What is the evidence that sound tra2x h5mzome*mab br ft d093jat4/g01 fvels as a wave?

What is the evidence that soun bpt )8zx ++(z.ztiojhd is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a stry8kc4pj ;atp2ing to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound cp8yatj c p42k;an 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 aifhah **w+y r4;q2 gvwwr into water, do you expect the frequency or wavelegy+w* w*rh2 qaw4hfv;ngth to change?

What evidence can you give that the speed of sound in air does not depend signid 1bfk,,fb4gm ficantly on 41 fbbd ,fmgk,frequency?

The voice of a person who has inhaled helium sounds very high-pitched. 9or e sm7s zk5br2r5lq zip(/-Why?

How will the air temperature in a room affect the pitch of organ pipes/c+nqfid dpn78imm76ib* e u(?

Explain how a tube mi+mu8v1gxk wd, 3)qktq0rs g8aght be used as a filter to reduce the amplitude of sounds in vario,0q s8w3v rmqka+gu1g)ktdx 8 us frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together(najjyvbp + q4b k+(4n r+pis5 as you move up the q4 a+ y bjp nv(n+4jb+(pkisr5fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hea s 9r*rx;b pw:xp,qii:r it but cannot see it. When it emerges and you : ;rx9p,irx*bp:iq s wdo 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,” whereas be)bo 8j4 by-qzau) g4k/fpm+ gaats can be said to be due to “intpgmba bfua48oy+z)/g4)-kj qerference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wou/ 9g,avxds7 tyjby7:ase18hd ld the points D and C (where destructive/sh9s xy y:,atd7aeb j78v g1d and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing kh9) epo vet )7soc,2aof people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient k2 seovoc),7ap9 he )tnoise. 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 a syvmc t:ks640u zmh44 wuperposition of two sound waves with slightly different frequenciy0swc4 m:4umzh vt46kes, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction, +(fn hft) q8 n;:kpcjudgg;o3with the sfnp)fho;u gn;3td+g 8:kqj (c ame velocity? Explain.

If a wind is blowing, will this alter the frequency ofz klvhm,qo,, 0 the sound heard by a person at rest with respect ,vh,moqzl k0, to the source? Is the wavelength or velocity changed?

Figure 12–32 shows vsklfw07jhrp8+cn554 (vzy(2sl y x rrarious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reaywr5( k r5s0x r(zp4vc2j+f s8ylnh l7soning.

  A hiker determines the length of a lake by listening for the echo of her shp-yvdq/ 3ri); 8oloao9fjwx 5 out reflected by a cliff at the far end of the lake. She hears the echo 2;o )ri8-qda3fjowlv5y /pox 9.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship)oll n6))las :kcnch+ just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean a6alc llsn))hk c:+)ont 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 wavelengths in air at s+ tftrt )kq)y n4-s*rla64 xu20 $^{\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 abo pwpnnj9* jc bt6uxem/53s+w 9ve 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 elapses befoxj65pbetw/s3 pw*+j u 9c9mnnre the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cxw0 ox(f5/dyp2 0 ssvaliff. The splash it makes when striking the water below is hearws5x /y a(2dosfv00px d 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike tq i)fb-xgfaltw w o+r54*zj40he concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the ot-of5xtr lfi*j+qg4 az0w)4 wbher in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of 02k1c0 uqwv, d ;:hglomywm(bdistance by the “5-second rule” for estimating the distance from a lightning strike if the thdw0kymgq (b o0m:;, 2 w1cluvemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ow-z 9uu8,bs4om 3n+ qpde;jb*edfhp( f a sound at 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 sy2b4 uzxa+4nroi z4;y a/lqp s4nj- w2ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB waf,xuao3qd2r (oi46 ghen fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’fidoxar(6g3,au 42q os.]    dB

