What is the evidence t 1u+,kfa 2tl,w f-vy5ypnfdg4 hat sound travels as a wave?

What is the evidence that sound is a form of energtr bada -768vev5ity f9q1 2phy?

Children sometimes play with a homemade “telephone”q*.1lr1ulne n43 p cgr by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, thg1.uln4 1 r3n*lr pqcee 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 fropelfz9t v trqc,+d8 ;j lr ,v2f+5qfg;m air into water, do you expect the frequency or wavelength to chan+q5fv ,,; ;fv+tc rdzre jlg9lqpft82 ge?

What evidence can you give that the speed of sound in air does not depend signjj1 n faa)2p/makg -/wificantly on-fpj)ng a2/w m/aa1k j frequency?

The voice of a person who has inhaled helium susx dcl+f+*u,rw5-o1dflu b5 ounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of g oa6+zee6.rnhusrf c+4p )g 4organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundr1 -vc mc*chj:w99oles in various frequency ranges. (An example is a car muff:v-9ce c1jmch*ol9w r ler.)

Why are the frets on a g) txx i,/k2zbeuitar (Fig. 12–30) spaced closer together as you move up th ix,2x/t)ezk be fingerboard toward the bridge?

A noisy truck approaches you h6bs5 e7y; s0 qleadh- yp-q1)g jlr*bfrom 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: See Se1e5sys6 e blbh yp ra-d0jq7lg*;-hq)ction 11–15 on diffraction.]

Standing waves can be said to be due to “interference ini0gcy 79xw,jj o9rv6l space,” whereas beats can0 yowvcx jji6r9g,l97 be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency 2cdh2 3;)u z+q*;9qayvbc m gnmj :iwrof the speakers were lowered, would the points D and C (where destructirq 2buj hmc an;mcqw * z:23yd9);+ivgve and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting eee57g(i ;6kf ov rm7c3ay2hu the hearing of people who work in areas with very high noise lev(ek73 5vy i 2u;7mrca6geehofels 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 noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig8m ckm hd-o76j nd-/2ee -cday. 12–31. Each wave can be thought of as a superposition of two sound waves with sli-k m ojhnead762ecc8 / y--dmdghtly different 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 shift if the source and observer move inn k x4;g2o1-qhyrbs k, the same direction, with the same vek2 s4gh-n1 ybok,rxq ;locity? Explain.

If a wind is blowing, will this alter the freque rb /opaqiy,yqa;318 ;rd9u- kerf+qk ncy of the sound heard by a person at rest with respect to the source? Is the wavelength or v r1r,b+keqq ;8k3 a/apf; dyy-oiu 9rqelocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitogw 4),*nnh1uoi1hs g iw.kpldk( 1f /mr 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 whih wigwn1g liufm(,k ps14*1/.n d)kohstle? Explain your reasoning.

  A hiker determines the length of a lake aegsu6 )ah z6 ,8n+jfjjs6 yb4by listening for the echo of her shout reflected by a cliff at theub ayz )ha,6j6se4fn+js6 j8g far end of the 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 bel 9 :)yz g8pc4mops6tm zjhl2(yow 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 at this point? Assume the speed of sound (6)m l4 2pyocyzztp8msjg9 h:in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ink(iirrg)fj1--5 wf *3ob 3.mt hj cmko 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 l2 t8)a/jg vqd9;jqsv of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How)a2v q v8;lqds j/tjg9 much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it maq xbn4e5,,q bsvlh) *mkes when striking the water below is heard 3ls5h4v,e q*qnb) m,x b.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, seek zk346yb /1nj6xa qk9ynb8mes a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: bkneamnj/k96zqy bx8yk1634 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 “nuj( 3kq ti50i5lakw-5-second rule” f-50wua(3q ilitn k5j kor estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound hoay-0b9rwiv*4.jh e*q 2 uzmat the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity euz9u )p-qe/ ;8 e,nlq34qk txrdh:.u -ntg tqis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when ffl 0.t *tfu pqg7ae2u2ired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, no7g02 fuu2t* aelfqtp.t dB’s.]    dB

