What is the evidence that sound travels as a wavo ) wrux.es4gdtv 2q,3e?

What is the evidence that sound is a formt4 t7j6pwzdmvsh)au(6u9t ;k of energy?

Children sometimes play)jxp; 1a odqv s6cz49k with a homemade “telephone” by attaching a string to the bottoms of two paper cups. W4dx o1qpcv9szj6a k );hen the 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 *,vm+p *bpydu n tw6 +mupoofo4,+/ mbfrom air into water, do you expect the frequency or wavelengtmd4bn+ t+p/ obwmp6 m*vo*u+yuopf, ,h to change?

What evidence can you give that the speed ,yoq0 yy4klw+of sound in air does not depend signifi klqyoy04wy,+ cantly on frequency?

The voice of a personw byjwgc .).u+ who has inhaled helium sounds very high-pitched. Why?

How will the air temperature qcuxioy6x 4/ f 2)df8s,rbn ur,ef8d5 in a room affect the pitch of organ pipes?

Explain how a tube might be used a*lz)/ (z-al alc deh*is a filter to reduce the amplitude of sounds in various frequencyd /*l-haz ci)zal*l (e ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer toge9xd zsieq55 jbw6-zo rl) mmqm5da(9;ther as you move up the fingerboardmoaz;qlmmewd z d (q6ris-j559 5b9x) toward the bridge?

A noisy truck approaches you /6:d6/.owxlgdg cb kh from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-fk6holb/ w d .g/x6gc:drequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in s(e (:(ubb gkrqpace,” whereas beats can be said to be due kqr bu: eb(g((to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poiw-s* :wsmq -evnts D a:*wv s-eq-sw mnd C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearjz(5pbvpt (8+xq7hve ing 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 qpzbv 5 vj+e8 (ht(7pxaddition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–3 ui g p ,*48-ztsv9xvd klfwrw(c4i0j71. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. jgrdfivlwv(9wku z*is p -c470 tx ,48In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shif ryw. v/efp27;+y8zigd 3-jj4vcpl tuunm5z :t if the source and observer move in the same direction, with the same :vd4 5wugnrcyz+;vetu pfpj-ly /7i 2m .38jzvelocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pe7 ;a/ vos5e+4tdvznpa59fd d vrsoz /toed7nfs+v;a 4v5v5pdd9a n at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a choye(vi9q5l bhs-d.) e ild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through Ebi -hs(y9)oq5eldve. , will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout r5w9td)v8y mtb5j :rsneflected by a cliff at the far end of jry5vn)tm :d 9st5bw8the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlinpb.nat/z1e0(v0 w2g pql, lpsd.4qf yro 8v a+e. He hears the echo of the sound refle /ptp2a0gq. b.van1f4+d0w vz ylpql(8 r,esocted 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 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air agbx 1 v8vqho5l owko,7fa,:2c t 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 drift8 0 umc*ze2eg*z3 k2ta)z jfteing just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the b 2c*2*jezagzmeu3etf)t 0kz8ackfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from o0eu5k0kbki( h/2 cl)mr l* hbthe top of a cliff. The splash it makes when striking the water below is heard 3.5 s labblh)hlk 0 mour520 cei/* kk(ter. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stor2c ab i*wlzj pn l6m2)kb0hb6of69r)ne strike the concrete pavement. A moment later two so2f b9mjw 0b)) nch62 zir*6bk6rpaollunds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rufee;0 7gdx:qo le” for estimating the distance from a lightni 0 :dge;fxe7oqng strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paa eex7,;gsi24xp wmk)in 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 intensity i)bu6o p o(o*ck4,tty;;ta iars $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when ifvat8 iwh3gecc+:kund6v)4 8, b6r sfired simultaneously at a certain place, what will be the sou6 ge6w,h 4ba+ cvrusfcii:) 388tkvnd nd level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancogmb(la .gd0+e from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: d0( amggo.bl+Add intensities, not dB’s.]    dB

