl. w;l:d64v3 edgsc3s8the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,kry+k. s0p wrpat (rrf i,t(46 A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounde(i.rrrtk 6pt a 0p k,4fs(w+ryd 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 jnt q +a..7ymvnlz7 i39jpd(capart. A person stands 3.00 m from one speaker and 3.50 m from thd.3jp7yc. iqa9 jnzn 7l +v(tme other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz 7 s5zss 5vm,u9fqsf0a, 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 th svqfams50ss fz7,95ue 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 2a9c,ek)czw -omqohv v19ko )3.64 m and 2.76 m in air. How many beats per second will ) w9coeok zvqk3v1 hm9,-) coabe heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of ap0:oe6kz ynvc4- s. z.j 9p;sdfi ;tzr certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you m ydkrofz9ps4z:j t 0v6n-;iesc.p;z .ove 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 :3ua kj2wl lx1v5jmcf 6w5 0dmyou detect if a fire engine whose siren emits at 1550 Hz moves at a spe kml2w1mwxua05 d53j :6jv cfled of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source33syyp f9h;bn i-o0up is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the tw ysh;3n-0y 9ibpuo3fpo 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 equisp tlkxx1nnng.*(8do se :775cjs m6jpped with the same single frequency horn. When one is at 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. What is the frequency thmn.o5 t 7:nexx8g*dssjs (6ck7plj1ne horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sxz- t 7.zhl1oo41ylzw ound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is thly h4 t.ooxz11zl 7w-ze received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a kokiv3,1 n-w8l,zjv swall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected waveznk, 1,vl3jk-i owsv8?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wa1)4 j;,o5ppz.o4qpfhhi l+ vud1ci qgs 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 frequeplohzd41)v.o;q 4u,j i c p+fig ph15qncy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultras:klp w (fm (wpcs(ox (bkcsg7).,ty3uound 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 artek((w.y( psu7 (:cp m3cftk),gbol sxwries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ul m+;88l( a,jisginyu etrasonic 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 emsqm4e f: k+q:mits sound of frequency 570 Hz. When the wind velocity is 12 m/s from the q q4k: :sf+mmenorth, 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 movinbmkuqp wy0v u+/ okt1- 8wh6jca,j,7zg 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 t++3mvq1 .nx,aga 1 yaowuf .4ebg. f3bx)df enhe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mafv. .denube . mn+x yo,g3 4f+ 3)1wabaxq1gfotion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of uq vm-lq8mv 2k;7 yi.vsound is only about 35 m/s qum7.2qlvy ;i -kvm8v
(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 th:a0jsr 9,li f v(jbokv q**qnzz,.l (fe ocean. Determine the shock wave angle ii( qvrqfs.0nf(,zl*a lokvb,j :z*9jt 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 lq;e:f w*,r9 slelm8bujr:8) n sqlj($/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a planey b; m: gzj dc.:la3ktts3o74q exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the pl ;ayg.7:bcl sd:mto4q33tj kzane has traveled a horizontal 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 20,0g8 xu/c:hlgp gv+xajj, z;-9elti7 r300-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200jug ,- zrxh:t3 alpx/j 78eg;i9glc+v m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hum uarmfh;k*, q/an audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a rw.m4 d yuh( uze+7+llsewer pipe symphony. It consists of many plastic pipes of various lengths, l4uh.eu7ml +r( yz+ wdwhich 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 th4:qn,ut.f ) dhu r8qrji 4d pvsk;f;p.e threshold of human hearing (0 dB). What will be the sound level of 100h ru8 dvip qqfjrndk. sup,ft)4:;.4;0 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound 8upqqdt+4h+cq 5q (z:vocuzu q5r**iare heard simultanitv 5+ c5*q(8qh uqq*cz:+ uzupd4rqoeously?    dB

  The sound level 12.0 m from a loudspeaker, plvmf.utq-z :s*c bb vg qd7aj3zr; ,e *(d3tn-maced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directbfqdq * - bgt-mn7sv*um(dc j:3ae3;r .zt,vzions?    W

  A stereo amplifier is rated at 150 W output at 1yyvz wx n 9z)8kx7er-pj;n/i *000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in /z8xivne*7w yz 9 jrpxk);y-nwatts at 15 kHz?    dB

  Workers around jet aircraft typically wear7 ti8 l8:2:qwonkw b2vk cqn0t 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 i 28b:7kq2 c: ntlnq8wvwto0 kby an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systemso6a z-j -*gm wu4ango6, 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 frequen-h x1 ( w,wot6xy 5dgs;6gmzwzcy 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 cmolux/ 6479 nvy82mn 3ymh5k nqsh r:,cma sfh0 long between fixed points with a fundamental frequency of 440 Hz and a mass0ucn6 asy xhnok m:9r2 4lh 8m/5v,7y3 nqhsfm 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 abvcl pe:d.1hz. q xw/k/ove a vertical open tube filled with water (Fig. 12–35). The water level is allohzd /p:1/xkv q..ecw lwed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of 59 wx7ttrw 0njbo2.d e1yvt;u mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance uxttdt0.v51r;on j2 y9wbew7 (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to rest. p:++,gf xahlu ezpv2 -wj(vonate 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 500–1000-Hz range coming fro9t. jr(z .qb+,( z4mpsuttwcmm 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 source than the other. What is thtr (. tps.jzmb,m( ztuc+9q4 we frequency of the sound?   Hz

  Two trains emit 424-Hz wbj,mie9k6.) j laqtg/l/ yy4 khistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approach,llk/jky)9q/t 4 m j6ya.ebig es. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hrzga48nya/ dnhp2m3 7 ;w6kmkz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (g3 k8ayn;7mkn m6zphr dw4/a2assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to t te14pd5y(yy ayz1t2 khe difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a yp5(t21edykt1y4z ya 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 toge(vn+ 4 vs-ylube5m*+ umlbq9ether, produce a beat frequency of 11 Hz. The sho- * nvm(b bel4+l5uy9s+euqv mrter one 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 ausl;j xlu 50reg11:. gehix4 s 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 be.xjrls0xhg;eu l s 4:1eiu51g tween the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood floz* 6x11zalgon w in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves werezo *1xn6az 1gl 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 is flying toward the x:yje2o3 j gz: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 tj2 :o 3y:ejzxghat wave reflects off the moth?    kHz

  A bat emits a series of high frequn0zk jl* c+h*t8m949 vahvtz qency 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 m0k* ach*t9zmz4lhtn vvj89+ q oth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12kc*o) 97yzntm–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhok9oc*nz7yt)m rn 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 canocpbd2eq ), l5 ut54wn be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m l 2 twoenb, u4c5lp)dq5ong, 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, slender aluminv 3j .06kgu4+2sqgu vb8o hploum rod held in the hand nearqp 3kbuhjo6 4+v.u8v0 2glsog 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 hg ks0 2s(x)gxs t0ew5rearing for the human ear at a frequency of about 1000 Hz2e5 g)tx0rs s (wsk0xg 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 ;i(9f2iv(hbnc p n2xd ground hears the sonic boom 1.5 min after the pla 2cip2 ;div(xhfb9n(n ne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 t6y1yq5n:mv l$^{\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