  A person standing a certain distance from an airpla 7 x23q9mm pxgbje0g+ane with four equally noisy jet engines is exq0+bxpa3m2e j9g gmx 7periencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of-3k ;rrgx1ub*.1i ut 4j qqrewi1(qgm 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB r1.kui mg jt4rxbe g3wrqq1-*1q;(iu =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal co8h9i urh(tufu bfn2 1,3/vibqnversation. Use Table 12–2. Assume the sound n9bur8vhfi qi,1h/uu (fb t23spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area i84je u8)j oi b3rwh.bd) iqs.ts $5 \times10^{ -5} m^2$ (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 A6adm9(h5.u3hpg qn fk is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudsph3fk.daq5m6p9 ( guh neaker 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/ -5s /d9ln,pe)wa 0tdh:yo xx9flytj in front of a loudspeaker on the sta/sleax /nf 09 wdo 5,yjy-h p:dtxl9t)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 difference in souxfku9ly4-ku :nd level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levek9k4lu:y x-f uls differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sohjv: r 5hfk7(uund wave is tripled, (a) by what factor will the intensity increase? Increase by a factor o57u hkvrfj(h:f    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but ) nc ,- p hqdv-7p:-4sviemc-gnbalk0one has twice the frequency of the other. What is the ratio of their-nhg0sp)-7 k-n qab-c e :cmv4,d livp intensities?   

  What would be the sound level (in dB) of a sound wave /tmr oozx+ yxt;bov84oi5:rb )( cp .fin air that corresponds to a displacement amplitude of vibrating air molec) o 5yztx t:v8rb4 ifob.mp/r+o c(xo;ules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem asg;r,h p fpf76w loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) ppr fh6 w;,f7g   dB

What are the lowest and highest frequencies that an ear can deu7sgp8 1e u1cntect when the sound level is 30 dB? n1eups1u87 gc(See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the u.yyzs*ws(+4gkp cow .+hio93z 6ahcratio of highest to lowest intensity at h*ys (9ug+wziyz3 aw.s +oo ck.6p4ch
(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 frequencnwr0qxg ut :x2y*-f8,f*yq p vy of 440 Hz. The length of the vibrating portion is 32tuv nq *gqy8yxrwp -:f *f,02x cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long.ik,. viku(9 qw What are the fundamental and first three audible overtones if the pipe is q(ku.kiw9 ,v i
(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 b9dhgkyym.k-,pia ;w + lowing across the top of an empty sodw k;p -mg yihkyd,9a.+a bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pia ov(a/kdd8 a 1sd00pppes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the length1/s d odpa8p0adk0 va(s of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as *9iv.hpfko7d its third harmonic. What will be its fundamental frequench*.7fv ikp do9y if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and lbn 8y/gziqd.l1-/ cdis tuned to play E above middle C (330 Hzcg n. -yd 8lz/ilq1b/d).
(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 f,bm 4zyxyh)wpl 3z9; of an open organ pipe that emits middle C (262 Hz) when the temperature is 21b4m9yx; h p wzl)zf3y, $^{\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 ath x 38nlg1:eba 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute q+ycpblz.599i na* utin Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 n y+pq .bi alu9zc95*tHz?    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 l um na3 qlvp-29i(m76 arpv)rHz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is a3 (auvrvqn2ai9l7l m)rp-p6 mn 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 atn.b fk40p9sjyzdl s -erb0h7 0 two successive harmonics of frequencies 275 Hz and 3pn0bkr.e-9f ls4sh 0d y zj7b030 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 eykstw8sc6mp5v8e(4/dr 5s t$^{\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 owcs );oj6f8my8gotp*z4)5hqhq7v vf . ylv/jrgan m;h/ soqv8).zy) vgvoq 58hj4y7pf* t6lcwfj pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately vmp*s:3 9uil4f(bben 2e a8n*kb :runss-;y u2.5 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 stn*iafbsv: p ku u8( 4sb* s29nunlr;e-y3mb e:anding 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 onq*1law+pp 1ae6q 9g dxe beat every 2.0 s when trying to adjust two strings, one apxg dq1pwl+e6a q*91of which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2;7 eq-ayi: b+p 4,mlyxfxy-sp62 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 anotherhe5wp+v)s 7u i (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequeh5wus+pv ) i7ency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produce i (br-n4suzy,s 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasonii ysbz4n-,u (rng.    Hz

