What is the evidence that sound travels as a w tft5o;ki6g5f is.u( lave?

What is the evidence that sound is a form up)gnv: 3luow(n0;o o of energy?

Children sometimes play with a homemade “telephone” by attaching - ja:2n 7gjgeoa 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). Expnoj7jg: g ea-2lain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air iwd bpq;9qzne9cp6;1 l nto water, do you expect the frequency or wavelength to change?dl1qq zp6 wnc9;e 9bp;

What evidence can you give that the speed of sound in air meh n57*zmw)qb dnm u.b.:4qg does not depend significag) mnqmbz4b.e *d:7wn .mhu5 qntly on frequency?

The voice of a person who has inhaled helium sounds9+7saw pw3 /.bnmqkdt very high-pitched. Why?

How will the air temperaturee39i7l- aqdjn z .xtnw*a0 *,erv wu/d in a room affect the pitch of organ pipes?

Explain how a tube might :qr 4himr r .tk0+58 eiuv9ujrbe used as a filter to reduce the amplitude of sounds in various freq.4:u 5jrv8 +tikumqh9 rrrie 0uency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethertfl -h x2s+ka6 as you move up the fingerboard toward the bridgxfskt2+-h l 6ae?

A noisy truck approaches you from begs1fqbz13fg( hind 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: fqs gz31(b1fg See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inter()xhoeq r8 d*de;qzmh. pr-7 vv2 azd(ference in space,” whereas beats can be said to be due to “interference in vmzdxr-r)*8a dq7e2.h hd(vzpe q(; o time.” Explain.

In Fig. 12–16, if the frequency of the speakers were low8p5uw8gns1lf*usm 6kered, would the points D and C (where destructive and constructive interference occur) moupm5ln 6fss88 gw k*1uve farther apart or closer together?

Traditional methods of p y+d4mzqw,,5s1ih v)d hqp g9dxbqq0+rotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition t0,xq+bs)ydqw ,z9i5dm4qh1h dv q p+go 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-k fzv+k (8hly a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two compone(zkv -k8y+ flhnt frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source -b;p9;joc m.m x6a xlband observer move in the same direction, with the same velocity? Explai.p6jx9 -m;;al xmboc bn.

If a wind is blowing, will this alt+hup/- ;+4idtd jkk wser the frequency of the sound heard by a person at rest with respect to the source? Is the wa+hu;d- pk/stki +w 4jdvelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monit65(nvlx 4ga 7vpo: : ooixfd.nor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reaso5(x: 47nf.i6o avdo nolgpxv:ning.

  A hiker determines the length of a lake by 7 um3nq*lymp/listening for the echo of her shout reflected by a cliff at the far end of the lake*u7nmq3ypm l/. 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 shiof dkis97)4 xzp just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2f )o 4xsd7k9iz.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waxiggnz 0 puc+(p7lw8)hx0.,r e xgx/bvelengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just+ d/s5v57jk/qdt9u b a*uaj(x.ym dfs 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 much time elapbsv/q my s(fja.7j9d dkxud*a5t+/ 5u ses 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.igpg cr*iz7.m j-a (rs,zp+j2 The splash it makes when striking the wa(7 aj2r.z-mip gc pg+z*rij s,ter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the con1wtdyf4h ne6.crete pavement. A moment later two sounds are heard from the impact: one travels in the air and the othethey4 .nf1d6 wr 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 mimx;vcp8q(:s; 8gmalvle of distance by the “5-second rule” for estimating the;;g8q 8mspvv:alcxm( distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound ao 1+mqqyv *9dx7 ufb2it the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose i2e yz 4vjuw -*n05g7ptw. mazintensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a souq7gri ,ffc5 ;und level of 95 dB when fired simultaneously at a certq7g,cif5 fr; uain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equ*nq9g4:e ja ohally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, j:ae n*ghqo49 not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wher*-yurwkh a c-43bs9y meas for a CD player it is 95 dB. What is the ratir4amb-c-ky 9 3uwh*yso 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 from a persqw)ve sb( .3:(kaugilon speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphe s:ki)l (3qb(u.w eavgre 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 eardruh*27ucbvhf-vfk ( q )ll:yqr(m 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 hj977yhcb8 *e8 ku kpiamplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m fc7ipuhb79jkh 8y8* kerom 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 placedcu.:qz ,t20oke jtqy/4 ahd4/evd3ty 2.8 m in front of a loudspeaker k.q,0dc2 vyteudj3ota4y/4 e :/thzqon 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 sound level of 2.0 dB. What gk iu ia.)pgi3t6c lu(4 c-c6ris the ratio of the amplitudes of two sounds i)kgc 66(c3u cp.u a4igr-itlwhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound w., abxrvuqq+ wrph1gbrb6(6+ +oxy,w ave is tripled, (a) by what factor will the intensity increase? Incvx,1yhpb b++x , qboqg+ 6r(rwruwa.6rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frdl/79zu/rr yzl / 9xkiltg s62 gk*2crequency of the other. What is the ratio of theikzr*gy2dzgu 276/lrt9l/9/ i xsrl k cr intensities?   