  A person standing a certain distance from an airplane with four*3 4swx9 5mhtkn mrm qsxo4y549i0s-khuc sl* 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 um0 *ks orl44-n5wy9stxskm *5hc q sxi3 m94hengine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas ei2b4 hmflc,vj2e8-tw)k0jcfor a CD player it is 95 dB. What is the ratio of intensities of the signal and the 42w8vcbe -ft2ic, h)jm0k ejlbackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persocht9oj890g rxwf - 5wun speaking in normal conversation. Us uog9f90w-rch 8j xw5te Table 12–2. Assume the sound spreads 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 ea(u 5b ijmp-rv;1 ei:tcrdrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whil :)rj2+gtr+ fun fng;qp 2js1ye the more modest amplifier B is rated at 40 W. (a yg 2rujgt+: f+)qj2nfp;1nsr) Estimate the sound level 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 when placed 2.*p4mgv/-a* tp ypc0f s8 m in front of a loudspeaker on tgft40-/v*s amp*p p cyhe stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What isqlu15(keek81ekm ( z)tk3-nb, qol ck the ratio ofkulq)m k1kl,z e c5eknk(3( o8tq b1-e the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a s 0yuqaaj*;3gi1/zwd sound wave is tripled, (a) by what factor will the intensity increase? Increase by a fa/u31i wdy agj*sa;0zq ctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amakj(rkuf6as k16q q8 4plitudes, but one has twice the frequency of the other. What is the ratio of their intensitikka4 16qqaj(8 6 sukfres?   

  What would be the sound level (in dB) of a sound wave in air that corres+; gqhz*4 jhm7z2auaiponds to a displacement amplitude of vibrating air molecules of 0 zmgujihh2*4 q a7a+z;.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what oettt/l ;rdv1 :wnu.)sound level to seem as loud as a 100-Hz tone that has a 50-dB td /) vtr1le.wntu:; osound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencip5h3 x19 l3x wxn2dgzbes that an ear can detect when the sound level is 30 dB? pw35xd z3b xgn2x9lh1(See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound a27h s3l nnz: t 5mfqa49t:an ;rxw7qylevels. What is the ratio of highest to lowest intensityqza t7:9wl7n;qh23rna5t ay4 :ms xfn at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a viol.( zxjkgq )1iyd :ubf.in has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, aqf(:zu ydx.bi .j1 )kgnd it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whatl32 i(ll21jsyp247lvws g tah p*q,dk are the fundamental and first three audible overtones if the pip (llp h4sgqi a 7t21ywk 23vp*,2sdjlle 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 wojr6z6jx q, / y3bdy(hzv,fmk(uld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tub6j (zdmz v3(k,j/q,yhxb 6rfye?    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 r *mplx gnlmcx( r--r9,ange of human hearing (20 Hz to 20 kHz), what would be the range of th9rgm(*l rxpl-x-mc n ,e lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency o0h 62q3zb-, ez5fhl rw7p mtbuyhi)6s f 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origi lu2375iw, 6-) z fbhehsh rmqy06pztbnal length?   Hz

  An unfingered guitar string is 0.svoe)sm0b -65 o8uki m73 m long and is tuned to play E above middle Cu0kv56omosm si-) e b8 (330 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 le v2pz xj.w6 9( eqp-2sogsm:qungth of an open organ pipe that emits middle C (262 Hz) when2j9epszqu:pgm-.v x( o62w sq the temperature is 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 lg2 6 +0qylemnxn3f xt:jq4m /20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the howmi b (ig u6q;;wb/:4nnn ga5rle be that must be uncovered to play D above middle Cg5umiwg: bq bi;nn r/n4aw(; 6 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 2jqo.h )0-2fnr; nn:pp wzam k+64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies -0 o+npj:2z;k n)f n.wpq rmhain 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 long is open at bot y-yr 46dpi. ntx16etdh ends. It resonates at two successixtrey6p 6 -iy1. t4dndve harmonics 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 j,/srjf8 ,nws $^{\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 fltny)d5*2ln v or a 2.14-m-long organ pip * n52lyv)ndlte 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 to thf.n 6y69xkzxeil2 2ule outside and is clos6inyul 2f2z.e lxx96ked 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 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 whe 8t u5;*mpr xzkhji / gc,vz/gvpz:l*1n trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the o/t8 hg1*ju*z pxvzl ,c;rvizkp :m g/5ther string? ±    Hz

