What is the evidence that sound travels as:mpb23tk;az ;a)ikce a wave?

What is the evidence that sound is a r;p. wflye+9 yform of energy?

Children sometimes play with a homemade “te -km)6dy*tyww gj.3b jlephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, th.)3m6t j-w y*wdjy kgbe sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the 8ppyz7d ,xe sm/:)p ba 9ytmc5frequency or wavelength to chazd/7ctm p)a98ms ,y byxpp:5enge?

What evidence can you give that thenv qe(w3 :/px6s8s) hw7tqemx speed of sound in air does not depend significantly on f e(:)q w8/6pnqvsh7x tes3xmw requency?

The voice of a person who has inhaled wp998dr 7:wx3 ulpp cdhelium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organuku ga4.) 8l 4vlxcyj3 pipes?

Explain how a tube might be used as a .-oql+zs m,8 .vnnw4k/ xdwfefilter to reduce the amplitude of sounds in various frequency ranges. (An example is a car4ek 8 .xn-fdws,.zq lo/nv+ mw muffler.)

Why are the frets onhuh1992wd :g -r xrzj-7x3wolj /fmxk a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the b9/7fgxdkx m1h9 wr-23uw jx:zjo-lr hridge?

A noisy truck approaches you from behind a building. Initially you hear it but c3qsi xs 4kav:7v2w p:nannot see it. When it emerges and you do see it, its sound is sudd3n4si7kw sx:p2:vq avenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be wh3bh:auwtod-ny n*1sf3s (+:x1oi osaid to be due to “interference in space,” whereas beats can b : +1unxsobh*oawio3(f1y3hdn :- stwe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were low un+ q:cqevg55wo+e9c ered, would the points D and C (where destructive and constructive interference occur) move farnvuq5 w+o qcg9:e5 e+cther apart or closer together?

Traditional methods of protecting the hearing of people who work inqk* mz,hoz39;o c) ild 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. Instea9 *hlq,om)3 ozdik ;zcd, 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 wave can be thought of7rvtzu4o8i.2 g +75do zhw rmx as a superog mr2x87+rdwh.u 7tv o4z5izposition 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 sh7qrffa7vxs 02 4rp*6yobp w k+ift if the source and observer move in the same direction, with the same velopfb p* 4o k0aqr6+sx2r 7yfwv7city? Explain.

If a wind is blowing, will this alter the frequency of th:p-g kdsskb/ 9gt ;/uoe sound heard by a person at rest with respect to the source? Is the wavep s;-b ok9ug :/gtksd/length or velocity changed?