  What would be the sound level (in dB) of a sound wave in ai cyj wvz.;:wmg5o/0k fr that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 0ycf kgj/ wovz:.5w ;m300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem aul6eeuin 1;6 ,tm0,ixni8hxes loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–61einh,xm6l6i u, e;8 utinx0e.)    dB

What are the lowest and highest frequencies that an ear can+edl-lv*, kaf detect when the sound levella+kefd l *v,- is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a 9yxzcn9z 2ry +huge range of sound levels. What is the ratio of highest to lowr92zzy+ 9ynxcest 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 fundameidd3vr,r9:; t1 ptf bbntal 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 th drtf31;rbd:p b,t9ive string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thrs f)pmlyys+0( )b iz ncwv22:gee audible overtones if th)b f0(p s:n2g) +yvmwsc2zly ie pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of mzi c5gn:jo71an empty soda bottle that is 18 cm deep, if you assumi:c51 onz 7gjmed 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 range ofmt affg0acx+g *x 4b30 human hearing (20 Hz to 20 kHz), what would be the range of+xb xcg3t afga 00f*4m the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenc,ab4a.+rte56or ) dtm; remcay of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of ir o+earmt4. dbtea;am,cr 6) 5ts original length?   Hz

  An unfingered guitar string isc4 2j+dgbfz 7w 0.73 m long and is tuned to play E above middle C (330 Hzbwd47cj2zf+ g).
(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 emitss 17-x enbv1uu middle C (262 Hz) when the temperature is 2x1nuu-7v 1sb e1 $^{\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 s;b +auawb2k5u/5 z ktat 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 1enqq + c9/bhqdog/*b2u u9nhg59 o, qn2–10 should the hole be that must be uncovered to play D above middle C at 29hqc ,qh59 q99/no 2dngbeu qgu n/*+bo4 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 *e++mb2nk .b xe(1b ruyo9rhdat 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed piyukbrb (rne*2b+ 1x om9+e.dhpe. ----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 two sucr tv 8hnbdn9qxb8l/9;cessive hab;9vqn 9/8t nrbxld 8hrmonics of frequencies 275 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 .dbi9w fzky p3+ux pi 7zl5,- 5lq1nkb$^{\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 or.wh ye1;sin l): j7phigan piw) ;h7.h :lpsj y1einipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is e8w 1spn* fzl0approximately 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 01wpn *l fesz8to 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 st 159qrqg peoln0a;6-kwy/omq rings, one of which is sounding 440 Hz. How far off in frequency is the other strinl pe n;qm5k a/-ry69 1qoqwgo0g? ±    Hz

