What is the evidence that souwh tr)pj +.di141foipnd travels as a wave?

What is the evidence that sound is a f u)3fx qe4p8)tkvbc4g orm of energy?

Children sometimes play with9j kggekot,,)2xgw th 262qhv a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the strinqh, gkj 2ggevx2) ,9t6 2kwhotg is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into/x.ng5) ilwd i water, do you expect the frequency or wavelenw/.5inigl dx)gth to change?

What evidence can you g.iep f1 injqjk;s d*s.8uuc(.ive that the speed of sound in air does not depend signifi iq.(; s.8kndue1 *cspifj u.jcantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched.d 6ewuc/1x.yf Why?

How will the air temperature in a room affect the pitch of80 au1g*0f5 u tz kvkm.ze(fal organ pipes?

Explain how a tube might be used as a filter h e ecq04htt/6 //y;jbg5thmtgmt 7 c8to reduce the amplitude of sounds in various frequency /jhg/q c t /yc6h7 0th;e8te4tbt mg5mranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog4-3j/upj qg;hl zx ;wjczn (-xether as you move up the fin j/gzl 3z4px;qjjx(-ch w;u- ngerboard toward the bridge?

A noisy truck approaches you 97s7ttx ) ,(h2 plzn qgd4ys.npvqi 0cfrom 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-frequency noise. Explain. [Hint: Se)9x ncs(q hd,lpvz nti0t27 pqy4s7.ge Section 11–15 on diffraction.]

Standing waves can be said to be due to “inte vc+c 0o+anx+:9vu rquj gl6;wrference in space,” whereas beats can be said to be due to “interference in time.” Explnxurla+ w+j: 9+ocgv 6c0q;vuain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points bn.hqer)gc9 , 1wve 7c4n wox3D a3co9nge .bh1xq4cv)ne7r w,wnd C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who worq l((gn8q l.ys dss:f4qgr5f l-ub1q;k 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 sqgq(l y; f- d(8b:qsl1.n5lsq4 rufgto the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in F b(6icblc8 bs sstj73f )2q1m;g:fgdxig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly differen3f1dtgs :lfi) x7cb;j 8cq(m b2bss6gt frequencies, 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 shifvb5)2(9lka d m, pdvvifz p.n8t if the source and observer move in the same direction, with the same velocity? Explv.8bdv952k)vi p( fn,p dm zalain.

If a wind is blowing, will this alter the frequency of the sound heard r 46dzvh+wup5 by a person at rest with respect to the source? Is the wavelength or velocityvud+4 r56zpwh changed?

Figure 12–32 shows variouet kh,5b vw:2fzr/m,gs 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 reasoning. ,e/:vr5fbzt 2whm,kg

  A hiker determines the len 7 hn.vqlgt8v(i 5bv0b gzs/9fgth of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the eg5 vbhv87tflqi.b0 nsgv/ (z9cho 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 waterline. He hears thev( tm+z-9+r-gxj a,j9e nxy gz echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at t+jr- zmn,a tgg 9(xx+v j-yze9his 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 wavelen*:p 39i sazzcii3 0x 7ukusn(sgths 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 above a school pb m: oz)-izl9of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). Ho9-zim:o) pzblw much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cli ne)prq+1;v jfff. The splash it makes when striking the water below is heard 3.5 j veqf1r;+)np s later. How high is the cliff?    m

  A person, with his ear to the grouw5 96t0hmu ftz(+ghes/j xz5h nd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other 59s5 0u hm+xhfj/th6z (getzw 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 :jg6bxp k0 w;kr/n ,lzapfp).error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike k,f 6 0l;gj:p.wp)x/b zrpnk aif the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pai,6s6a,l gwrg dn 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 levelz d.kkry4(env t7 1jp( of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prodb,:nxpkpud f 1.uw0 s;xa 0av)uce a sound level of 95 dB when fired simultaneously at a certain place, whatvfa dp)u sw010:.ap, ;xknxub 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 airpla s wtftr.+bp;kv)+d)2 01qbtct bx y:b d9t:fqne 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? [Hi+ .; twd:ky f 2 )vtsdtpbrtcq+)9bbtqf10x:bnt: Add intensities, not dB’s.]    dB

