What is the evidence that sound travels as ag wg-if(mi08u wave?

What is the evidence that sound is a form ofp)qwl7oha2y q9bp 3p2 -mc8gn energy?

Children sometimes play with a homemade “telephone” by attaching a string )ng0eiw/yg ) gwx-4uzto the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels frxi0)- gnug) 4 /wzwegyom one cup to the other.

When a sound wave passes from air into water, do you expect the frequ p7wyp*gew +rm5d ks795j vpvqyb9(v5ency or wavelengt*9vw bp9py5jg r (5pev s7+y7w kdmv5qh to change?

What evidence can you give that the speed of sound in air does/6;njzgvhm( qn9njmyqvp58 8 not depend significantly on frepq8nm( jm/v;6 y9zv gjq58nnhquency?

The voice of a person who has inhaled helium sounds very high-pitched. 9 ..fekamx q4(vehjj6ul n+cm7sy 71k Why?

How will the air temperature in a room affect the pitch of organ pipe-kc ;0kn 0si s0fn6ca5tn bprj.i3g -gs?

Explain how a tube might be used as a filter to redb67 iaw-2w-kn n bnr2duce the amplitude of sounds in various frequency ranges. (An example is nd-n7- bw6inba2wr2 k a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spbc90 751xpw g*pzkugv ra-h)qaced closer together as you move up the gq17zp9w apcbhg k*uvr)x50-fingerboard toward the bridge?

A noisy truck approaches you from behind a 1 g xde*0pvj3k8w qgd4building. 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 Section 11–15wdpe1gj3k x8qgvd*0 4 on diffraction.]

Standing waves can be said to be due to “interferenepe)k.bi c4 .rce in space,” whereas beats can be said to be due to “interfepr) e ebc.4i.krence in time.” Explain.

In Fig. 12–16, if the frequency ofa)q c +nlt,a7d the speakers were lowered, would the points D and C (where destrucn dac) tl+a,q7tive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting th wszh3dlsd 8, 0,t6kime hearing of people who work in areas with very high noise levels have consisted mainly of efforts to blockw t,mss3d6lkh d,8i z0 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 Fig. 12–31. Each wlh8o,j0*, bc0h ypeu/p maf .cave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component c0bco p/pl.*hy fu08 m,ejah,frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the s o / ;ue q;oo)i:x3fk/yr xxsrbn.hgll/ (u+q+ame direction, with the same velocity? Expl//ulf+) yo bx. so;u+qgr ohx3x(;ki:/ln rqeain.

If a wind is blowing, will this alter the frequency of the sound heard by a perso)zc4uhr-;c( :jsntb v2vt -re:r a )eon at rest with respect to the source? Is tce:h:r(c-v4tv;2j eb)onzs-)r utr ahe wavelength or velocity changed?

Figure 12–32 shows v4x3 t:h f4. k*crovmsaarious 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 hi*m. xr: o k4av4h3sftcghest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ekm i.w2s,y vk;cho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. ,yim k;sk2.vw Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hearst /u;4 .yu0+csicsrln the echo of the sc.tc04r;+y n/ul ius 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 in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airm/ r b*7qd,rj pc09s4/cmwot y 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 of tuna on a foggyr -kpt+ )lrg9t+0jzm.y-e( hu kjb7gz day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before thebgg9 zekr7yjtruh- .+ lp-km t0( zj+) 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 makes when strikingl/ r/x1, dsebm+ nu/oz the water below is heard 3.5 s later. How high im,lun//s1 o dxzb+/res the cliff?    m

