What is the evidence that sound t:4 f+orfqv wt):zednqu 7j+jf5a9, weravels as a wave?

What is the evidence that sound is a form/dv3nprk8.q.,m )wvt1jpayd2 ,kkm w e4z f 3r of energy?

Children sometimes play with a homemade “telephone” by attaching a stringc+ rmmlzuk u 9 zuxep3j2-3sxd2ju490 to 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 from one cup to the other 4+m3eu lp0cj2s x 9-kj rzd93mu2xuzu.

When a sound wave passes from air into water, do you expect bjrbiw4 -r: w/the frequency or wavel4/ b iwr-r:bwjength to change?

What evidence can you give that the speed of sound in air does not depend*lr+qb wg er02 significantgr q2b 0l*e+rwly on frequency?

The voice of a person who has inhaled helium sounds very high-pitchitdt n7x i5r h10cw2e)ed. Why?

How will the air temperature in a room affect the pf o)vx xpf;/zq+/w 9*pg d*jkf+(wcititch of organ pipes?

Explain how a tube might be used as a filter to 0 n,iiyalwu81reduce the amplitude of sounds in various frequenci ,0wul 8ynai1y ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced g6k4,glhk)uw695y qzklind (closer together as you move up the fingerboard towar9ylqkz4,k( 66n hg g)udiw5lkd the bridge?

A noisy truck approaches you from behind a building. Initially you hear it b8o/025il xcgzz puvs3ut cannot see it. When it emergessu8ix/c3ol5z0 gp2v z and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” w a jvglyc).51phereas beats can be said.al5vc1 gyp) j to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were ea6 y v,r- .sj0sipb-clowered, would the points D and C (where dep a,-r y6.es0-isjv bcstructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecti/gsa;vwpo g: v+m+hr ;ng the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones inr:;gv;mo phsw+ v/g +a 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 wave can be thoughtsbawq- xp(8ogay9);9hmfza9 m ;+ moo of as a superpositm9aw) bzpm hax q ;oof9os8y-a;(9m g+ion 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 frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the samez0.p6qm j6uli)haat4 - e ph;d direction, with the same veloz a.6jmp;htp-e4q) 0l uh6dia city? Explain.

If a wind is blowing, will this alter the frequency 1f)j64 fx*xgnhdnc*uof the sound heard by a person at rest with respect to ) d *j16nxgx*hu 4ffncthe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A daj .t/95lnrp e +1ov (fo4vmwmonitor is blowing a whistle in front of the child on the ground. At which position, A through E, will tojo(+pw41/n 9rmvd 5tf.a evlhe child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines t-c(3 c*jyjp: fp:w4jbm6ztr ghe length of a lake by listening for the echo of her shout reflected by a cliff at tjwc3jcjfg4 rm y(p6::*zp-b the 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 sideb5 r*eoaab3 j)e1 pe*n of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and p*a1 ro 53nae)ej*b bedoes not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wav8bf fnz;,bh3 melengths 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 boa*3 k71 htu 3q3u nqo5zkusp)ixt is drifting just above a school of tuna on a foggy day. Without warning, an e zuk x3pth35uuqnkosi 13q7)*ngine backfire occurs on another boat 1.0 km away (Fig. 12–33). How 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;owto p* 7 spsl8r2ej7 splash it makes when striking the water below is hes7or; wsel2t8p* poj 7ard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr8* /b27hlit1kk2fz;v dz ufokbl+5h dete 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 apart. How far away did 15kbku l;oh2t*idv28b +zdhfk /f z7 lthe impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-x(*ssn bn ;)ftx xfp(1second rule” for estimnts(xs* 1fnp;fb ( )xxating 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 at thvh gu6z9q)i hjv0y:2 he 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 :h1 e(vcwcza1 of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firew xz1erx:suy*lw8uxw 2n )/uw)9.n bo d simultaneously at a certain place, what will b 9:nwew*wy12.xunwl /usz xb) 8)or uxe the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanmjydp n6d0s7d9;b3g c e 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 als06m7yd n; 3bc9p djdgl but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 59)f1ifu:dsj/ 2z2hx) mjtxi.gf v4og8 dB, whereas for a CD player it is 95 dB. What is the ratio of int /9h sfm)vf1 d:xjfzg it2.go2x4)ijuensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power o( r duj :auck-rj: s.f(t+*ajsutput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mou rafjd: sj( u(kt*s:c-a +.jruth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum s,jceknid08x mo338hwhose 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 k2 g9isg-2yd sW, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would ds2 kisg92yg-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 2.8 s /g om,y,:itpey d)u:m in front of a loudspeaker on:s,m t ype)y/ioug:d , 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. Whseg2*)tqi/nke(g zqa0) u c+tat is the ratio of the amplitudes of two sounds zin )e )stk0u(2cq* atg+eq/gwhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensi orfsy3(o/ g; hhovq:n+ehn4 0//shizty inv ogf0qh+yi(nz /3 /4h :nseshhoo ;/rcrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but onex-b19b 25amvx6 :div j8aicg y has twice the frequency of the other. What is the ratio of their inteni bcj1x6m9bdvv:a y8g 5i- ax2sities?   