  A cassette player is said to have a p *ujn*a;)wd u1z p)ho dnb x5d1we0f-signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is b5n1a -zjudp * *w fpxuo;)w1 d)ehnd0the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conve ) ru2;wz(jyj6di s)dersation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mo)(;d s2rz 6uydwj)j eiuth. $\approx$    $ \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 strig mn0u:z f,j*ykes 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 i /m58 znsuic3zpc;/ h+ a(jatss rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound levelc/sazijut 5szh n+ 8/(mp3;ca in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB wf / oz36vq4tg8r,z ljq oaxt9/hen placed 2.8 m in front of a loudspeaker on the stage. 8/r9 6xt,gl oqfvt34/qz a ojz
(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 ur12w uuk9): mvp gze3of 2.0 dB. What is the ratio of the au em 3uupzr 1kg:w)29vmplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factoredugq0 npt o o:facxi):s:1)5 will the intensity increase? Increase by a factnpfxo:u qsd )i0):1:5 gtoac eor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have emjndsbq8*l + 5+1pp derzr+ 6squal displacement amplitudes, but one has twice the frequency of the other. What is th+ m*r6rjqz+se pd5ls bnp +8d1e ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in a6 zqudzn2.u-f ir that corresponds to a df6zu- zndqu2. isplacement 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 loud as a 100-feo b,x6m1m; sn 6lp-hHz tone that has a 50-dB m el1h6- ;bnxm pos6,fsound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect ww82r,ryy4 ywfdy 7.tdhen the sound level is 30 dB? (See Fig. 1y4d2wt.7dr8, wry yyf2–6.)

  Your auditory system can accommodate a huge range of sound levels. What i, xyi kb*jx5 i,;dfzb+* cbxt-s the ratio of highest to lowest in*b,+fxjtk i ,y*; d5z bi-xbxctensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of th2-occ)df+(z ht;o j 1l/aef* 8ryfsfle vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what r/ ;) cet2zlo jdah1 fs- *(yfolcf+8ftension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamentalkm z0 5+h4gdio9xff; y and first three audible overtones if the pipe ;og5 0i +ff9ykxzhd4m 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 thrfsxq0is+j ; 0e top of an empty soda bottle that is 18 cm deefs;i 0qx+js0 rp, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning j9u .z(t;tw yathe range of human hearing (20 Hz to 20 kHz), what would ttzw; ju y.a(9be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thij 9i2ju), 2z ; gd whw,4mrz5*ftatbefrd harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original,z 2r j )u mbf;a i42,efwhdt*gwz9tj5 length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovsc6u u,k oj3ip i04q t2t)eo7me middle C (3se3oomt p02 u ui,tck)j7 46iq30 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 middle C (262 Hz8 u,ccf3 u ug h69u7u6/w,ddirp8oiwj) when the temperature ju8/,76i9c h,c gdo83w6ui u df puuwris 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 21eim)5zobr ee6tx 2(u0 $^{\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 hole pxb9 6uoysm55be that must be uncovered too syp5m9x 6u5b play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, ilyx*,:ht +r khq3 efs*4tp7y but not at any other * th,:y4xi 3qyesf tkhl+r7p *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 tube 1.80 m lo3fs2k8c(tr wmng is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz.frc283kws (tm 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 86rm 9d*sup.wzx 5ftckl;z : d$^{\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 withinc7)b uozb :1+oryd2-nr unj, m the audible range for a 2.14-m-long organ b yr-mzob )ou 1 n+2:nd,rcu7jpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approwp5 hwcf07ty-(9von b tv dni0 .ba0d.ximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to wt(wncdvbt7i09b5hv .o- yfp0ad 0. n 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 tgmrf qgx783go9b u1b2c ::hgpwo strings, one of which is sounding 440 Hz. How far off in frequency is the b:g8pf 1gmrx9 qg c:uo7bg23hother string? ±    Hz

