What is the evidence that sound travelsm h*;v/bc i ztt+-cps- as a wave?

What is the evidence that sound is a form of en j+9m)0e7zyh c(u sceuergy?

Children sometimes play with a homemade “telephone” by attaching a st nymg/ /x9qtncds9(ax1 an6,r*ey4vu4t sj1fring to the bottoms of two paper cups. When they jr9s mvtx e(xyasn4g/utf/, c1n9qa61*d4n 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 freqpdbdy2f(* uas ew9-vbh n 8ae6 0f:;iy /sk0bquency or wavhu(iv6:2bq fadwn;k* -ep98 s0y sb/a d0feyb elength to change?

What evidence can you give that the speed of sound in air does s c;wr7(t.kpa nwcf;;not depend signifina;fp rk c7 .wc;t;w(scantly on frequency?

The voice of a person who has inhaled helium sounds very-:u e2 8zx4j,ykdnbnr high-pitched. Why?

How will the air temperze xef ankb:u2q6p+uc*-* l j(ature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amptcy+tfiiomt j3 (i 47x,mfrs.-r28j plitude of sounds in various frequency ranges. (An example is a carfpi7ot rti x8 2csfj, (3mi rjty+.4m- muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you f hnx k(d;d-.)+no tmbmove up the fi-( dhnkotnxm.fd+b ;)ngerboard toward the bridge?

A noisy truck approaches you from behind a building. In h aknb3o;. hmyg9m9r q:(zqr.itially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of thehqk. b99n:(h yom;m za.3qgrr high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference i8 e4a7 vvy;dkgn space,” whereas beats can 4 ;aegv8k v7dybe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poinw no-l4j91 xjqts D and C (where destructive and constructive interference occur) move farther apart or closer togetjqnoj4lw1-x 9her?

Traditional methods of1iqdcn*2 n j h55ah-gl protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise leveli n-dljh 255*qgc anh1s. 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 the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as - bf0y6m*oi1(3l4cd c pk.q) yifxuuta superposition of two sound waves with slightly different frequencies, as in Fqy.c6b tou10 y43 fx*muif)lckdi-p(ig. 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 move in the 0vx;xtw h1b,o same direction, with the same velocity? Explaix, wxo0;v 1bthn.

If a wind is blowing, will this alter the fy2bqu.kbpf(1h.- aoqp( n nwo h;a,a.requency of the sound heard by a person at rest with respepa2fwoq b..p( ay(h . ;nbkqano-,h1u ct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various p q(h/0nj 3bbduositions of a child in motion on a swing. A monitor is blowing a whistle in front dqh b 3b0/nu(jof 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 ofx(/gzj7 .m kzm a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. m(jzm7kx/z.g $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hedras 1 sq)ix9 tp,bz8m ..z:je 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 not vadp.stzj1:9 se8,rq xbam z.i) ry significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airtdln6m/f3 bmo( b oot)xta8h2z.8;dl 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 o,3sh sqso , (*rum,oaff tuna on a foggy day. Without warning, an engine backfire occurs on ar sssa ,*3f( m,,huqoonother boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes1yoyv9h5 o- ns when striking the water below is heh- so1 yn59yovard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concret-:hwo g:z+/lfdz8*j( wvpm yde j.(m:k -eqaf e 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 dy::*/wmf :av e kg8.-d(wq-j ( zpm jh+zeflodid the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile .s r3o3,ihjsz+ky0hzs c l i9*of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 33i3 hhj solyc*rsz.zs+i,k 900 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain le mc 3sp1-k7sosvel of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity is pr 6 3rt17pbfg$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousl +9g2 ,pbsaatiy at a certain place, what will be the sound level if only one is exploded? [Hint: Add i9gs2+,a patib ntensities, not dB’s.]    dB