  What would be the sound level (in dB) of a sound wavxi mowu0 /p)6pel7r4c (dhy m ;b:uwd0e in air that corresponds to a displacement amplitude of vibrating air molec6;0xiw ledcoh0 u7/:ury4mp wp( d)m bules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sounmsrdum - t*m/vb/6ou+d level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig.smm+om* r6u-/tbvu/ d 12–6.)    dB

What are the lowest and highest fr; wz;0)2m muwwud4l x6iyg 4cvequencies that an ear can detect when the sound level is 30l0ud;)4yz 4g 6wm wc2ximuvw ; dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range oe6:h+ vo4axr df sound levels. What is the ratio of highest tovxr +d4o :ha6e 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 fundamen))oagofco,3(o p 5 gartal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tens)5)a 3goo( pagfocro ,ion must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first tc5vjh; cj).j60mxi xh 5+bepuhree audible overtones if the pipuj) v0c5cx .hb5 e ;xp6j+hjime 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 frequ2iz 9eb+t) e ub,;pshdc6oeg. se0k ;sency would you expect from blowing across the top of an empty c6g eses.sdio,9e ebh;zbp) k; ut20+soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the 1kwi s3:)2pz4thx wrp-a1ik h range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths pzxstwi 4hk3kaph2r:i1-1)wof pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hy/ kt1 jcop2)k dz2ps1as a frequency of 540 Hz as its third harmonic. What will be its f2skyk/)jc2z ppo 11dt undamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m loc 2p zyjn 2 2wgzbi8*l4knh.8ung and is tuned to play E above middle C (330 Hgb*lnj nhz22pu8k4zy 2c.i8w z).
(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 emit pgg+ hn5kxacqv2x.9y2 1svr8 s middle C (262 Hz) when the temperature5. x+8ck2v9 vp r1gyg axhqs2n 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 23e k):n( : zwhd+svhza0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute i0up f-6 ,o.)leq pkgndn Example 12–10 should the hole be that must be uncovered to play D abovp. l, 0)f kegu-pno6dqe 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,q+8 l fg 57z4(aodfm(yp.spe i and 616 Hz, but not at any other frequencies in betweems4z(fo fiy glqa(+8.pe p 57dn. (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 tub )kgubrq duhn: :1ip:+ .h7pare 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencie1 :u u rgbh7.n)::kpdh pariq+s 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 2 -0diih:-nbqxz:nvn p8g zk.$^{\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 f6evhvy * c;lx6or a 2.14-m-long organ piv eh6;y x*l6cvpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long jb;xl fykzl78kmmh,7 4)zj/kw5k o1 n. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What 547lhlb;nofk/ wy )mxz 18zk 7k, jjkmis 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 adjust two s - m )fy55g9hpyrlodyu7ty7: ftrings, one of which is sounding 440 Hz. How far off in frequency is the other stt5d)yg y5lumo : y rff-y797phring? ±    Hz