  A person, with his ear to thet8e3a/..rk wljzl woqx6k- o2v; sie( ground, 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 in the concrete, and they are 1.1 s apajook8 ev/t3 i.lrwe-lszq;w 2ak6 x( .rt. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made8yysthp ;, i8q over one mile of distance by the “5-second rules8y;y ptq,8hi” for 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 ac np n rj.lwt79unc7cn:imbzr 1*(.e8 sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level ofwdwg r6p9 v) (14ltuaq a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers d:k mz9z:jqkjk*zm)a:wflh1+st nl,r( +; xg produce a sound level of 95 dB when fired simultaneously at a certain place, what will be,+ :nr ksgwkjk1mm:ahqj z *d x9;l:fz+l(t)z the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equagm vbv,8:mr r0lly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensitieb :0m m,v8rvgrs, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas p (/afg hr)gei6x4 3ldfor a CD player it is 95 dhd6g)43r/ fxl ig(pae B. What is the 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 v9xa9lhclvt 1 g3cz4:of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over 1az9vglh94lcvtc3x: 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 st 7v h-,xcxka2l igf4(3 +uorct.ka1f vrikes 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 is rated at 250 W, while the more modest amplif/ .m, jhdinwq(ier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspea/nj.wm h(iqd ,ker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in oneiqimj :4 0 *xy-is(front of a loudspeak eim iys-oix0(4jn*q:er on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB.(qtp, 5(c,k f5enyz6g cs4v ph What is the ratio of the ampln 5p ect,6vq yh4f 5kp,c((szgitudes 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 factor 6/ao b l)dd paw/n96ozwill the intensity increase? Increase byaa o/dn9 dpw6zo )/6lb a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has;n8. eep hs b3doi*/hu twice the frequency of the o./phi d ;ee3*ushn8 obther. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a soundrbhzt ,l. t yv,:8nyou;rn,; w wave in air that corresponds to a displacement amplitude of vibrating air molecutnb, ,nh r,lvozry t.yw;; 8u:les of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lf cvp81f5wm.f evel to seem as loud as a 100-Hz tone that has a 50-pf8.wvc mf15 fdB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequaq b)kbqo,;2s ofjwgw)qw)6+encies that an ear can detect when the sound level is 30afooww2qj), )sqb6k+gbw;q ) dB? (See Fig. 12–6.)

  Your auditory system can acco6fi.nbxcr n9f.t4:jmn y*3t*2t xvcmmmodate a huge range of sound levels. What is the ratio of highest to 4c:nyxvnm6*x jtm b 2ft.9fti3*r c.nlowest 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 Hz. The length zallgg3p+l5)42 ra bo 4guh (rof the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strig4 3l+(h2z purl5l aagr)ob4g ng be placed?    N

  An organ pipe is 112 0t5uj0dp th;c6e2z*l t g7tf ucm long. What are the fundamental and first three audible ovtl 027 g f5 t*z06thcu;jdupetertones 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 be uneu+ok 9/h1 zyd7 w,yl,4cacross the top of an empty soda bottle that is 18 cm dee k1b 9uzudc ,ew+47yeony/, lhp, 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 the r2lnk2 em5k0brange of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes r5nl rk 20k2bemequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third har49 w3oyv8ow mmh.ps0vmonic. What will be itsy8s omwh4v.vo90w3m p fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovenzv64 .go-x ne3a*wno middle C (330o3a -w*v4nnze o .n6gx 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 Hz) wp hzy,x0;0+g9mgd syc r9y, lwhen the temperature is 21 ,phzm;ysgdy9 r0cy +x9 g,w 0l$^{\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 20o)gk3a e9qe9u n9tz( q $^{\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 hole71b9yqh xp ih2 be that mus hy ixq9bp271ht be uncovered to 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.bvh,qu 8re0i at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequenciesh0qeu rbv8.i , 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 long is open at bothwxu, w r:q-3ts ends. It resonates at two successive harmonics3q,-sw:r xu tw 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 3. rhcktw)8i:fhpo5g9kz1d z$^{\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 ranyxu+ptdjbx.x 5 uvv+- rc5.(age for a 2.14-m-long organ pipe 5 - pb5(ax.xrd c.uvvx+ujt y+at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ik5fmu 26kl)tc s approximately 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 stan5 k)t2kmfl6u cding 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 1fog9*p (y ouievery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ±9ug1 (i oyp*of    Hz