Figure 12–32 shows various positions of a child in otj1ym1gm1 2o0ake s *motion on a swing. A monitor is blowimm1a s t1oyjk 1g0e*2ong a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shoo3yip 8i: a ;//mvuu1ile3o lrut reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Esyu m3u 3aeo:voii/8i/r lp1; ltimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hk,kfv vdcqz2 f *7:mj2is ship just below the waterline. He hears the echo of the sound reflected fro*,mjfk zc2qv2vk7f:dm 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 wavele05hw:b8 rkh3wwvh f8bj 4fyc :ngths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tqd1mfm9mty.f ,:wyyrm + gx :w79lu9muna on a foggy day. Without warning, an engine backfire y9m u fmr:f+mtwd:ygwy7l9x.q1 mm9,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 splash it makes mggj dcc j; +n0g1t5k/(cw9xm when striking the water below md9wgc0 n/cjtg;k+cmjg51x( is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pa 6ro i.bf/qifm0-;z45cea3 ol qbjzq3vement. A moment later two sounds are heard from the impact: one travels in the air and 3jo6io-0 erz qz.q bqa5flc4i ;b/3 fmthe 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 gl+xk 7s816xzkkmf ;m mile of distance by the “5-second rule” for estimating the distance from a lightning szkkm;xl6 + mgfsk 8x17trike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the js0dp,/xxvv-ly* osj d/y1m+ 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 inte3s 5v+5jo:az 7thh+ab vefo. onsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro 6tzax np-/:n b,/xdoxduce a sound level of 95 dB when fired simultaneously at a certain place, what will be tna6o:t, zdxn b/xx/p -he sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane withp j dr8miz0z.: four equally noisy jet engines is experiencing a soujpiz 8zm.0:rdnd level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a siq,eo +vzw rc*c1jt9,egnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each de, cwtj+v o1rcee*,qz 9vice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person sp7zwtl-md3 zp 0eaking in normal conversation. Use Tab0wp-dz z mt73lle 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 etaec2:lv8jm4 k+rt f+ gkac./ ardrum 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 igiz 8idr 40:yk;a ;shds rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decihyisa0;d:k z 4g 8rid;bels 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 2.8 m in front of a smemf1vp (w /jtk:q .ua7:ta65 -ulgjloudspeaker on the slu1j - 6agttew.af7uqmm5/s(: : vkj ptage.
(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 tz:vas4 3wl+0z6 l ns6b bp2jfsound level of 2.0 dB. What is the ratio of the amplitudes of two soundstla4+ pbj bz 06wn3ssz6f 2:vl whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave isp4j/ ;tg/p ufu tripled, (a) by what factor will the intensity increase//4puftgp ju ;? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dw 1be /imm.aa*isplacement amplitudes, but one has twice the frequency of the other. What is the . aiae1/mwb* mratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that j - -ocj ym 6a*ixt86f8xsny/gcorresponds to a displacement amplitude of njj66/t*xgfy -8saycxmio8-vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemsu2(3bxr dp(u as loud as a 100-Hz tone that has a 50-dB soubu (3rpd2x(s und level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can det;j ss)a aeaiuu/w-:x.cwe 0e +ect when the sound level is 30 dB? (See Figeajsw) / +0x:ua;i ea.wesc-u. 12–6.)

  Your auditory system can accommodate a huge rh rzn)rlz1gcg;6 nv26 vat4 n.ange of sound levels. What is the ratio of highest to lowest intensityn6l46.1crng)nv rv h;g 2 zatz 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 ofei4cd(r8jp 9 0wub0gh 440 Hz. The length of the vibrating portion is 32 cm, and it hagj0 09dw i(4hrc8epbus a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamentag5/xwcdqrdx5 e q2k6/l and first three audible ove g er5 xd/q52dwq/x6kcrtones 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 blowingw(svzb7z* u /l across the top of an empty sodb u(wz/*lv7zsa 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 spann;w;pizl-0px6*u(lewxt jopdk 05u80 lc)r asing the range of human her;aj;0p o 5xplp(8)we0dzx60u wt l*csiu k-laring (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Whao-xpe 5,m9wny;ljr5j t will be its fundamental w er5njly-, 9pjxom5;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 abhxm ym*/ oea 5o.+9augove middle C/ 9aao. xo*5y h+uegmm (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 length of an open orgb*;b xs zymze d1k31-can pipe that emits middle C (262 Hz) when the temperaxb*z1y scm kb -;1ze3dture 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 20b t aw7x-tgb(+ $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exampl)fswio27-sl9em- w/d 4vgpic(e /.dddy3m uye 12–10 should the hole be that must be uncovered to play D above middle C at 294y-4sid g(wd m.7muwdv9/d 3)pifescy/o 2e - l 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, 4 gqwkgzwn8l lf4dj5-4dw*: v j3f (i;q omud0(40 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show whkfj il;df 4qow 3(5qmvw :0 zjd-*dwg4n 8g(luy 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 tubefbzl;i -vz0) v 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What i )vvfl b0-;izzs
(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 d;.z mc*as)(dqu t1om$^{\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 ft6 yx+i8/czj audible range for a 2.14-m-long organ pipe 6tciz8yj f/+x at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxi e5dcwrr5mury5yc r/c is4b)m7) n69 xmately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. Wh rn4mc5d )rr /)5cymxe6cy75su 9wb riat is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust twc-xy8hxp ;kee1a 6-a qo strings, one of which is sounding 440 Hz. How far off in frequency is the other 1qa 8xe;- a-exkc ph6ystring? ±    Hz