  What is the beat frequency if middle C (262 Hz), ct ,zu2v.fio and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at hqx31shs9, dr5v us9 fan unknown frequency. If neither whistle can be heard by humans when played separately, but a s 39vqdfsu15h shr,x9shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 bea/ y 1 yycccz:9l/)mpbqafbe,1 ts/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is ,mc/ yyb:)lc yfqp 1 c/19baezthe vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the ,3lkzgjaq ip;.mwld gfe*y:8x4 d17x same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will bej7dz fgwel,m 4x ;ql:p a.1k*xy38 dig the 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 t.fj(l( dwe v(n+5mf lto play middle C (262 Hz), but one+mf.((efv n5 wtldl(j is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, Bb5v m),9g: 1ircxacws, 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.1,vsa ci)bwr 5 :mg9cx 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 stands8)0 t(nr6./2vohbrp q rsn jho 3.00 m from one speaker and 3.50 m from )q2r(rtj.hn sp/noh0 vr86b o 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 ek sx8 :qgn:.+0vmt hrHz, but a piano tuner hears three beats every 2.0 s when they are v+rq::8kxt.hes0mg nplayed together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of waveleng y1i2p u:-j e70dd8 fenknb-jpths 2.64 m and 2.76 m in air. How many beats per- fj2:knjep- i dn 1udy8eb7p0 second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain /x3;d4sww z; ml9fntf fire engine’s siren is 1550 Hz when at rest. What frequency do wsl 94xw3 ;/nff;tmd zyou detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engi 0d7d /)qsayi9of ip,ine whose siren emits at 1550 Hz moves at a speed of 32 m/s 9i, 7/afyi p soq)d0id
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is m r 1,o;ppcrt1q+ cm0lhoving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are th; lq0+tm1,ccrprop h1ey close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency hor2 vkpm-t *5zron. 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. Whar* vo-5k zp2tmt is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50 0xfl5vs-/obp.0 kHz and receives them returned from an object moving directly away fromslo- pbx vf50/ it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at)o/m6 meh0brtq du6 7l a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectq/dm6b0etolm 7 ruh )6ed wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playec *5t7l-f:dvg1u r2hv h0ho*(ysclq ad 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 approadcsyu *q oc2lhh-g vl:h (f71v*t5r0ached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves tw (9k9k-eb +w tdlwio 4g5i;alo 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 directly away from the sound sourlkb9d4wlw(i ta; +ge o-k9w i5ce?   Hz