  What is the beat frequency if middle C (262 Hz) an 8v*,ep3-t+ksmkspqnw e. h3 qd $C^＃$ (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) operatec,2avzf0f acy+npq6 6 s at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultfv+ z, acn6y2p6qfca0aneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 0fmqf h6ctake- +gv b/n1c 3p7beats/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 you71bc q a+kgpf-h m/vc3te6 n0fr reasoning.    Hz

  Two violin strings are tunq q-b.ly,4hhz-1scuxlu l d4xw+ 7z/ hed to the same frequency, 294 Hz. The tension in one string is then decreasclduqb-lxl/ x 41+w,.4hq 7us- h yzzhed by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if :xz( l)mx j 4)7njjyectwo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the ot(cmjxznj:l jey )47 x)her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fol5m:d: 0lbrljk lo)8e rks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A anb:j805 :l lod)e kllmrd 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 wa+ 9lf2* u tqg)37dk:.kpnbgri .jqz apart. A person stands 3.00 m from one speaker and 3.50 m from the other. +ui*ga7pl9wznt :)qkr gkf qd3..j2b
(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 tuoob)l*: r xmut( ge:i,ner hears three beats every 2.0 s when they are played togethe:e:g *ub()tmo lrxoi ,r. (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;n-ega(c yu b1 m and 2.76 m in air. How many beats per second will be heard? (Assume Tn ayubg -(1;ce = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1k ge:wy2fv 63q550 Hz when at rest. What frequency do you detect iqgvfwe3 y2k: 6f 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 ( brff( o cm7kw*+lji .*wwgo/you detect if a fire engine whose siren*( grf l/.ww(comjb*o7iwf+k emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mb/h/fx2-pf hv oving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they fhh -bv2xf /p/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 thy:clds r2x,7xe 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 frequencys r l,:yd72xcx the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and v ply443s3lh:h loo..s+u hafjat *;ereceives them returned from an object moving directly away from it at 25 me +a; f4 hoj:sll hp3*l oyt.a4u.3svh/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a walli5j*5t -i 72c3glg nvjnbv0ni at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.ij 3-njt2gc*v0ignvl 7 5i5 bn0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original92i 1:*bn(rlx tjq imh Doppler experiments, a tuba 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 speed of 10 m/s ?t bq(m iil1xh9 :2*rjn   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speed uin;e0zo0 (idk(j l;(df84rzo rnmm9s. 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 blo(mlzod8diin0 ;ej0;(rkm uf o z9r4(nod is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencqhwoat, 8mm ;2 e8+e8jrocpw *y $2.25 \times10^{ 6}$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 velocity i zdm-cxff(6.ui.*i)lv5 rb dis 12 m/s from the north, what frequency will observers hear who are locamd5. fzb uri d-i6*i().xvlcfted, 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 la5 u.i9 fdg3zb.xo+ 1 hfj;inqpnd 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 s*ju,t.vtoitj fu2)soan(0 *wound is 310 m/s (a) What is the angle the shock wave makes with the dir sv *otf ( w,oau*tt0ji.jnu)2ection 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 a/f)- qsnbo3phtmosphere of a planet where the speed of sound is o)fo-pnhsqb 3 /nly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 oi3dg5(4e h urm/s strikes the ocean. Determine the shock wave angle it pr35(georh i4 duoduces
(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 *e- 0h4w 6at6abk+iegxlbg 6s$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhezpq/(s 7( y3g.ybgb**2pbfnir m8ul iad and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distanb i8/ bfs p3y n27**mg(iy(zgurlq .pbce of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulsez/ryq/y4,jz :hkff8mdw s:b29jl m-h s downward from the bottom 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 freshjh s2 :yzzhf yw4lm9:-jr /k,8bmqd/ f water)?    s

  Approximately how many octaves are there in 3pbt g-f4y+vu z :tgo:the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewo*:ezrvcs n 5 l:0v2sqer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bs:5*rel02n :oqv czvsoth 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 cl+m qagjhj.(4 9mto/tl ose to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoesqj la/+g.oh(t 4j9m tm?    dB