  What is the beat frequencrz x;pk til(f1 ,(-j.vxz-ytny 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 23.5 kHz, while another (branmr;0hrezk /n5-zwl w(zbs u*-d X) operates at / 0;5-(nulkhwz-*rz emz rwsb an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 8ktpm0mtgb oe-m1 u3,lyd:2d 9 beats/s when sounded with a 355-Hz tuning fork. What is the v plkem 231 ,oby0 d-u:dmgmt8tibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequencf6nxlbe8iv7f +ud: o/i5q ) x8f vhq+fy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the t/ qbeh) 6dxn58 :qfvfliuv8+ o+fi x7fwo strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play min.07s nclj8:ge3qxr4m di f)s ddle C (262 Hz), but one is at 5.0°C and the other at 25)de3x.sjl rci4mn8n0 f qgs:7 .0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a(cjm uf 4xga8 )wm+umevx72d7 frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are2g ew m+)m478aj(u xx7udcmfv 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 on h y)k ; 0nap12ggdj+zklb0t(3tqz)qne speaker and 3.50 m from the otheyg g p)0bkzd3(2+tanjq k0)zqhn;t 1l r.
(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 bzr5sxp iru+r(:1o;r gjb*hzt4v-2 df e vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the oth:+- hrprvt(*rrf o5d4g1; zsz b jxiu2er ?   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 a l 5g4albyr3.vir. How many beats per second y.l b5l3a4g vrwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’sun xc wn n/zs(58ozw46 siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 3n(8x4nwu wc z/zsn56o0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do1 6ev+.zv mrha you detect if a fire engine whose siren emits at 1550 Hz moves at a r1hmev. 6a+zvspeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward y2mx4sq 6no.7un e h.mbou at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are. 6sh7emn 4oux2b n.qm 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 fsut*x 5ry vsqp);vl 47requency 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 frequency the horns emit? Assume T = 27 ;y) *sv4qp5sruv xlt0 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic so xyfd32 cy2 hqsl. ui9n;2il.bund waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivedh23f xi .;.9qsl yydc2lni ub2 sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of t.pe-ug-0e ee 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.p etue. ee0-g-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 mohi; vcm6vxp3nu((nx:ving 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 trn :ipu3h 6vvm;x (nc(xain car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo26zlli3 n4c 9hj5u fkbd-flow speeds. Suppose the device emits sn4l9hflz5 kbu23 i6jcound 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 source?   Hz

  The Doppler effect using ultrasonic wayqub) obd 4 )62 .27haknxwqvives of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity qp aofac1,/du * via8p:1ksa),vndb r,)p v)tis 12 m/s:*uban,,1p pr a8)dkt)va )sp v1d, o/aicq fv from the north, what frequency will 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 att +nvpx bs00a/ 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 m/s (a) Wha(b:f3tfyw74pvs8aamto h- +r t is the angle the shock wave makes with the direction of the airplane’a thrt+w7smb-8y43 po (a:fvf 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 soundz.vpj3p2k+ b g is only .gkpjpb2 +zv 3about 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 strikvgytpv3d/g p eu-ei(;0b*; tn es the ocean. Determine the shock wave angle it producesgbeud/;;t v n-yi gv*3p(et0p
(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 :* . ;;pirkhdcmyd.hf(ss d3v $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly over0+-ecat d a3oshead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the -+ 0tocs3deaa time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pul f4slco4)p cm8ses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designescp)4om8fl c4 d to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how mad n9j a 6r9c)m6kqijazzd-:f*ny octaves 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 xxyfj*fdw;fx)1 i ::dmany plastic pipes of various lengths, whiw;xj:dy i x :*)f1dfxfch 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 theojh8qdb(cne 2m8 mc0 pip 29w9 threshold of human hearing (0 dB). What will bedc m8wcjbppio929 n 2e0m8q h( the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound leve5/pldjld6lz hti y)e ftlw/yq(8 j382l when an 82-dB sound and an 87-dB sound are heard simultaneou lh8j lzj8 2f5y e/6 ld(qwtptd)3/liysly?    dB