  What is the beat frequency if m:1e)ah2bycvazn e 7s6 iddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates p4km 8 2y.e/m bwlykkv27fgc -at an unknown frequency. If neither whistle can be -mb/2w4kvyy m8gle2fp.kkc 7heard 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-gj s9gdn ket+0c9;k:q Hz tuning fork and 9 beatg nq0ds9eg9cj;tk :k+s/s when sounded with a 355-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 Hzq(tc4:9yzjd; 8 b6pge2gr10 qea)dfi ps2s ji. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings a20 rdc i t fd;j24ee:)zjgbp9 p gy18(qqsi6sare played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to plb5: favt(1fq g w.a-gsuxp 9c,ay middle C (262 Hz), but one is at 5.0°C and the other at 5.asbtgpg,:f1 v9u xcwaq-(f25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork ,avnwgm rjl;*j -t6 s6B 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 sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequenciewmal,gvjj; t66n*- rss 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 a6 px:1 8tluv4e *ezy56pp :- yjfdgcllpart. A person stands 3.00 m from one speaker and 3.50 m from the oth e6fyutv 5dljpxg:86czpl4:y ep*-l1 er.
(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 snr 7d4ft9u7 ww0drj6:kd2 dbl upposed to be vibrating at 132 Hz, but a piano tuner hears three b rju6 4ld bt97nrdw f0d:wdk27eats 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 ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. zo18qjumxz .v, g tcw9ota3b3;8sg 0gHow many beats per second will be heard? (Assume T qmoc93 bxog 3jg;a8 t,1.sgvu zw0zt8 = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ofail ,*hg1bf)txv( -g z a certain fire engine’s siren is 1550 Hz when at re )g-gx zbl1,*(vif hatst. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginelhp: r-oyp8i1g9x uabhn*o *: whose siren emits at 1550 Hz move p*o1lbu: a:y -ixh*onp 98grhs 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 moving dz(02,d.lnksp9wla- j f- dvacvihb oyh21..toward you at 15 m/s versus you movhd1 2y.n(2b cljvak if lphdsw . vod-,-0az.9ing toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are eq08 lcil6)ylcz a9su7o8fe 7ww:rkn7y)hak)p uipped 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 the horns l:iry8)w7n7hca)68 es wo fzulyap)c0k k97l emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives thvpj3y5v11opowe)r 1x em returned from an objecyp1 pvj)31v5o1xroe wt moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits allcf3 xax)7j1n ultrasonicaf )xcx3jll71 sound wave with frequency 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 q62 oggwxv 8y/flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while atgx 2vow/y8qg6 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 blo1.ldc x9e48l qhecg9tod-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 beae9 8lqctleg9c1. 4hd xt 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 wan djx l7:+l;4rsd-3mzvc2j yvves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When ewqncu:f7fc::nrv::p82+x( y x akhq 3icas7the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, +:i7rnpxqf7:wc (hxfq euac 3vy2 ::ansk 8:c
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its lx1va:7u d jn1speed 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 whew nby:p:og x 0)ba1(a7f tvaj,re the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the d)p j0f1bn a:7v :wta,boyax(girection of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of x skfk*ovh4 n0f/gc( 3a planet where the speed of sound is only about 35 (xf *0kngvkh4f3 s/com/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 shock wave 717 (vifclyh dau8gnf wb- u0:angle it produ0177 gy( adl hc-vfbn:8uwi fuces
(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 akbh7b+t* 5tt $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane8/p2.hpauz2j csa s; n 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. Deh2p ;aapjuzs/2.s cn8 termine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downwma(cg w/s3b 6nard from the botto6g( nm/wc a3bsm of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audib18din* rpry ck0r 3zsr-w6f 8ale range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a see;q/o1ks c)ldlri8y /wer pipe symphony. It consists of many plastic pipes of various lengths, which are open oqs8 /y)ec;iro1 kl ld/n 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 th zb3/2in ,srk sj2y/hyreshold of human hearing (0 dB). What will be the sound level of 1000 suchby i z/ksn3s2j h/,yr2 mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound al*m+ocxs a w:5re heard sim5xlsm *:c+wa oultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1)xp v; nuk/2fcqrjgo( g +l4f705 dB. What is the acoustic power output (W) of the spe(g fjv)o4ck;gqr l/ x+2fpun7 aker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The p91+assc n: 6on 4:c:)gag:awmp l/vi5nowb c bower output drops by 10 dB at 15 kHz. What is the power output in wa nac :)gscoo/6n:95gpbn:4wc a+sw :lbmavi1tts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective n1o)byh xl vhbw9; g1q+(b7t vdevices 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 efl bgwhy1v)+qn( vx hobb;1 9t7fective 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 syif+q smn7*t.4g.wx6;j 3hdzvmvaj f +stems, 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 fr7xu9x8 8 pc:f z yj7ass7m8nz9tq;rusequency 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 j q-(,g.abm- i/cgsv/e7cot w cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length cg-bqi7tao/g.,w /m-jsecv(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 vertvt ld-tkd6 7japl j8y5xla17/ ical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance f/5-k 7a lyx71ltjljtv8 6dadprom 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 odmm7f ka :5k)u3kh( :on-wpa jf 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 (in its fundamenaoah mwkfkj3 n(d:kp5 m)7 -:utal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one2pr b44pl.b nw 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 rangeph5yta wh:2um5k /xjy;lz:r 0 coming from two sources. The sound is loudest at points equidistant froy:lhptkwr;z/5 jx :0a2hy m5um 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 o7bnp7, /llcir n the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traic/nibp7l ,r7l n?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After it i:nqb: bf; k0fbm p9vvy;, sv,passes you,n:;fvyf v 0im,9,s:pbkqbv ;b its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cwrgmb9md2 5i6ars 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 fulid952wr6gmb ml octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, da.v+ 0m7xe kyproduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othe+m0dv k.7a yexr?    m

Two loudspeakers are at opposite ends of a railroad car as it moves;5ns.airm 1 gg.(tqa ;2t z tgcet(v;b 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 listens from the position A, in front of the car, (b) he is between the speakers, a;a 5 (e ggti;vamtst2n. rc1z .bt;qg(t B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is no*x wu5tr9.m nfy3x ul-qry)rq 1vy;c6rmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and refle.5 l uw-quc*mqr)9yr16fy3ntvrx y x;cted 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 od 900o kqkg,(ofts8pthe moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.9tkpg0(ooo q0sd ,f 8k35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mof t pi4b5pwd;z66lm.b th. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. Hwp t p6fb5zdl.i 6m;4bow far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to32fc8 uk 8khmn 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 F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close tkkun2h3 fcm88 o F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compn rfvuy8z/*5 byc+ez w6(wx)hromised by the presence of standing waves, which can cauc(h*f)/w ryzy xw8e5v6bn u +zse 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 rod+ /qew48hey-om/ i d*tsu2qsot(.oc es,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, riowsq o*demt+/u h eiso(c / e.4yq2-8tnging 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 frit3e2pt; *m+hphu 5ca equency of about 1000 Hz is3uc*p ipmt2h a5t;+ he $I_0$ = $1 \times10^{12 } W / m^2$ 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 z ,- :w,mzy1e2o isutaon the ground hears the sonic boom 1.5 min after the plan i,uayemtz1, 2z -ow:se passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 19; mn.qw2 /fkbwkt;as 5 $^{\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