  What is the beat freqfz *ydtp/oq+38f-4xnxf4g b f uency if middle 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.) dpw8m*yn l*q5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humansqw) *pmndl*y8 when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wiyh i18c,e c7jrle 5uct+6jlt9th a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibratjt r+uch t i1yc,j5 9lc6l8e7eional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The nn/l0w2pzj+ztw1s( t r /tl:rtension in one string is then decreased by 2.0%. What will be the beat frequency heard when the nwrp+ 0ztznj s/tl12wl/(t:rtwo strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flkmu;l e*5+zh sutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at lz5 uh;k*e+ ms25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz f(s1-q qtp9vg1/zg pj; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, tf(/vq 9t-ppj1ggsz 1qhe beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one sp6hoo rkh:/gv .yw zrt56rb1h9eaker and 3.50t6bh rry1rg6k zw /o9:h .5ohv m from 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 tunegy ohyo/ pu9oh7j0 +3yr hears three beats every 2.0 s when they are played together. (a) If one is vibrating a9yg yohho7u /y+p o03jt 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 wavhzt y5l3h)d.. kb7w m- 2tt(hv 4qdxdh(gbl)jelengths 2.64 m and 2.76 m in air. How many beats per second will b)hyd7k) dttqg .d4wm35thb.-v( 2 l hlh(bxzj e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginyz;t rd w-wq p7k0.yp,e’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 0.;prq,-wypk7w zy d t30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequykjd5 ;*3.,b dw qka0tfn i6vcency do you detect if a fire engine whose siren emits at 1550 Hz moves0bdt *ick,y6 ;qad3vf5 jk. wn at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift w76:n9h2rd r ykjs+lm in frequency if a 2000-Hz source is moving toward you at 15 m/s rr+yl n2k67 ws: dmh9jversus 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 equipped with the same single f-9)fktze 2ui qrequency 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 frequence2 fkq-9iz ut)y the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receivesiz3 juyrp9uf7n 9ca+49ot+;sc -e7 oynt*fhd them returned fr3p-jue*df+7 oyuc9zrn yfh+ct9 ; saont4 i 97om an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sp6yxqrl 3 vbizdkq;(w3m1cnha 3 w)xu.b.dn ; 5eed of 5 m/s As it flies, the bat emits an ultrasonic ;hl(v ay.6 wd w; x)kxq.3r iq5m b3b1udczn3nsound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving 5w dngtkqpg 5v8;h8 )qflat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest 8kn) ;pqg 5 q58vtgwdhin 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 r(km c-;f6xr mygs 2kgvv4.h) :l6vmj 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 4rvrl v :xvj(gfmgs6 m2-.kmyh ;k c)6m/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 using28c mey7+w0brs ..gf-nv-iip; .j onnv euii. 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 sounu. )/ xvemwv5td of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency wx.t vme5)vwu/ill observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 2/,dm+vlnolu v/ xg(.b t,qql00 $^{\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 M 5lcsut ,f4+htp/g2axrzc2a 3 w:cdsb7 (sxb*ach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shocksca7c (+abblxpc dhf*u w53g 2 ts:ts /4xz,r2 wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of x:df5mv;gy yb4 8gx 0osound is onlyfy ; o:gvdy0m gxx8b45 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 m/s strikes the ocean. Dh1 oy07l6jnjzetermine the shock wave angle it pjj 6l1zonyh7 0roduces
(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 k:4 fb.6qc5bsk nr+ mz$/theta$ 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 dwel 3xeg0t0dpj7k;k8 k9dt ,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 distt0wg0,9p7 ke k; edd 3ktjd8xlance 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 dej0 o cbg00nmq+ 4g 16tcushxv+vice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it to40 c+vcmgg0nb qx01s 6+jh uis designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human aud6 uxwt+tir7y e6t1*h wible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pip;c: t2pjrdu2+kffbe 3o. 5gpl /m6 wmqe symphony. It consists of many plastic pipes of variouf 6fm2 b/ldk 2mw5optg+ .eq;rcp:j3us lengths, which 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 thresho, 9zs:s n0m7i:r0 t )ttqy nbtx)p0.c 8gqnfknld of humanb0,sx0.fgs7im nn: qz :kttpnq0) c t) ytn8r9 hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sounu6y64w:*3amhbo eg hz/m5b lgd are hea43lawzm6 g:gy /6u*oebbh5mh rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in tuj6 u. dponrdka0b36+xcy 9f;he open, is 105 dB. What is the acoustic power ou 63r kbpd0. dx9nauu6f+yjc o;tput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W gp;a3 6ljbm.vt,x,()nk jplhoutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wa)(b3v mng. x6t; japl,,k jlhptts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices.41ohp1 jl ;apskrht g8kx-2m 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 radiuo24.1h hl;8tx kp1gr a m-kpsjs 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 systems, the gail9*2y3 nhc:s tb36 4xdkd km4tbf uw.in, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a freqaej7,4/awdvjo 2h 6rcuency 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 points with:tq6x+a mlr7f6 br;m0s tpfj( a fundamental frequency of 440 Hz af6 +bq07rpa:xr6m tf(;slt j mnd 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 ab 0coabl) as9d65k, uj;hrh+r r)mx7a 5q3aq filled with water (Fig. 12–35). The water level is allowed to drokhbqd5xr )rqj0 rs;3,aha+ uaal 7c6m9a )5o bp 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 of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is ope s nw sjxobfs2jf7q 42z(5vc;:n at one end and also 75 cm long. How much tension should be in ts(7jns z4 :s;qv j2x5fcbwo2fhe 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 resonate as one ful5/8nr flcg4h9 h kw:snl 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 rant;vek1wc*p( u a r /(l3myvfr(ge coming from two sources. The soundp3 1 vv(fe/w(u(yl ra ck*m;rt 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 is stationary. The conductor on the ek;,i1um /iff9qh8g koj 4ib(stationary train hears a 3.0-Hz beat frequency when the other train approaches. gifkmj 41i /8f ibuh,o(9; ekqWhat is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. rh/-78jf 0xb5kak0g/xj z f zw-px2soAfter it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)s-5w h7k x/f08 a0zxkjopz r /xb-fgj2?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dimyh2 f:l5qj1br f 3w/lzxn(ym-5em9nfference 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 goe ll-5xf9by(mh1re5 q/nmfwn m2: 3jzy s by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency,iu67cmq294i( ybynxp y+xif of 11 Hz. The shorter one is 2.40 m long. How longuy iypbm q64 in f(+xyci2x79, is the other?    m

