What is the evidence thatx)nb if4z20m j:kyp 1sg0 7ln6ed3oqb sound travels as a wave?

What is the evidence that sound g yhrko oqjrv 053a495is a form of energy?

Children sometimes play with a homemade “telephone” by attach.8d on :q(ip 2gq0pigling a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, g qgn2pi0q.(d:p8i lo 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.

When a sound wave passes from air into water, do you expect the frequen3q;sb2fp: ;2ac7 uwa lka3dy pj *xd9fcy or wavel 2 7pw *u3 bjfa2yckd axfs:q;93apl;dength to change?

What evidence can you give that the speed of sound in air does not depend 61qownjkx8g4 significantly6qx4 gw8n 1okj on frequency?

The voice of a person whnor2hqv uhgd)*s /07k o has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ, o2fsp kwq6:gjm )ku2 pipes?

Explain how a tube might be used as a filter to reduce e-y wnjdh*(w8the amplitude of sounds in various fwyn- hw(d8ej*requency ranges. (An example is a car muffler.)

Why are the frets on a guitar gsqu9iky5gs;g( l*f5k 4e: f m(Fig. 12–30) spaced closer together as you move up the fingerboard toward the b*k4egk sl;(:ig 9qf5uysfmg 5 ridge?

A noisy truck approacx+k w/(qeo 8qkhes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its skxqe+(8q/ okw ound 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,” whereakxg9(uvwj+ tv fq/ kz u*2t3e,ajhd35s beats can be said to be due to “interference in time.” e (u/tj5 *+9avdg thzu3xv2k, qjwf3kExplain.

In Fig. 12–16, if the frequency of the speakers were l69ne uty)irva,xz)e+ owered, would the points D and a zv,tu)ye6ex)9inr +C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of pr0joc tit; 5lb sut;+e48wgf t6qj0w 8eotecting 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 in addition to the ambient noise. How could adding more noise reduce the soundju;46gfiw t8wsc0l0b e;oe+5tj q8tt levels reaching the ears?

Consider the two waves shu5 gue42ljd.vown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two ve2gj4lu.d5 u component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shiftz a:hg+bxm ,f/, ecyd2 if the source and observer move in the same direction, with the same ve:b /e+x dgm afz2hc,y,locity? Explain.

If a wind is blowing, will t .0aaxb; vzt-r;a-rev6upg ; yhis alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity v;e -yz.6 pv tbara;ug -;ra0xchanged?

Figure 12–32 shows various positions of a child in moib(2kq*ycf / btion on a swing. A monitor is blowing a whistle in front of the child on the gro2y(bfqci */kb und. 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 shoi-(m:z2rj7++y j.t jrydcr bhut reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Esjh d(7z. i:y+-rt2y mjr+cjrbtimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below t (vnhk2t5 l2. lx28cu er(wbtphe 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 does not vary significantly w 22lnx krct85lh2(t.uvew ( bpith depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtsfor- .lj2hlf* epe73 hs 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 abov1/on pfcv /3n 92eoxrqe a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (ap/ 9qvo31 ocxefn n2r/) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whe3binkzv3zr(2fl 1 04h ro4 omqn striking the water below is heard 3.5 s later. How high 34l3r zob(0 2znr1qohik4m vfis the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pav((l0p9wlcz lx12lp 5ihtdu 5oement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are (tld0i(5 hu pwocl259l1plz x1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dist*er.kv ji+jl--1w;- eigxg toance by the “5-second rule” for est *g -.xri-e+o iel-wgkt j;1jvimating 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 the pain level of n( hyu/2gmz u8120 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 soun0jlurcf* 65 qdd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta5kkn )6bw s6 le4.5zjbwveuq3neously at a certain place, what will be the sound s.w3n)q 6l6jkvbk w4 5ez u5belevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noi8) a0flt u2ubssy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut d0b8atus2 l u)fown all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wqe3s z*85kjnk /ptou04 kwa 52sxd0jdhereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise fopxtqz34 5dw/ek52u* jojasnkd0 08 ksr each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person b1kf6cvye 6 fon+2o,l2xks8l speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on th o,ye kl1o 6bffcxk6+vl22 ns8e 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 staj qd)u 2n(lw)rikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whibd.,u4 h1: lbfpwp5x xle the more modest amplifier B is rated at 40 W. (a) Ebw5bdf x,.hlupxp:4 1stimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when pgmrqd.)j bnvd /1zkzqcig4o 2;2 7 f8glaced 2.8 m in front of a loudspeaker on the stage. oz7v2 g4dnq; 8 .1cf 2b rmjqdg/)ikzg
(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 diy ,67gn eks *naf9 qacf95jtk9fference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whos 9ca6*g fyajq5nfk7 se9nt9 ,ke levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wy+28kx mtrnz/ill the intensity incrk8 +zmrn/yx2tease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one mb .ip51yw ,jbe ng4/thas twice the frequency of the other. Wnjt41bgb ,w. me 5yip/hat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air tha(ij;/ s *+*u ibhxyrhpt corresponds to a displacement amplitude ohr/i j* ishxb(pu+y *;f vibrating air 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 tone th6tiwh 98ql hk0at has a 50-dB soun968h ktqw i0hld level? (See Fig. 12–6.)    dB

What are the lowest and highes3/w j65cas:12 abk2q k*cdthywza /z tt frequencies that an ear can detect when the sound level is 30 dB? (a:zt a5/q dkcjtz2 /a12b3scwhw6* k ySee Fig. 12–6.)