  A cassette player is saip*kt18 -b 9hrifhdt d0d to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgro9hft0i hrtb8k 1-p*dd und noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound f6n. *nc9aoff from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rougfc *9f 6n.oanfhly 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 eg:s 9w s5/haq r1jse5an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is ;xl4evkg m5c ffe) w4bnx-m6,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 loudspeaker connected in turn to each axw m vl efk4mx6;4b)cfen ,5-gmp.$I_{250}$ =    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 dBw 12ul h+0a52uztyna) d7anu mad 7f4u when placed 2.8 m in front of a loudspeaker on 1a4a7+nu2 faud5)7umy h02az wtndul 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 typicallyjw:g) /m oaf.t detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes ofo:j/wt)m a f.g two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tri uqj) wig7i6*spled, (a) by what factor will the intensity increase? Increase by auqi7*g 6sji)w factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitu,v7tlj mbia mlmg+ +mvinz6s+20--esdes, but one has twice the frequency of the oth2im7l - s +,+m nvavb0etgz6s lijmm-+er. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound-uwuqz, v eq-8n -wkn; wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at w;q8 v -ke-uz-u,wqnn 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1q6 . +igx*zt 8 zgc;hxazaqr5g1wq63p00-Hz tone that has a 50-dB sound level? (See Fggw6qzzgtq 18i.*3x5xr q +6;aphaczig. 12–6.)    dB

What are the lowest and highest frequencies th z+c+pg :y4.blr zk 3.97gssb:r vhw*tfpwt u(at an ear can detect when the sound level is 30 dB? (See gt(v++u*w: br 7s:.fbc3kpy h sgzw.pltr9z 4Fig. 12–6.)

  Your auditory system canummmb89z /k/01ulgsx accommodate a huge range of sound levels. What is the ratio of highestbm01mks lu98/mz/u gx to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Huu ; g2dyra:0wz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must20y;gwua rud: the string be placed?    N

  An organ pipe is 112 cm long. What are tp q *gu+a-o imgzin7,90l5e nmhe fundamental and first three audible ov0,mpan*q u9 -+lgo7zemigin5ertones if the 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 s hc hg9t-tqoz6j55g/ of an empty soda bottle that is 18 cm deep, if you assumed it was a 9t 5- /shjg5hgoqc6zt 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 rangeofp:q;mn2y5z f7x3 ow of human hearing (20 Hz to 20 kHz), what would be the range of the lengths y5q :2 o3pzonxffw7; mof pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third h)e*omnlds 5 xwp cxe((s8j9 s8armonic. What will be its fundamental frequency if it is fingered at a lenx8d(x8 nc5se)jesl (p s9w*om gth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mid baw:70 /pvhuwu6kuq(dle C (33(hvw bu:7wpquu ak0/60 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 ax pfm h6es9:,3 ;xtliyy;s* bC (262 Hz) when the temperature is 2xsyx p,f69y;*sebi;m:tlh a31 $^{\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 2y v/irw;5s4izdcjq5:bz g- 0f0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examplz5o v2tt(+zo be 12–10 should the hole be that must be uncovered to pl5z bt2zot+o(v ay 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 H :z8sco 7yn.bgff3 to7z, but not at any other frequencies in between. (a) Show why this is tcs byfo.:7og z3 n8f7an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two sucgr/wjqlon 3/ 51oc wh,cessive harn,hcjow/o l3w/ q 5rg1monics 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 7t(: 8bt 5z0y+veh s(omncbfa$^{\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 ran 4. lbgwt:bp7nge for a 2.14-m-long organ pigw npb4btl7.:pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open 2l +bsdtsod. 3k 5qpx4to 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 c p.+3 5sldo4qx b2stkdanal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to wompn xs sw tl8*710m9adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ± t8 0l* m7xmw1s9n spwo   Hz