Two loudspeakers are at opposite ends of ry5qcs+fq . gtm8 o9 f l*1j*r5h/rt m(g2fboza railroad car 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 i1bo2mrm+5 c sfyqrl zr. th*o 58g(fgtjqf/*9 s 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 theul.) hd9sb.j/wo4 m rv aorta is 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 th/.4ru.o9)jblvw s md he waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth a,av q+s:, dnwmt speed 6.5 m/s 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 by the b+wa,sq,:mvn d at after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Thep0j+(w v3jjo3v jt pd9 pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can tjj3opwj tdp +09 v3(vjhe 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 uh 5m),q q7xhyxsed to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which over, xm7y5 qqxh)htone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pr gst:sx zih;;*esence of standing wat s :zxi;*;gshves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv fd1s .b1bfajbb 5*kxhn5t;/x olves a long, slender aluminum rod heldb1f;tb 5ajd1hnk . x5x*sb /bf in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human y f4 .0txvh6kwqpl/f; ear at a frequency of about 1000 Hftp /ly; x0.wv6kqhf 4z 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 Machhp,wncv 6wz9 )px/m sitf* -r) 2.0. An observer on the ground hears the sonic boom 1.5 min after-9nrsw)fxvph w 6 it)*pczm ,/ the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 wcd-mw7z xbyhb6*cm:n p0 t+*$^{\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