  What is the beat frequency if middle C ( 5r(x,olh- lqn262 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 kHix bh;c:ob ( *loe5r5kn(ch0 iz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a s o;xhrbi*: n(hec lc( 5b5iok0hrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beatg.45 +bvcjij ls/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355v cb.+5j li4jg-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 2xa; r8 oz7/mer94 Hz. The tension in one string is then decrex8o zea;/ 7mrrased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mid/3vlh big 5z6)iz5d ppfm)lme xub befq) ;919dle C (262 Hz), bu1 m5evfx39 mqbdf z); hez5p6 iu9gb)l)ib/lpt one is 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 frequency of 4236udqamd5 sw *d r(xpu17 etw41 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencieqes 2dw 37u *pdwtrm(x65da1u s 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 pers kskb1,gbcs( (yo:rj ;on stands 3.00 m from one speaker and 3.50 m from the oskrog :( c1syb;jbk,( ther.
(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 hh c-ckep85i sc 9u0m+hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what9cs80h k 5ce +uphmic- must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats pe)x;uugq ,sz6 ar second will be heard? (As uzaq; sgx,6)usume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of ucn7w*-vauuck c24odl 8: (fta certain fire engine’s siren is 1550 Hz when at refu 82t4vdu7oua*lc : cw( c-knst. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frezdu5cd r-:7.1 hdyfgq1yik9du fk a7pnc :t8 *quency do you detect if a fire engine whose siren emits gdftpy1yr5k 7. q9zna f-*c18d dkhd u7iuc:: at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source i ,siiv3wqu)y4 s moving toward you at 15iu wvsy)4,qi3 m/s versus 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 frequency horn. Whemr+-nsbv00;zl *;t,jo fr lpnn 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 frequency the horn0p0b+-zsfv*tr;l m lrjon;n,s emit? Assume T = 20 $^{\circ} $C    Hz

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  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat dl6 lom (r.dm8iq0wwd ya8k8(emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency doesodd8ril yq wl8a(d m0m(8. 6kw the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originav)6x:hcabttf 1y l .9ul Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if al:.bh69)yutfvctx 1 the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasounw*0w ge x4e3-v*hwxa nd waves to 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 bww h ve0*4ag-enx*x3wlood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freque5(fmd+i .zsou 9 g3fvuncy $2.25 \times10^{ 6}$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. b:8k( qj*iup cWhen the wind velocity is 12 m/s from the north, what frequency will o( ub:8 k*jipqcbservers 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 mov./co hge3vdl8ing on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 mb31,u r q3 3,hmgrua/u cyn8lu/s (a) What is the angle the shock wave makes with the directy33guhl/ rrau, nm,c qu 31b8uion 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 d1- 8tc3p.urz ynnenj1b;d 6+rj /bplb:9 lhi speed of sound is only3 uez.brli dljp6h9pb1n+1ndcj-tnb/ r; y 8: 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 wz(t*a9bm 1wwo*9 fasocean. Determine the shock wave angle it z as*99w(w1mbwa* fotproduces
(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 i+mx;gfc x4 .j$/theta$ 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 1.52/ a04y*+jwtsync/ umo 0vpiql;z vh3 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, thzvv 2 cm/p; w/+00oyu3yhs nlt4jiaq*e 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 20,0rzte 8 fa,99hj00-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is d9hea jf9z ,r8tesigned 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 audip.d:yu- rusjoa6z 5ma9v *r+ vikxq19ble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipefejyq -tg(r .f 5zs,aej2o0dj)1s p4b symphony. It consists of many plastic pipes of various le 0oa5sq fedjbtejz, .124fpjyr(s-)g ngths, 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 the7hi(h5f40 j khmbiw / f 3n8c,qko7ia);iniwreshold of human hearing (0 dB). What will be the soi ob8,3;w70 k5iic4nakhi h7)wnmef / j fqh(iund level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hif,gp.w v:jenu k8fs7s ht: ,x 2i)j5heard simult:h2 svju.:ehw 5ji),,fipn sx8f k g7taneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What 7 xi0gv3di9qm is the acoustic power output (W) of the speaker, assuming it rg xi9v3 7qdim0adiates equally in all directions?    W

