What is the evidence that sound travels as a wls)8l;hp 6 dyoave?

What is the evidence hak,2ei v* 81fit2kjrthat sound is a form of energy?

Children sometimes play with a homemade “telepho)u/5v tuy h2n7z5gdmjne” by attaching a string 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 h5u2d57) jtm yug nz/vother 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 frequency o n-4u9e dbvfa mx r;up.kv9p w3fa.y,;*apt5tr wavelength tuu3 tx -ykv,vnr ;9.af pd4;t5ebfam p aw*.9po change?

What evidence can you give that the speed of sound ss2bnfd ;+)+kw6 nrpdin air does not depend significan +dk2;sn)drf6b+ nwsp tly on frequency?

The voice of a person who has inhaled helium sounds very hi6v1 gvxzn9u w:gh-pitched. Why?

How will the air temperature in a room affect the pitch 3kstbht dpzty)c(9n*kn 6(f .of organ pipes?

Explain how a tube might be used as a filter to redvbv.0f4zj vtt,p w3j- uce the amplitude of sounds in various ff0jvw.-3 z,ptv vtb4jrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer ovbe yoc d+* e4*;bp.tf,gxy 8together as you move up the fingerboard toward the bridge? *p d .cyv8 b4eg,yfe;+o xtob*

A noisy truck approac9abse4 q 0omx8hes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sou0ose9 a8m4b xqnd 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,” whereas bpdn6epy;u8: e eats can be said to be due to “interference in time.” Expyp: ;nee6du8p lain.

In Fig. 12–16, if the frxl ewlw 3,e yik*(qi)4txpd,,equency of the speakers were lowered, would the points D and C (where destructive and construpe,i lxi ,,*et)xqwy l34(w kdctive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peop a k 8:xow.gb34kp.iorle who work in areas with very high noise levels have consisted mainly of efforts to block or red4k.igbr ok.3owx8p a:uce 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 wave can be thought of as a22agmne bf- h) 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 frequencies - m2anegh2)b ffarther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in m0pjo* bk*tel0dqa6pkc8f,7 the same direction, with the same velocity? Exp8p0fcp*qla*k m je7otd6 kb0,lain.

If a wind is blowing, will this altec3-e/3qra b92q h gmljr the frequency of the sound heard by a person at rest with respect to the source? Is the wavelenrq/3c g-hq3a9j el2m bgth or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. mihp 0amb z.y-yqt,,0zq /4raA monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequenc .04/i0tq p,z,a-ayqm hmzr yby for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her+fod3 :ud te:c shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after uf dote3:cd +:shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears rc6lfor *s0ui ;x5 ku7/1erih-0fbkpthe echo of the sound reflected from the ocean floor directly of k1;6f hb7/l iukrx*us0e50ipr-rc 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 wavelengt 5u7xbg3)eaifhs 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 schoolmhxg/g9 9s 0vl of tuna on a foggy day. Without warning, an engine backfire occurs9mxg9s hg0/vl 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 makesn)vna s g6bn 8au96ud/ when striking the water below is heard 3v/undgus anb6an9 68) .5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge sttqn),jo.wz 6s one 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,z.n6)os jtq w they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent r v*8fwnq j6y)vzqyd:p1s t8 pm9- wo1 6x8dumerror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperaturtn8) 81pvdxmdwm89-*wyv q: zy66fu1 qs jorpe is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB?az/tfb*sq2z,vi p3 ow 0;o f(w    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 intensit rhqyv72:dp0cxqxuwx4 (- 8q/s7woid y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dftw00;iftpv7vk2u b -B when fired simultaneously at a certain place, what will be the sfbv70tk wtfi v-0;2upound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fou1s) y, iccsj1mr equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level woum y),j sic11scld 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 sigun4 ol1wbb0( jnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. Whlub( ob10j4wnat 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 of sound from a person speaking in normal conversao5bo9wdabf :k l0we *0tion. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the afoowk0dl 5e0b9:b* wmouth. $\approx$    $ \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 whose are ,(ful,(4 izp9/4 eb-senauyw)ocg fea 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 25 rjfca q:z.8bgc 83yi:0 W, while the more modest amplifier B is rated at 40 W. (a) Estimate tbz8iy:jfa8qcg .r c:3he sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in z1;a.e vf5zcywf cl*te p,l)1front of a loudspeaker on the stzplaelyfe t f)w. 1,1vc;5*zcage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What omhql9hp2 czu)o1h,0 is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: Seep)czoh2m, 0 uqol 91hh Section 11–9.]$\approx$   

  If the amplitude of a sound wave isw zhy )2g(agc1gaa i0u7z.e:l tripled, (a) by what factor will the intensity increase? Increasi1g.:az(ugc0elwzgy2 )a7 ahe by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have enyr hiz3 i((k;5f)i oaqual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their if 5iz)ih 3kaio ((r;ynntensities?   