  Your auditory system can accommodate a hugegq1h9acn.3ny nz f gxe0fv040 range of sound levels. What is the ratio of highest to lowest intensity at n evqx4000nfng9hyf zc .1a3g
(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.z mx m58/,dwaiez7yhg0 r4zn+ The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stringxd4/+am ,7yz8mz rg ie0z5hwn be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and da;8qy(ix gv:*k(gqj7: tem h); qtxpfirst three audible overtones if the pi;; htd x:qgv(ejp qgtixk:8)(qm 7*aype 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 expectocylwq3t1 m9g 0 g8ej; from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tub1g9tgcqy;3wlm 8oj0e e?    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-tu,m*tj6hy/ kozs7r ayxmm57)kbe pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?y 76mr/7*kz)t,ko s 5hm xajym $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonicf-ja) oqr ox4w:*wd0 d. What will be its fundamental frequency w4wj-)f0dxodar* o: q 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 above midd1)+ ttu/wxyd qle C (331/y+udwt tq )x0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emi0vmbuk+ ombs+)fg, z(ts middle C (262 Hz) when the temperg s fbbo v,)zk+0+(mumature 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 20 ( qhrfc:li )+n52b eyk+p2 zfp$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 sh- /mgqr4u d*wnould the hole be that must be uncovered to play D abu n*/wrg -qd4move 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 resonat b m 23.rxw2 ou/1kr0clbr;trxe at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (/w1 ro3;20.mbrt 2rxxlukrb ca) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube ogo04 q1be y3n1to 2ye1.80 m long is open at both ends. It resonates at two successive harmonics of frey o1oen 4gy01 3tob2eqquencies 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 8pj4+kaj:h ko$^{\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 for a 2.u t8 y nvkc+p/4wkic2914-m-long organ pipek9cytv/8+wu 2cknip4 at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximaf ssvfgrio q7v.al5+5m *89,nw5ciqi qp n2o1 tely 2.5 cm long. It is open to the outside and is closed at the other end by5qspwi5 ,lfr789o.2g s *ioi +f 5vcn 1vnmaqq the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adsh99fpo r2f4s just two strings, one of which is sounding 440 Hz. ofr2sfs9p4 9h How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (vc ih; 77g(qed(2ie *lacjat(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 operat s35pv880x kqvcnx s+1b6cedg es at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 55g 1xken0 vqdb8p638v+csx cs 000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whhuoxdgw,wf;3 jo*to3 2u, 1gven sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is thh uwufo;1,o,*j 2wx3dt gov3g e vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29 dy3ui86 k3/oikf jp8j2z ih9b4 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency kpjuo8b2j98 dizyfki3h3 i/6 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 play72spl(. gxgaq +.hrfg5i r x byn/*6mq middle C (262 Hz), but one is at 5.0°qx(i+gxr6/mh b5 2*qfprg.a.gnl y s 7C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, aneaqf ug*pq /jm..8,ab6y9jn p d C. Fork B has a 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 are soundeg ,fb9yqna*8 .puq.mj/ap j6e d together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker am2 o9ajfu-;deu)fpxu(dex(ya+ f70 zp8 zo-hnd 3.50 a+j 0u (d78hzypp)( -xafuooezfx2f-u9d ;emm from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vnai+ebpx6x ,3de)c2rn h 5. lum qlz*;d 5ehu1ibrating at 132 Hz, but a piano tuner hears three d n6x ,izldqc5almpu e 1 )r;2+5uhhe.xnb*3e 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 2.64 m and 2.76 m in air. How manmc8kbx( t9 byg kf(-a*y beats per second will be heary*b(xc-(t kkm gb9f8ad? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a 7 1p7cgol z(gqcertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of c77zo(pl 1qgg 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do6 u.ucglkk+; o you detect if a fire engine whose siren emits at 1550 Hz mo.cul6ogk;ku+ ves 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 : 2y btpi8gthp;zdm9sq a3t9/is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two f/ztd:p qma3tgy 8bt9 ;9s ihp2requencies 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.1*vg(mtw k5p x 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? 5p1xmgwt vk* (Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultras3 p* .xdqm5ysu9;sr tsonic sound waves at 50.0 kHz and receives them returned from an objectdpyr;*s t x3u5 ms9sq. moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 q -ahedrzj- +sxe7()m m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frej7r-a)ex- mdsh(e +zq quency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movi 2k5jy t*ju*yqng flat train car at a frequency of 75 Hz, and a second identical tuba played the say5*kuyq jj *t2me tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds3n,6c3f ry pdx. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries atn p6 xf33r,dyc 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using irhtb.v1 hf92ajn4v.+; dmxcultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound kg*9(yg h)pvws,eser42 g2hmof frequency 570 Hz. When the wind velocity is 12 m/s from the nohgwe92(p42m,seryv k)g ghs* rth, 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 lamy:hp:fh ali 88-4xll xdzw9 (nd 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) What is ta t5, kzrbs,:xnw6a (the angle the shock wave makes with the direction of the air,bz:r,a6 n(5wta xkts plane’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 pl xhxtt(f1v 9n*tsv 4w2anet where the speed of sound is onvw4txn t9 1 s2hxtf*v(ly 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 oceancrk c+4) pzul9. Determine the shock wave angle i9 rlzc+p4)u kct produces
(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 h(+9ljdl d qerq-:h+-o9 , kwwfq7 acq$/theta$ 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 1.5 km abogx*4+rfrloz xls :3xa/,+ f gtve the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 gfx4 glr xo3s+,fr:*azxt+/ lkm. 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 20,0.geqnzj vc ,shpa(0,sxl7,o * 00-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 t07e,ps qghs, nlo(*zj.a,xcvhe minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human zdj8sac- wm0y71cq4lg bj48pv es j( +audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It - z-delh pu86hu.llxbr b5 -h+consists of many plastic pipesr -p lx8--d6uz lhl +5uhhb.be of various 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 frpxg b,vjam1 ,ues+ey+ nl0/8uom a person makes a sound close to the threshold of human hearing (0 dB). What will be the so jb+ ,eme a,08+/lgy1 unsuxpvund level of 1000 such mosquitoes?    dB