  The sound level 12.0 m from a : o)cp:a. t/xhb ca/gfloudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in a)t:aco:p h/ .xgc b/fall directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output o 7xf6aqjowvr fo1 + ws-w2v;8drops by 10 dB at 15 kHz. What is trvax-fw+o 82wf 1wo7;jv6osq he power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their y bzu /gw*1nsz9;n5lcears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and n9 n*5ug1 / zzbcs;lwythat 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 systems, blk; e( wk8rzb2w6yzm /3ashl2c jz4 0the 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 tuned to a frerq kun1we) 6 l)lei1 7rx*snp7d8n;tzquency 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 a fundamen* ( +wwpavu.uvtal frequency of 440 Hz and a mass per unit length+vwa .(*uwp vu 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 vibrationhe b 67fmt:/yf64qdi 5er/kj o above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube op7 64ftrq/5e hoe /yd fjkib6m:ening 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 one eil: eq/tu6t 3wnd and also 75 cm long. How much tension should be in the string if ut:e3w6 q/ litit 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 fullyv3*wj3jx9op mz1s4g 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 500hxk5, q- r00 wbkcyi+w–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 minimal at a point 0.34 m fart0kb ,h-q0 w+rkwx5ciyher from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz wkc-,.o6hk; mu:fa(xr bh )gcl4wqa:l histles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spe-4ol,;. 6 h(q:)acakrxcgb fw:u hkm led of the moving train?   m/s

  The frequency of a steam train whistle as it approaches guth nhgri b1x ;+w40/egz10a you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume cons4gtxga e0 1z /hgw;ur1b0+in htant velocity)?    m/s

  At a race track, you can estimate the sprrlk r-p1 .u)feed 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) as it goes by.-p fr krr)u1l on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency oijo,;b6 /ra bg6kbkg,))8 wt,o x qhsxf 11 Hz. The shorter one is 2.40 m long. How long is the otherqwos,gxjk bbik)g /x;bor,,8a 6ht 6) ?    m

Two loudspeakers are at opposite ends of a rax f0o,+xop 8tn4gv cq9ilroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–3tn04v x+pxcf qoo 9,g87. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aortat/ibr1wq(t c0 hfxyq1 w.1( yh 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 1biy w1y h(0/ctf wqxt1h.qr(the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the mo s/ 15pfqmu kivs3dem(-1j6bz th is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frjf1msudvzime/ p 3(1sk6bq- 5equency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequenmw.2soo y6fe*m1p 9yncy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, ans w* o2yepfo.mnmy 196d 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” (Fign2jm*fv,vrm9m6o jbr;l49gy. 12–38) was once used 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. Whvj ,r no ml9 m;rb92jg6*4mfyven 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 stqt5-cl c qm v(56e3mxm.fzfg2anding 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 freql vq mxq.m2(fe5-5mgfc t6z3cuencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumiaaft u(r4l .-rcfb9 +:07ro dr4j vchcnum rod held in the hand near the rod’s midpoint.f7 0(av4btj lc c+ rr.4cudra:9hofr- 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 ear at a fki7ict/pi -j p7e.mm*c: d:qhrequency of aboq-7m 7.h/mcptk i:jic pi:* edut 1000 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 the gr u:97x)ju; d5 co+(h rjpfttfgound hears the sonic boom 1.5 min after the plane passes directly overhead. Wh 7cttodg 5hr u:xuj f9+)j(;pfat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is e9;)gx mq) z)phjyzt715 $^{\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