  What would be the sound level (in dB) of a sound wave in a l k52cr*ok: ol khs6s9h5z xtt3x,5jeir that corresponds to a displacement amplitude of vibrating kks2h,to5xl5 359j otsze r 6c*k:hxlair molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tonh7d;mvd8cm9v. *pq3- l wlwez e that has a 50-dB sound level? (See97 -d chq w3.v8mmllep*zdv ;w Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wr xqwsm.dqj+ wigq+wj66 5riv7a1q5(hen the sound level is 30 dB? (Seerjij+(i s6xwq.5m+ g1 av7 5qqd6wrwq Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thk) ubeay1yba(h8caei /n9bz,e 5k;n:wu bk2;e ratio of highk8;1u2azu9e;)/ybe ken,(5w hk:baibanb yc est to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The leng y8)3t0voq tw et;0lftth of the vibrating portion is 32 cm, and it has a tl feq3 8tot t);yvw00mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What ar1d:gr;kz3 qx6 jzcr -ee the fundamental and first three audible overtones if the pipe6jzkxd3 rc;er :gz1-q 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 acro/2; wz)pgubf ass the top of an empty soda bottle that is 18 cm deep, if you assuwapf) 2b; zug/med 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 pipak uh7.a,oq *bex5 a7ces spanning the range of human hearing (20 Hz to 20 kHz), what would be*co7ake qau7,ba h.x5 the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strin,8ajt 2t nqbc l+ 3-s-r eah8fz7c5bhzw+p 4vbg has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency ifaws8-,l j+8cp t+2c hbner3q 4bz 7zva-b5thf it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.i23gr;zpfqs(z9 gg b/kkks*073 m long and is tuned to play E above middle C (330 Hz). (3;kig9ks/g 0*bq fzrpzs2gk
(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 7j8 s x)fi.qrl,(valvopen organ pipe that emits middle C (262 Hz) when the temperature7s . lvj)l8q(riax,fv 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 aghz ttt1;6wbup8a 9vg kg/pac z+1/t4 t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpie +se+.vs wx5rice of the flute in Example 12–10 should the hole be that must be uncoveredx .+svs5weir+ 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 at 264 Hz, 440 Hz, and 616 Hz, but notmx ;-ih; csm0j at any other frequencies in between. (a) Show why this is an openhm is0cj ;m;-x 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 l9 fpv/f.+1 grtlnqu ;yong is open at both ends. It resonates at two successive harmonics of fr1yln vg ;pu.f9+qrf /tequencies 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 3kc+xq 8e3.x*f rscen$^{\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 foj2- yx)9b nacqr a 2.14-m-long organ pipebcjq- 2)x9a yn at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm sct0 4*afyu)d i5 a71 mrvva8wlong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (ia 471vys 5a)vftd8i0w*ucr amn the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat ea7ge,js: a8 bx(hhz.yj c9- lpc nt,0pvery 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? ±0tnzhjya,p cxa7.,l :j (e bshgc9p8 -    Hz

  What is the beat frequency if middley m6eewbxcq+w*s 9 r(mc;,x+h 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 anotherexc) 93;iv;*s4 wzcuf ziamg;sww4,k (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frv49z*wxi 4smkcza3 ue ;gw;;w)fs ci,equency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beatsi bmoae e 5sw,j3sa85j76kpcjb4t/7 i/s when sounded with a 350-Hz tuning fork and 9 beats/s when eao5mb p7 /,btj8js 4k6ewcis7 5jia3 sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frer ql2 5r)af 6ly c1js8nkztv;l9w-h5iquency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat lr1i; cwvf2kl nt rz6y5l8a9s5qhj) - frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard i:eadjr(dpw8hbn0 m4 *f two identical flutes each try to play middle C ( a jrbe:(p4d8*0md whn262 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A,xgvc;zaao 9ip.; -i 7;)gjkn t B, and C. Fork B has a frequency of 441 Hz; when A and B are soundoixt; jgc; ziapg-knv. 7)9;aed 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 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 pxok +i i5 ydyyx-gj-r3u,db-;erson stands 3.00 m from one speaker and 3.50 m from t,-3 ry jxk-d-ygy5iob u+di;xhe 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 pc isw)i,2)m22f kcka132 Hz, but a piano tuner hears three fc2ak iksm)cp i 2w)2,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 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 2ta 9ws;qo)xd deka4(av3v- a+.64 m and 2.76 m in air. How many beats per second willsa qdaa-(exo3 9 vv ;a+wd4)kt be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 155h ijh 7 l3mk km61h7e2hqtt9x.0 Hz when at rest. What frequency do you detect if you move with a speed of 30 it7 1h k3.2t7h xmml96qhhkejm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine j7j5+qa (-5olsuiq,q vhu.ncwhose siren e+jou(q u.vsihl5-ajqn c,7 5 qmits 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 is moving toward yof5l)ep e*p-xo,fks5,w l:cx ou at 15 m/s versus you moving toward it at 15 m/s Are the tw- ,*s ,felx)le5x5cwkpp of:oo 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 e.dxjr qf8a.6 qquipped with the same single frequency horn. When one is at rest and the other is moving toward the first at q6jq.8fr ad.x 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 5d t9z;nd.gu4 vo5n(4*ltjy pv0.0 kHz and receives them returned from an object moving directly away*d v odtpn9nv4jg;(lzu5y .4t from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of nylram8ab a;ecfdlw6;c3+16 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency;b yd8flnal+6 3 arc1mce;6 wa 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exh;wpwsyliil/nz*y71z7z 16b periments, 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 the train car approached the station at a s/wy7p b6sziz* z7whl i 1l1ny;peed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasytg*k k) ;6:g9tdnfgu8nu8cjef7kl *ound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is*tgnfj8c9) y: u;l7 fntk8 ggk6eu dk* 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 wavq:etnt,sv+l b)gap25es 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 vel4/sply;y od t5ocity is 12 m/s ;s/ lytyo 4d5pfrom 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 l8mb)08 k3pwcbe ym n*uand 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 m/s (a) Wha*tj8 + e ya d;d/vp0gggy*acn0t is the angle the shock wave makes with the dire gy0y0j8vggdpatc *;en+* d/ action 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 whereo8;htz s20qd c7 q/hls the speed of sound is only abouts t0/h 7lq;zhsqod82c 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. Deter98m ;koul ik/wmine the shock wave angle it produ9m8;wl/ oi kkuces
(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 8ehu lcx,4h1mt u5( ma$/theta$ 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 exactlya4 xo7*ef0yx h 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travay4h70x feo* xeled 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 thaup3(i;x z 7 +spo4ydait sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is t+xpy; z7aipus ( o3di4he minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are x)o,d;fwc 1pt there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display pua4yt(b ,q m)+x r3x*m/ggac8ld + fzcalled a sewer pipe symphony. It consists of many plastic pipes of va 3uyp/c+qlz x*dmgamf r8t,( b)+xg 4arious 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 7 o *if tgsfq:vjj+y/(u9pu1iperson makes a sound close to the threshold of human hearing (0 +u s1ugqov/pi y79f t:fji(*jdB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB souxv8fyel9.udcehb-7d:.t g 55jhamy eb*+0xx nd and an 87-dB sound are heard simultaneouslvaexeyj5y u-0xc fex9.: htbd7+. *m h8gd5lby?    dB