  Two violin strings are tuned to 0j:h-o djr v sn;e7+dythe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the j;ydd-esoj7r 0 :n+hv beat 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 migrp e)(rlbz.12guv 0a ddle C (262 Hz), but one is 1pg)vrelgz0 a.(2ru b at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, an/4 wdlerfm3m ea(9i u*d C. Fork B has a frequency of 441 Hz; when A and Blie3w d(mm*u a94fe/ r 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 frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from onv(9pg-tnq -e63mp(ak j t6adoe speaker and 3.50 m from thvtn6ajk-tpd a-9qg ep6 o 3((me 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, but a piano tuner hearvs(+n (vv-bijufr 3j 9tc p4d4s three beats every 2.0 s when they are played togethe(4r(9civvj u bvn-3j4t +spf dr. (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. H rr7lt( +l*shjow many beats per second will be heard? (Assume T = 2( *+trlh7jsr l0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire9o59qijizgldr/l t yvh6awuxa7;94y 5qb1 ) l engine’s siren is 1550 Hz when at rest i9ailx4l wa19/hro 9 ygv;l bytq6z5u)7jdq5. 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 frequ jesa9xk;svm l8wdre.-9l r+gx6 ;v6 tency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of t -rmkge.;vl 69vadxs+w6rls;exj 89 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 toward you atn hew/3tpu 6,3sr px2l 15 m/s versus you moving toward,xs 6u2lnr3tp/h3wp e 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 equivplmm3;g8r xcplxc*:9 )* o clpped 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 ip; x)*po*c8 xm: 9m3vglclrcls the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.08lgays5v4 k j9 kHz and receives them returned from an object moving directly away fakj49lsy8gv5 rom 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 an ultr, cibk:knl2 g6asonic sound wave with frequency 30.0 kHz. What frequency dkc, l: k6gi2bnoes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a ticxbch-gnguk(d/* yi2s2*dyf1m* .q uba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a spxgcfu. qk 2*y-d d1*nsbcy/(i2i*mg heed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves d)dpnq m uxg +wa 906zmdy)(j5to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s dira g)0p+dn9ud(m6 w 5qyd zx)mjectly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of4rj+/sje0k gv frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velochdqlx( bb2f64l xvb m).xg+jf :-8grhity is 12 m/s from the north, what frequency will-xlxfq28f4g+d.lgbb ) bv rmj6 :(xhh 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 moving on land if its speed d/2hkm2aal3+ 7z e 6kxhajb 3hat 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 qo1b4(qy(.s t)kgl i3yrm4td 310 m/s (a) What is the angle the shock wa (r3y4.t g lkdsm41ytqqiob()ve makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet 0km k8om;mmw7where the speed of sound is only about 35 m/ 78; 0kmmwmomks
(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 ocea8mfgsm- rysz25nd; i 8n. Determine the shock wave angle it prodfs-r 5gd;28 s8zniymmuces
(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 v,n 7j41 c(pdxw2bp ad$/theta$ 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 abovoial :zksr1/ a89fssyh6. ( iae 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. Ss za:89r 1lfo .6ski/(iahsya ee 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 20s gsceq: b:v4d3b/ dj1,000-Hz sound pulses downward from the bottom of the boat, and then detects echo jeqg c 3/vs41d:sb:bdes. 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 thef 8 jqrx-3bug/re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe syj okb-8 oh4sy6mphony. It consists of many plastic pipes of various lengths, whobk 486o syhj-ich 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 m,:mh)drpp m dm q ks.8wdp 6+92ty+thtakes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 sudhkrt)m8st+t,w y+9:6mp mpd dp h2.qch mosquitoes?    dB