  A stereo amplifier is rateb 6if ;gkaw;8gd at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outpba;; gkgi 6w8fut in watts at 15 kHz?    dB

  Workers around jet aircraft typicall*du 6mq1jaihfq))-3ee aetl.y wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance )qei 6e13.te ulafqa -)hmd *jof 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 sy2 ,; 7y6cw ysbuzibi)nstems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuni5: 8gjb8 hsoced 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 poi1cro 5rar j c+k5nom cv4-v 5;tpgd4u4v *xa0qnts with a fundamental frequency of 440 Hz and a mass per unit length c4a5vgr0-1 vd4ajurmo45;x*p 5o +cr qtvk ncof $6.1 \times10^{-4 }$ 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 wis0va1dvf t;u* th 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 disvvu0; adfts* 1tance 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 at oneurz+15+wg ekj end and also 75 cm long. How much tension should be in1 ek5u++ gzrwj 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 tooh(dv-eo )ul me.ersp6 p3vs5cq2t ,* resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range co afb)mh 0dtsr11t( 2n-vpwfp7ming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly wptds7t 1n1wpv-rb afm 2)0(fhhat 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 stac/mdnq)2*pxhfe3w u,tionary. The conductor on the stationpcqwf *,muhd )/n2ex 3ary train 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 th f mlh.7dabzgz 0c,8/rain whistle as it approaches you is 538 Hz. After it passes you, i0 g dhc8z ,z.bfahm/7lts frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate tt mwq4d2i 4kt9he 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) at2kw4id9qtm4 s it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 H 7xu /- v; 8j)vn2poe0fbve g+ueit27uk2qqsdz. The shortet22s/b8duq k-7gep7eno0j qv ;fe2 ix v)uu v+r one is 2.40 m long. How long is the other?    m

Two loudspeakers are a0sbg8y nfq(c. t opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have iden (y8gfcbn.qs0 tical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what y4g xs7 lye+ia9s6ny3sqx3 (mlv.,xgbeat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected ,yy+ayqx3s3xng.gvl lsm(e 7 6sx 49ifrom 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 spekx+h 5i2t kzo s(ltoxwl*8(e0 v:f5y eed 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. W20yts e8k(:w5xt fk*oox+ e hv(iz5llhat is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series p-v-4nq ph6rumv 9, b4ov;0bwt8mcquof high frequency sound pulses as it approaches a moth. The pulses are approximatnpqupub 6vvo9h80 mrq; cb4vm, t4w --ely 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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) ntbedo ,kha7y 4tv ,(0tyjw:6a89 bnb was once used to send signals from one Alpine village to another. Since ,kbbtayv6dy,ht7n (4 n9bj8o0:t w a elower 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 of stand 5s1d.j clvwc* s);ymging waves, 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 ccslg)1y.; 5jw *ms dvin this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “3q/0tjofmqa6cv2e708 w h-,cpp :hi i;yevlnsinging rods,” involves a 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,” or emit a clear, loud, ringing sound. For a 90-cm-long rodq oi:vy, /pve0ahmq862w3f7 -i ; t0jecp clnh,
(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 at a ybrz+6t;c dij+odt bh: 496abqu) 3iro3dn(r frequency of about 10+ybu63 dazt) 3qtdbi:iroh(6 cd brn49+oj;r 00 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on n)et,nqx-7 kqthe ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s aq)nnkxq,e 7t -ltitude?    $ \times10^{4 }$ m

  The wake of a speedb con4bf0h; d.z,ix3p)dx(b paoat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h