  The sound level 12.0 m from a loudspeaker, placed in the op1 :1asyy c en 9r*om9rm0-pbowen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equalln1:0-a9 y rypoe m*mc9o1wbsry in all directions?    W

  A stereo amplifier isjonzjj s+4d-kk3y:f 8 rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Wofz jk-j3y+ k8sd4: jnhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typiigxq s1zo; z2rq,l ;n0*ctg, gcally wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distan* 0zo1qtq2, s zil,r;ggx cng;ce of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatio24j6t;d( u1s7l hlh i j,fger1p3zqi lns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 1 pg):/ef-gwwg s9bdg: $\frac{1}{2}$ 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 fundam1eee(mvsht3 5 na6ct6ental frequency of 440 Hz an6mvesnt1hee a( t356c d 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 verticalr3d2tnoc ,9gz 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 c9ozrgt 2 n3,dabove 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 nearc 1lduh/jnl4,i4w3 -0 ivjqbo a tube that is open at one end and also 75 cm long. How much tension should be in the stri0/ljounc-d 3l qiv 441,jwihbng if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observedzyi02,oo0m uo to 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 pureedc+u nc4f z8b)6dgu5 tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the46zcuu8d)cd fb +5egn 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 traqb +wnj,gs9v0gt49e g in is stationary. The conductor on the stationary train hears gjt+w9 ,4q 0g9bevng sa 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 53 lw ru8g ;1naihwl7n o43bbo+,8 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (aa wlo wo b7,gh41rbluin;38 +nssume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars justhk; er .t-kuv7m8cuos 5/b pf2 by listening to the difference in pitch of the engine noiseohuk57p8 - us;/c v.m2e fbtrk between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, pro8t ;f o0fdrgr.duce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is r;d.fof8r t 0gthe other?    m

Two loudspeakers are at opposite ends of a railroad car as itc4tc*a9m 7oc v7p dex0 moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the positionc x907t7poedc vc4 a*m 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 : m sue0eo2aap3i44yxflow in the 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 the waves smi03ae: ao eyup4 4x2travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward +:fwt n(7s/s iaez4 sfthe bat at speed 5 m/s The bat emits a sound 7nisz:(feasfw /ts+4wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound puls7hrjdji29i z o j;n2b1es as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one9 7jh zijdo2b1rij; 2n chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine fzn1p--z bnb)jep .o 1village 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, thfnp oz - n1.j)bpez1b-e 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 listeni .(pd;(uww* yrv ;vjxing can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m lon ;i. x*( vpdjuwy;vwr(g, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a longxq cgw;,;if2p.9k t kg, 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., gw9.;2 qckx tpgkif; 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 freque,a8t5n bl,it*:bm aewncy of about 1000 Hzn t:tba5wmbe,lia, 8* 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 zoo5zmf yjz d6007xd(ground hears the sonic boom 1.5 min after(0 z dfxzy d0zo7m5jo6 the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat .a2 yqzqs*;izis 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