  The Doppler effect using ultrafc uust 0*)z0z*ax *hjsonic 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 velocityh 82jd0f (v9 oe4ajcde is 12 m/s from the north, what frequency will observers hear who are located, at rese4 (9 hae jd2covj0df8t,
(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 a n 9k*n6a8vmbvi8z9ght 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 souzee*;w m)5 ;pz)nyjcknd is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’n) mpe *;czy5z) j;kews 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 atmospjv0 y 1z 5j6l2gyj4rgdhere of a planet where the speed of sound is only about yg 45ylv16dg 2jrj z0j35 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 8qnq2 ;0qmeixwui u4*3 500 m/s strikes the ocean. Determine the shock wave angle it produu2i*0qui43 x mnq ;wqeces
(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,ta-..b wzacao e(x 1$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhe25x -nbss4tv,3 uev +.mblyol ad 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 distance of 2.0 km. See Fib tonl mlv4.+ sxs5eb3,uvy -2g. 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 p)e8*wqk5fp c *(9q7y/ozvl9 q ul ofvaulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to workf)y9f9p7 qcv*wz(* /ole 5lvoqua 8qk is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octav/g*vt8 vajm6by 8 ydf8es are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of x (83knxbbxg 3many plastic pipes of various lengths, which are open x 33bk8 (bngxxon 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 thres(g+k rffc8l4ndw7 uk /hold of human hearing (0 dB). What k4 (+c8ffnkdlwg/ r 7uwill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and,).cj6 j2def7gjk erg an 87-dB sound are heard simult2 gjc 6edjkj)e.grf,7 aneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dc(a/ f*q bvj9g)m,depB. What is the acoustic power output (W) of the) e p9,(qd*f mabj/gvc speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ou/.y)cf0iz uln tput drops by 10 dB at 15 kHz. What is the .i/l un)c fyz0power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ovjykj 0alj9ul4 e5/1luer 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 y/j5j9eu1 jll k0l4au would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicationsnob /m/ad/iq1hh dh4 ( systems, 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 pl3xy lzg9lau,4 -+2icea .bvin 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 vig -vqm01 wkakt4x91-ibqgs2a olin is 32 cm long between fixed points with a fundamental frequency k2q0q1g -kxm4v i b-19 gtawsaof 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 noj8 r*c:(bvy filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so,(nj b8vo:ry*c 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 of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open ab07s-t fl jh3y4j0grv it4v3bt one end and also 75 cm long. How much tension vv0h34fj74gt l-bi sjytr0 3bshould be in the 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 resoemk3noq 9g8epcy ,- 1mnate 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 inm,dx863 hwaye 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 level is minimal36d y8xhwe a,m 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 8i . 9:pfypbkq7b a5h e1o-ykqstationary. The conductor on the stationary tre qyhb .a87-b9 qkkiy:fp5p1o ain hears 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 kr:*zuhcv+1qs,s ;i 9;eruimapproaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume cone:rz9*uki; u,+vci;h1m sq rsstant velocity)?    m/s

  At a race track, you can estimate t0eit uhfv+o +84d r/czw/mv-rhe speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) av-+u/z ew/v8drf r0t 4oic+mhs it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beatgd ody3 b1wg8/rmq07t frequency of 11 Hz. The shorg0r y dm/3q 7b1godwt8ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad carsw l3o-c er(zhhl0i .((a k1yb as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he 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, aehc(alyz k(h-i.(b wor03ls1 t C?

  If the velocity of blood flow in the aorta ko j p7jq*tdw7;3 chc0m-r k2ois normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves t3q; jc t*dpj7wh 7crko k2-0moravel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth ezh-vpd0t f:nv (e8(gat speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/-(z v( :n0etgvfhdpe8 s The 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 series of high -/m:b bxbryfba u79z.d-tv5g frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long rg-bx7 ut- 5bfbm v9:ya/d.zb. 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 too-j+a z6w,nejy-y4d6 lq y3vc send signals from one Alpine villagoev+-jcyq ,ly43-y nw6 da jz6e to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence ofo0,iwh)uek c/ standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 muei0,)ckho w/ 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 lve ymd u2csikcr5/ m.cc-n*1 -ong, slender aluminum rod held in the hand near the rod’s midpoint. The rod in c*i.mc k suy21e5/ -cm-dvcrs stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear ad1q q--d/vltmuh) /dysi8, jk t a frequency of about 1000 Hz i,m-q-dlhdut1/kd8qy v)j /s is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the wf6a(4j op5hrsonic boom 1.5 min after the plane passes directly overhead. What is the plane’s5rjp 4wof 6ha( altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is m*7cji4-;fgwa0md0hm qd *oa ,+l*buw cn1em15 $^{\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