  What is the beat frequency if kl -yc7 lbr3dfw9l ,t2middle 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 s rqw.m+ ;v/pvkHz, while another (brand X) operates 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 tr/w+.m v; pqvshey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning f8j; c:/ dsiquhork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your 8i ujq shcd/;:reasoning.    Hz

  Two violin strings ar cz; 5 j2vnuxb4c5jx9qq.u6wre tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togeth xz9 5xrquwv;cq 6b4jc.n2u 5jer? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes ea,7uegb7lxps)ax;fy tzs8 1pkh 4 cn+ 6ch try to play middle C (262 Hz), but one is ) g8skxest lc74p +y a71fub;znxh p6,at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fc,a4lgi , a/tcrequency of 441 Hz; when A and B are sounded togec al4ic,/ g,atther, 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 ep/01ja you.,zb8gqy-s y *skm apart. A person stands 3.00 m from one speaker and 3.50 m frq k- 1uj z.8eagb*0,po yyyss/om the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hearh3 2mov8a3stt 75oglscy: 2 evs three beats every 2.0 s when they are played together. (a) If one is sl57vm3e:23ht ctg8ovoy 2as 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 r 01q-lf( vzzt2.64 m and 2.76 m in air. How many beats per second will bz01-l fqvt( zre heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenu u(az,hpg42 1dwrq;wcy of a certain fire engine’s siren is 1550 Hz when at rest. What frequegru4dwwz;q( u,2 h1a pncy 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 aabisc-x /7 yvi-h /6yhc 1 pzkmy.u6(j fire engine whose siren emits at 1550 Hz moves aibyhi 61c k -a zyc(.p-/smhx7yu/v6jt 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 towo0s3c1p21 y8kx p;0 vr ltcup2qbhg. pard you at 15 m/s versus3tppb2;v kpuxpcqr .hg 8l0o 1c02y1s you moving 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 eqxy+bnv-a:j (zuipped 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 beayz:(-vx nb a+jt frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.2jijbv. 9 n7sq0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received souiq7 jb.vn9 sj2nd frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As n)jt uvzf+ivx86 )8+0ledd o( vgct p/it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in th6fte+8nld+v vg )zd(x)ptou 0 j /cvi8e reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a 7+ 8l: ox;rya h1ik1un+( zgzhyt ,o4exh:nbd tuba was played on a moving flat train car at a frequency of 75 Hz, anh z1;ne io8d1 yug+x,zaynx l:b hr:h(7o+tk4d 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 ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. q8dj kn +.qsk,jigz**Suppose the device emits sound at 3.5 MHz, and the speed of sound in human ,ksj.zig+ nj *8qdqk*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 directly away from the sound source?   Hz

  The Doppler effect usingiy52l0yb . 5t eolh/je ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity uv ycyzk46qm0 ygy ; omqo-j9jh96+2zis 12 m/s from the north, what frequency will observers hear who are located, at rest, yg m z-26hvm6y9o9qo j4uyzqy+j k0;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 spe hlrb8kb77gfw us;.z;ed 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. lf cddz0tlaa .5+6i8k3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mo8 f0+zl.aaik 6d dc5tltion?    $^{\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 wmcykzc07 v w j lc(pipj0:-qaaa6u:/,here the speed of sound is only about 35 m/s cc pmjuj- ly ,qz0c7iaak: :a6pw(0/v
(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 tm z19r9 co 60y+qwavldhe shock wave angle+9ycova9rq m60d zl1w it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle dh2+1epg*0tn c(m: f */xeu.ya+cygjx) uxh v$/theta$ 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 kmd0bn 3/ qjn zqt5d tvamz2i4b x)3 *xll7.nel. above the ground flying faster than the speed vanx/qz52l z7 i.n0njtdl. q m3bd3tex*l4 )b 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. 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 pulses do/ vvd)kzdn4 odr5.hrgs91p *twnward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is v zdg1/tr9)pord*.nvs dh5k4 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there inrv qlb b;(fjm ;b0j0ee8 0ube4 the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consik2 4g.aldlo :nua7h :gti-m :a(gz a.asts of many plastic pipes of various lengths, wha47a m.gza:( .o:lg:-ldhguaat ki 2nich are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the 68csxleihx8- ,l v 8bgmba9 h+threshold of human hearing (0 dB). Wh6e- i+h8 9c8amlv8 g,hx blsbxat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sou6gdfb(p 9 2rf .wwr,dh*nj7 kynd and an 87-dB sound are heard simultag6bfkpd9r wh2*w rn(,f.jd y7neously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1(pahef)fgoh ,,ri 0) q05 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direction g h) ore0af,,)(pifhqs?    W