  A person standing a certa :y-rn;f- ddkpin distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB-dpknr- yfd ;:. What sound level would this person experience if the captain 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 o/s u .y.ktwnx0j; +mgr5wa:zpf 58 dB, whereas for a CD player it iswk5x0r:n/p + m tw.jsu .ya;gz 95 dB. 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 *5d0eey ,bgimt4v t+l of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere ctm5,+ydi4 evelbgt *0 entered 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 st.ncpau )s gn1ibcq: 9/rikes 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 at 250 W, while the more modest a*0rnz/ duu wkqg; 9xlh5/n5 pvj p4kl)mplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.55)n5kph* qn / /ld9urjz guxw0p;4vk l 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 whejrf;+4l3l.p z s;u;vky+u kbun placed 2.8 m in front of a loudspeake3lr;;.4 +kuuj ;+lykbufsvzpr on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in soundd9v/.tx-yh pp( hc*b otaqo,3 level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Soppaqh9yc d/-t3,ov .(b th* xection 11–9.]$\approx$   

  If the amplitude of a soundltok+- kgcl2(q dr 0 84dg97kbwk ytb0 wave is tripled, (a) by what factor will the intensity incrggtk yk2 ddwl -bc 97r(4bq o+80t0kklease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacementn*msg.umo tp nj k60/7b eo(a( amplitudes, but one has twice the frequency of the other. What is the ratio of their inb0 n tu6e kj7omsngao(. p/m(*tensities?   

  What would be the sopqatm8)(ha 5 hund level (in dB) of a sound wave in air that corresponds to a displ(8q haphtm) a5acement 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 lou 6:db-(bupnfc5(h nb k(z eeyc.ya09md as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6a .b6be ( dhyb(n5(pc0nf:9ekucyz -m.)    dB

What are the lowest and highest frequencim: *+dmvjph9o m6ecs :es that an ear can detect when the sound level ism9 6hoj*d+m v e:p:smc 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hugeo +xic,(ebkj5 range of sound levels. What is the ratio of highest to lowest intensity at i (e5bkcxj o+,
(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 o kf(vp3kq9 vq3ahv0.3v t2h wef 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 string be ( .vqaq9eh23kkwtfv 3 v3vph0placed?    N

  An organ pipe is 112 cm longvl605hp ht,gi. What are the fundamental and first three audible overtones if the htpvhg 0,6li5pipe 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 from blo 3agfv;2 /oo- j6upis:+ fmlbswing across the top of an empty soda bottle that is 18 cm deep, if you assum ;ifs/6-mv23b: ufoagj pls+oed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to buildlri 6v y)g)1a) d +3pnzfpvtr3 a pipe organ with open-tube pipes spanning the range of humanvzlrf 3)g yaip+rp6d3t))1vn hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequencfvq1ojsn i: /uo:qst: hty9 8 a32a*ajy of 540 Hz as its third harmonic. What will be its fundamental frequency if it 1j8 y*s3aos::f/ oiv9hjt a 2tqq:ua nis fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 00g.n.zt (joii :0 mhgf.73 m long and is tuned to play E above middle C (33iifjn0. t zmh(o .0:gg0 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 emits middl0sl)inmk3a 2h. qog2k e C (262 Hz) when the temperature is g02a.kn3 shl)kmoi2 q21 $^{\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 rfsa+i, *a8o x20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hol10nr-os *hxerc*:bgt b2a p pb+nvy*w(q,it0e be that must be uncovered to play D atyvpb b: c ei*n*a ,hs1* -20+x(g0prrw oqbntbove 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 H au/fvb latq6 1nga :30ub3j,ez, and 616 Hz, but not at any ougl/f n,a t qeu0 133babj6va:ther frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tubezr95b;+a -v1 1g uq 2 fmuobxt4l*dqkz 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whbgbq1qk -lvom14t dzf* x9;z2+5ra uuat 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 ph *c 54n5w/xo; uad 2ecg.p-/o hpuzq$^{\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-lom) 10a)bnneca ng organ pipe atme0 c)n )aab1n 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximate7,crj hvze3* rb enow6j0n19 fly 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 ansecnhrr1 6 n0fvezj7 ,3b*woj9wer 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 d l2zdad*i0 :mstrings, one of which id*diazm: 2 l0ds sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hfh b3h.u k xjf85.fpri 5gin(*z) 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)cv byk6176a lo operates at an unknown frequency. If neither whistle can be heard by ol71ckvb y66ahumans 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 t 6)v8c:d3 ou sb9knxk350-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 rkx6n cb:d9s tv3ku )o8easoning.    Hz