  What is the resultant sound level when dtg;:.ekbd10aspkx:;84b uf0 xp fuman 82-dB sound and an 87-dB sound are heard simu08tek:fms ubx ;b ukgp;p.410fad :d xltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What3clrip,-mjk) 1 umw ,hh9qok1 is the acoustic power output (W) of the speaker, assuming w oq,-h)m h1 1 k93,mlicupkjrit radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz.z2vt .ksw 2;sh The power output drops by 10 dB at 15 kHz. What is the power output in watts atz h;vss2k.t2w 15 kHz?    dB

  Workers around jet aircraft typically wear protectiv3f7xx4nnsu8h 5k hlx (e 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(s 3xh48nnflx5 hu7kx 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 systems, theay 7xlpm04 eo.pyt4+r4h dvl ) 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 j)dmc tvv1z kh1ccc+ c(/u2- xis tuned to 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 poin 1+ep*1lleyb kh)deka2r 5af9 ts with a fundamental frequency of 440 Hz and a mass per unit length of yekf2 ll aea)1r 5ep*+k9db1h$6.1 \times10^{-4 }$ 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 verticvdo1 +4p s,*k ulpuq1i7s6tws al 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 from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency us p 171tio4p s+6,ds lkuvq*wof the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is mhoy 1g f9c3r:near a tube that is open at one end and also 75 cm long. How much tension should be in the string if ityrm9 1ogh3:c f is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to j 1.sm67ybfnidt wa8m)*sx1hresonate 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 ka1vtuhk:;;hqfmt 7 6tone in the 500–1000-Hz 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 leve6;u qvhf;7amh t1kt k:l 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 3 qd)nl30fg kjtrain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train aq0 dkfln3 j3g)pproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you isbu9icy-rd6mri u /4 v.ymqx** 538 Hz. After it passes you, its frequenr 6u c. *mr qyuxm4iy-9*i/vbdcy 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 cars just by listening to tc:dk*l 7 sh*,ktu/ni uhe difference in pitch of the engine noise between approaching and receding cars. uc: k*ks7* dt nuilh/,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 frequency of +ll,e t; pv)ieps2wa7sv1z; a 11 Hz. The shorter one is 2.40 m long. How long is the othe7v2z es)al;s+vl1i, etpa;wpr?    m

Two loudspeakers are at opposite ends of a railroad car as it moves p 17itlm 00xqqtast a stationary observer at 10 m/s as shown in Fig. 110ltxt qmiq70 2–37. 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 C?

  If the velocity of blood flow in the aorta is normally about 0.3x2i- iumx.z+x 2 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflexx.-ux+2m i izcted 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/svs4.v 3 q:w)tup8vqq q while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected qvqswvq u q4v 38.:tp)by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses a.ra splpfmos6ak3ix-40/y : hs it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms lonhasy3 fpalxsorm4p k.0:-6 i/g. 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 send signals from one frpb9ok0p 8;z jee27 tAlpine village to another. Since lower frequency sounds are less suscz209teef8jpbr7p ko; eptible 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 to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the p7+m ts-bvjc-eresence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consi v-+mtb-sec7jder 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 “singin tv,,wqn1 ofp:pp9l*qcbw.lv*(cnw *g rods,” involves a long, slender aluminum rod held in the hand near c*f*.pv c9vlwwp(q t1qp,n* b:ol,nw 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 he9q4xh kuqng08aring for the human ear at a frequency of about 1000 Hz iuq 9h0gxkq4n 8s $I_0$ = $1 \times10^{12 } W / m^2$ 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 1fvvf+pudc1 . eq(v *cobserver on the ground hears the sonic boom 1.5 min after the plane passd.v pf vfv(*ce+1q1uces directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb5i:b4r ; rg7vc kiob,c7 lb5wdoat 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