  A stereo amplifier is rated at 150 W output atvzd; 99hcrw .f 1000 Hz. The power output drops by 10 dB at 15 kHdv;9 9r czw.fhz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protealhjf1+f1i b o-t2fm) ctive devices over their ears. Assume that the sound level of a je-m2htbf1f)f+ a1ljo it airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sy-unv*q.izp/34 lw addstems, 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 viol*vy qqjpuzy: mt: dlfbz56 :*.0-looqin is 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 poi0s 5drj6z1jac nts with a fundamental frequency of 440 Hz and a mass per unit length of0ca zd r561jjs $6.1 \times10^{-4 }$ 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 *2u uek ;yngo9wkl3/j 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 frequg /ukjyn3 29 kl*e;wouency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a t h7g;vzr0f l vb4;li(3r g*mgjube 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 (inrh;g*(gf zm iv 3lrblg jv470; its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full8ca3ku abeg(o533so u loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range comin+hvxegx)y *7i lku0b42 6jlskg from two sources. The s l*lkx)0exk4b 7h is+gy6uv2j ound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train isc 3s+ g 4pd6pnbh(u3ss stationary. The conductor on the stationary train heashsn33pgucd p6+s( 4 brs a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. e./lfk54w utv After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume/fw ve4k5. ult constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening hg mckz3g;t8; to the diffe; ;chztg3k gm8rence in pitch of the engine noise between approaching and receding 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 fql3x o iz jp8+eqkt.3-requency of 11 Hz. The shorter one is 2.40 m long. How long is the otherejq83 z3-lik.q oxt+p?    m

Two loudspeakers are at opposite ends i jon6wzwch yl(34s:4of a railroad car as it moves past a statiww zhc(oy3nsi 4j64l: onary 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 C?

  If the velocity of blood flow in the aorta is normallt wdehbr7vo2.lg )7x. y about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves wex).wh7b2. dvrgle7 t ore directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward3nu3t pknb;50n(av il the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequeni3 l53 n(nabpk 0tu;vncy 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 mothv0,s4)ks ug;kyr;s/qqf ncg1 . The pulses are approximately 70.0 ms apart, and each is about 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 ne/ rfkgk v);;uqg41s 0ns,syqc xt chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signalal j r2x4 a-7-8 ptxsiucu0umzlb:q6.s from one Alpine village to another. Since lower frequency-q8j:xu al2rpscbu4 xuz. am -70 il6t 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 to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pres6 : u m4qpyt1cu7h7rojence of standing waves, which can cause acoustic “dead spots” at the locations of the pressurhry7o64u 7qpj1 mtu: ce 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 rods,” involves sj6n)2xgz ro*e2v iwdku5:a9a 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,” o*i25ksoxeavj9 6gwd nu2 r) :zr 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)9qk7z jdoc 0q hearing for the human ear at a frequency of about 1000 Hz dqczkqj) 79 o0is $I_0$ = $1 \times10^{12 } W / m^2$ 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 observerl h;yuly*l ,,)o.xy+-no9 w0+sa+nk b kucndl on the ground hears the sonic boom ylx 0yow*uhnl,+ nn-kkya.b,s+ ouc9l) d;+l1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 41*f:rjzcke1 8 d24afql wqll$^{\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