  What is the resultant sound / ,- .af4ub/sirbta6w em3f wzlevel when an 82-dB sound and an 87-dB sound are heard simultaneous-bb3 au4 f r/s6eaftm ,.ziww/ly?    dB

  The sound level 12.0 m from a loudspeaker, placed ile-nw7 d6l:o9vzg y/kk qo6q :n the open, is 105 dB. What is the acoustic power output (W) of the speaker, assumiz:ook:nw6gkl96 -dq7v/qel y ng it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The 3f4ddo*t+i +3ife alrpower output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? ioi4 dea l*t3+ 3f+frd   dB

  Workers around jet aircraft typically wear pgoeu 2xbjy,uet4 s+ xa s;..c2rotective 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 bs2 t.y bxe uog ax.u,2ej4;+cse the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications 9 ic+: n)zj,x5d1ivf-9p:rwfgedtu psystems, 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 toqdq 6)cx,p6t y 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 kk a uhj;t,9l :y5x/bvlong between fixed points with a fundamental f /xk jy,kuh95va;:l tbrequency 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 watef(kwfibm0)ips zh+ +,u,s2c.g7 okf yr (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 from the tube opening to the water level is 0.12 .g)u+isi z7km0ws,fy(bfcpkh2+ , fo 5 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube th9ymjj0me3tb 4 wp 9at;at is open at one end and also 75 cm long. How much tension should be in 49m3yt0;pj e9ajw m btthe string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to re9ace;gb cf0 v;sonate 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-/ c9 66hphtc r (kn,wtaj2x9qlHz range coming from 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 mi2r9wt9(ah6qkhct lcx j /n ,p6nimal 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 cqst0(1o9 ptb4ol 67-x sb*ixvl mq1s on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of t41 t-1t7cb(x0qmvo6osl bsxil*s qp9 he moving train?   m/s

  The frequency of a steam train whistle as it approaches youxfb3zx:p-. *rj. xl/8 bbsk/8 jdkyel is 538 Hz. After it passes you, its frequency is measured as 486 .zl/j/ plsfdk3:k br*.xebx8-8jbx y Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just bpq7j 1g )nvcrxy8 5jqlrip.a 7,i)yz/y listening to the difference in pitch of the engine noise between approaching and recednc7 .1p 5izjxvyg q,))8a/rylr 7jpiqing cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat freqv 9mohwkod/g98 2kb*auency of 11 Hz. The shorter one is 2.40 m long. How lon 9*kmd 9aoh8obwkg/v2g is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a6 u +w (g9rrcn3ddvpa, stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at nc3gvu ardwpdr,+(69 C?

  If the velocity of blood jv:j 971: 9v335yqsixflqimd eou*hpflow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves werq5 o3j9vylsd1j:xu * :3p7qeh imi f9ve 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 gay*/pv njr7 jiv* 1*hm/s while the moth is flying toward the bat at speed 5 m/s Thr7*h v n* /yvij*apjg1e bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a serieswds5l4sza:y2z:ya0c of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abous5: lys42 zzcdaa0:ywt 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to se..6t/h7ml ir d:unk.vtu )qh3ougtb6 dzk y+ 7nd 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, bz rk+ th:yh7)66 kut.q dg./.iomtd3unuv 7land 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 s n2 1+xl(;r,ixx9g mmo-uv9ter0 ljflistening can 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 long,x9u o txrjm xi,+0;s(emfn l-l1g2r9v 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 amx5v ij.*f-/f gu4tqwluminum rod ht jfqvg*/4u-mif xw.5 eld in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the hv,cox *dguhrmu 27.i. uman ear at a frequency of abou g.imhuv7,c 2.*dxuor t 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 oibnce kt rj3izt/ 81mexj 73/hv) ez/j) yx+k+bserver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitub )j1 8tnei3 x7)/iey he+/jc mxkt+ jrk/vz3zde?    $ \times10^{4 }$ m

  The wake of a speedboauxm5y3lu7518wof a y- thpbr;ga4 y,pt is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h