  Two violin strings are tuned to the same frequency, -syw1 fpmeg4ivd w d-y1 s5c-91ail g1294 Hz. The tension in one string is then decreased by 2.0%. What will be the 45-1 wifc1is1vs gddmlpa9g- e1w-yy beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if t sf0 zb*aprp *:6aoo-v)1-xs2qa ayyowo identical flutes each try to play middle C (262 Hz), but one is atx0yor1:)p*a oz-s2 aopf-a yvb6s*qa 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B 3* l pun4inb/ua8e cp/has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz 4c/i une*p/ualb 38pnis 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 ap6lh*psp*vf 2 n3d +lhnzct :6aart. A person stands 3.00 m from one speaker and 3.50 m frc*s nl za:ln+*2hthp3dv 66pf om 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 supposed f n q.(sb 1;.mvgecms)o t3ea7to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 ) m3eca17ngovbmf( s ..ts ;eqs 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 oodok f:t it8a+ ng-;1ch kz (- qe(22smypjm5jf wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assc5:21 ynmo2;(iktkot+-j mpehq8 asz d jf(g-ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren ispfic+w1 gtpf.6e 4h o6jp:q i( 1550 Hz when at rest. What frequency do you detect if you:f4 1jg.ic +i qp6(wf6top ehp move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sirc,q; gbp+flts z02:o09xj ur cen emits at 1550 Hz moves 9xjf;sgo:+0r zpc0l,2tcuq b at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequenc/m2 w k06( o0a.ovgbw xp7ucqoy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exaca7o/gq0(b cu m 02vwkox.wo6ptly 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 sing /-oc0ll7tz cvg6:ey0 j jue;rle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rej0;e 07 ezru v: jlogtcyc6l/-st 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 wavs.w00) 8b tq zhf-wfg t60g5 av ygmvtx-um**des at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the recgf0 0wtsmu*8xyv-b.t5q ht)f6*m0a zgwg vd -eived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat e -e,kzk+3np 12 rmjnnxmits an ultrasonic sound wave with frequekr1jznm3x+ n2ne p-,kncy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat rncz/y-*l.ng88 nkj rtrain car at a frequency of 75 Hz, and a second idenl j.8rkzn 8 *r-c/gynntical 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 e*bqw.i r4;ys 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 exerq4; y .ibs*wpected 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 tlif+08ld+ggf n/2 xf ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 57ea-+i4 d o*9l rjgfe.n0 Hz. When the wind velocity is 12 m/s from the north, what frequency will observe r94dljfge+ *-ie.o anrs hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on eke5s+* nw5z -ma1kfeh)98 0yn e :idculr (xsland if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What i,jx 0-6 h+zy x()bw drytb9etcs the angle the shock wave makes with the direction of the airplane’s 9,wzb dxx6)b+ (y-hy t rtj0cemotion?    $^{\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 a:ve*ref5 cbib6zngfj4; bqbg3 g;* d(tmosphere of a planet where the speed of sound is only about 35 m/d6 eeb:3*n*v;(4 g c rbz5bbfgjqif;gs
(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 shock wave adwjpe v qx,5bsij/2kr 7 bti3.wu* i(;ngle it prbku xbi/vww7 s2e.5t3 ( qrjij;*ipd ,oduces
(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 23lb 5w /((hfuyqyft3t/ cz( xc;wor a$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ge9m2k pu2ivk bz)k; r,round flying faster than the speed of 9;bk2vrp,i m2)keukz sound. By the time you hear the sonic boom, the plane 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 203c5 llp h2 lkeh0v1wo7)itku 0,000-Hz sound pulses downward from the bottom of the boat, and then detects e21vkilwe)30 lchul0 5o h7pk tchoes. 