  What is the resultant sounhn2v: dgo7m(4p7qg7o, mfrmp d level when an 82-dB sound and an 87-dB sound are heard simul(pmn2vmoq77f :g7ghpm4 d o,rtaneously?    dB

  The sound level 12.0 m froja dd. +aq+2xvhzu*2xm a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in al z2+q x.dxd2*a+ajuvh l directions?    W

  A stereo amplifier is rated at 150 W output at 1y8tkay9prnhgj,8 :) b000 Hz. The power output drops by 10 dB at 15 kHz. Wha9 ,jry)ka:g8ptyhb 8 nt is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices overs,bp:6 fq4osm their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 1: f6po,s s4qbm40 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 sy: sa*mm/r,fr4v)q hfgstems, 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 frequ( (0z mm4k n(,67qln sp ovn+nsqxfw(zency 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 be()2 ;,m yf hblgnhho,etween fixed points with a fundamental frequency o2b h ;hgne ,lyfm()o,hf 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled zegr94b * zae6bqj,3xwith water (Fig. 12–35). The water level is allowed to drop slowly. As it does s g*e6xq9,rzb3jae 4 zbo, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that i7d fjiblyjm.c ,k* h4,s open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamenf*by47 ,ljk d ,cmihj.tal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop 4n3:vbf3kn)* c x l8f5lqt m o2lwl/ow($\frac{1}{2}\lambda$) 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 coming fry:yp 1 t)cab;hom 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 farther from one source than the other. What is the freqt y:b1cypha); uency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The couk;h*x*f e57 tz2w lfg8twp v8nductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whz85u2egfvk xhwt 8f*lwt*p7;at is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you itrh-p i/cju:e 13 gs(is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movin3c1sgitejh-/(: iupr g (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cax6fr,m1f a,hy rs 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 (frequenhr1 f, a,fx6mycy halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat freqj, nfkvs6q0bv +(m+wkuency of 11 Hz. The shorter one is 2.40 m long. How long is t bs+v mkv,wk6j+(nf q0he other?    m

Two loudspeakers are at opposite ends of i6 eonch-3*q,zv9fqla railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from tq6h q93c,-nviflez* ohe 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 norm f0k.fmsn cx+5ally about 0.32 m/s what beat frequency would you expect if 5fs0kxm.c+ fn5.50-MHz ultrasound waves were directed along the flow and reflected from 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 speed 6.5 m/a9 2vde fjq,qw q2-ti+s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detect,qif2ed 2vq-jt a+q 9wed by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it a.4mv69lcm g kbpproaches a moth. The pulses are approximately 70.0 ms apart, and each is aboutk 46gmbc9v lm. 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) was once used to send sign.t d/rh2ady;ylb 0 c+zals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is .d+r/blh zca02 dyt;y 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 sk vd crtyh 0n:(2y*t3mtanding 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, andn0v:rhk2ttm y* y3d(c 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,” invoo q5 2wh gr4wwjep5v+*lves a long, slender aluminum rod held in the hand w254+qo5 w*pr wvhejg near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency o*o) hjz:d .;xrdhwh9v f about 100h*9whv;.djdoz: )xrh 0 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 tbdy3 o e,:z8hpx d8*ho uws+sw7yj;-uhe ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is wuxy;7:s h,dp8h y+w ojbod8s 3zu-*ethe plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is f8,a g27wg0g+bj- ;b jrw4ns+ cllkfx15 $^{\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