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 auau9112 t8h xc1bzk.)om b a9am5tudrwdible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sym/9mv1 g60g,n pgrp* p7zszhv mphony. It consists of many zpv rm,7hn*zspm ggg/19 p0v6 plastic pipes of various 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 of /3xptr2a w+,n.b gr3ogid9e mhuman hearing (0 dB). What will be the sound level of 1000 such mosqr xbo2m.9g3id/aert g,n3+ p wuitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 8 s/(kk3qy cafiw--bsy f08t h/7-dB sound are heard simultaneoustsch -yikk/qa0 f b( 8fs3/-ywly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 d4da7 zp42s),gchp+dt 0csma rB. What is the acoustic power output (W) of the speake+c 40phpmd)saasdc r 2,74tz gr, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Th qd-c3(kaj fd4e power output drops by 10 dB at 15 kHz. What is the pj 4ddk3f -caq(ower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. jtz)uj7xx/wt +m :)pg Assume that the sound level of a jet axumt7t )jzj gwx/:+)p irplane 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 communications systeaes9i, roa82s ms, 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 toiq8s9h/ bl :vg a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental*s hu77 8drobifkp cof 51z14w f514rocw*fhu1z 7b7pk i 8ds ofrequency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with water pdy7ez v,,sv3/jb, gn (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distancey sdb,3, gn,vj7/vzep 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 xf)pl*8l-nr1 cnu vdf+r;0 gcnear a tube that is open at one end and also 75 cm long. How much tension should be in the string if )0 dg1 x8v ff*ccn;u-pnl lr+rit is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tbn ay5dmw9 8o0m g0j(co resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources,aty-q 1di,dae,vs. z. The sound is loudest at points equidistant froma ,a1,v,yiqs-.edd zt 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 the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on thezdflmr6 qvg(6xp/6 7n stationary train hears a/v7mqn6dfr6lx ( p g6z 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam tye fqo2(p.f*frain whistle as it approaches you is 538 Hz. After it passes you, its frequ(ey. ff2fq*o pency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estisfaawsgd7l:/(7nqkd57t ys* mate 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 certain car drops by a full octave (frequenct(k 5*dsy7w7a dg/qn7l:fs say halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a be6zv0vmazq 4 8pat frequency of 11 Hz. The sh0zza6mv v84qp orter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railrvpg6z;8/tobfg aw9hy :1th u ;oad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he lis;6w8: y1u pgtv bo9az;ht ghf/tens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/sm7vsw3 yzk+jonzq5qt w9 9 8f) what beat frequency would you expect if 5.50-MHz ultrasound wave9nq9)w3my5 ovk8wqjf+7 tz s zs 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 whzd3;p(nud9)ked 0kg gj gvz24ile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What )g gz;(n9j4 0devpu3gk ddkz2 is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of h4i8scb efb0 w/n7 jue.igh 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 dete4c78e/. nfb bi0e juswcted by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38z x8f 5suc9ky*) 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 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 F8zkfx *u5ys9c 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 stereo715 gyphsg*fs listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of *1sspfg7y5hgthe 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 “scctfv:,cvb7m 18b 9 9ny xda/kbd5 uw7inging rods,” involves a long, slender aluminum rod held in the hand near the rod’s min/v,u cx75 1tc9vdmb9a8y:bdcwkb 7f dpoint. 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 hearing for the human ear at a frequency-m9i k3bxz dkv 5t; r)(.tq6vmfdeqy/ of aboufv .9k)ixqted r;bzmk3ytd6(5 m- v/qt 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hear883j 2asr56d c obqiuvs the sonic boom 1.5 min after the plane passes directly overhead. What is t uc5 rbjos6av38i q2d8he plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is e nle0lju v2)y)y6(ghyna6b7 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