What is the evidence that sound travels as a wave p-4dx2bu/p2xrhk qgmbr*r +;?

What is the evidence thauv6. f40rr9u s 0q6 (/t5cnilyb orllbt sound is a form of energy?

Children sometimes play with1r: azhtgc,d1exfe8* a homemade “telephone” 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 other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the othh r*at:ez8,1g d x1cfeer.

When a sound wave passes from air into water, do you expect the frequency or 0s0hnf kvn )m1wavelength to change)0vhfkn nms01?

What evidence can you give that the myvv*7l 78 crc8;vv rqs ;vs3sspeed of sound in air does not depend significantly v 3c; rs lc*7v8vrm;qys7v8svon frequency?

The voice of a person who has inhaled helium sounds very high-pitched */,5v5mp9w ,un8xjtx/cg bl+jhricm. Why?

How will the air temperature in a room affect the pitch of organ p3 x2 xb gfbwcvcrpk26 dc(/+0lipes?

Explain how a tube might be used as a filter to reducex 3molq:l x0w3*i:okj the amplitude of sounds in various frequency rli :3qjmok* 30 owl:xxanges. (An example is a car muffler.)

Why are the frets on fl ntvoqw;5v3/x 3u ri+ am/(ta guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridxrvm(twau/; o5 v3lq n/ i+t3fge?

A noisy truck approaches you from behind a building. Initially you hi0l :h.spgu o+ear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: Se0:.h up li+soge Section 11–15 on diffraction.]

Standing waves can be said to be due to “in/ard8 h.b(e-vsejk ),k+ rvei terference in space,” whereas beats can be said to be due to “interferen s 8/ jbv, ei(ekhverr+-a).dkce in time.” Explain.

In Fig. 12–16, if the frequency of the sp5,cybgk(r) k qxu6o8 yeakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther a68uy )5xyocr kq bk,g(part or closer together?

Traditional methods of protecting the heari zwpv*dg ur7f.3p+6 crng 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 feec gwf*pr d6u+3rpz.v7ds 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 5v7.tllpe)1ri u eec o;.g r5jFig. 12–31. Each wave can be thought of as a superpositig5re r;.e157jv)lp o ule.ticon of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction,rpiv -ql q-x62 with the samevri 6qp 2--xlq velocity? Explain.

If a wind is blowing, will this alter the 4 yqp3)0wny0uln-thy frequency of the sound heard by a person at rest with respect to the source? Is the 3yw- 0n 4 yl0)yhupntqwavelength or velocity changed?

Figure 12–32 shows various positions of a ;oax7;1o- un3jezkbj child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A tzj-3a;on;1x7 job e ukhrough 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 listenit)w-l 54t jpt*sv7uiz ifd3r5ng for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length ivl5zfrsud)3 w*5tt74i ptj- of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shiph:;widxb u2 a3 just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depthx2a:iu;h b3wd.    $ \times10^{ 3}$m

  (a) Calculate the waveleng rj.4 dox-2hzvths 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 a:hj566u5 dg 9et uqoetuna 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 (a)g o ua6qe965tdeh:u5 j by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of aenmvho*z,l n(m +k r+( cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is thkrlmv,m(* nnz+ +o(h ee cliff?    m

  A person, with his ear to the1f w- +5prlw((k)wxz/t 7jkx 8sncfuc ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.17f x1xkflc(jt+ / -uz)kwp8c5snr(ww 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 (n6srue i+y(1yqmd u5ance by the “5-second rule” for estimatin+iu6uyyd(5 1 (nrqesmg 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 laf e )5r1o :o;gd.ndxxevel 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 intensityspz;+ovutzo- v(0/;3ylcsvz8r6zc s is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta6,njg-*j r su v;enlz2neously at a certain place, what will be the sound level if only one is explodejr;6-ln2jvn*g, u szed? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with rtkb1 zi5)n/o four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience i tn5z1/ bo)krif the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio u8.zpa;q qe-q 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 foezp8.;- a qqqur each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norm qfted9tn ywv- 5*-liz (-ozq7al conversation. Use Table 12–2. Assume the soun(9*zvfne zil -q-td7wtqy -5o d 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 zqz0f;ce7v ) ;7emk5kr1 )gpsfjl m 2fan 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 su c;it+(kkmalr68- vat 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a a8k;+6 ut( -srklv cimloudspeaker 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.wyb2s525dn fd8 m in front of a loudspeak25 2wd5ys dbfner on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difm.1nr3 w8c ur 8-vprd,bz0yfa* yu1amference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hna-r,v 03yfc8mubr1d1 zuyp. w ma*8rint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intr8a25mdvubfy-0 vok h p f1 2q0g5om5qensity increase? Increase by a fafhro8u5p2qgv oa1 kmqb-5yf 5m0 v 2d0ctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal gpy c*b3 k1q2 sszhjdm pe c1./64-mlbdisplacement amplitudes, but one has twice the frequency of t2sc6 ezk4-/dqhc3bm.l11bmjgp*s y p he other. What is the ratio of their intensities?   

  What would be the sound le2rlalkh/n ;,tc-u( po vel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 u 2l(k,l oa ;nh/tpr-cHz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thatdgumok kxb/bi,10op(* akb 45 haxau415 o,( kkbpk *dig /ombb0s a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thatny5 tqa-b:6hx an ear can detect when the sound level is 30 5bq :xnah6 t-ydB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sounds tvv4938xz 9qs)w 2na.bvvam levels. What is the ratio ofv2v. a9s893xsvzmtn 4q)abv w highest 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 viol ,2 gb f2ifub8qcyu8m(d4ezzys3- r/tin has a fundamental frequency of 440 Hz. The length of the vibbrqb mzg,ui82 (zt 4-cy3esf/ u2yfd8rating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What arnxz1/mz( s to2e the fundamental and first three audible overtones if the pipe (1/xsnzz2m tois
(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 w,eg/qzj rqk9y2k ,k w1ould you expect from blowing across the top of an empty soda bottle that i 9krjk/wg qq, z2k1e,ys 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-to8*efb,hpq 0 g56vy3 mo zhtr*ube pipes spanning the range of human hearing (20 Hz to 20 kHz), what wou*zgyh *6 8,5b3rhpoemo 0qvftld 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 ittrz6,ssel ;fxf*(m yq2bl:v )s third harmonic. What will be its fundament sf* t6lrmq:; (xvlsbe f2yz,)al 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 abozi8z68 3vd2qi sas(lfj c4n;j0f mla 7ve middle C (330 aij2fs8 qz0 lm3d8v;c46ia(7fnz slj 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 organf vy( bo yc4ocfg,71c( pipe that emits middle C (262 Hz) when the temperature i cyybg7(4, co1vc(fo fs 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 alu ix8s5n *cjo(s6 tbl2;.5phr o0jkst 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the *frhktelq )vkbn(: :p11;ah v flute in Example 12–10 should the hole be that:kha; kq*(1btv)vlfp hren 1: must be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hzer4 7 jprcixx-p6p n0+, but not at any other frequencies in between. 0cj4nxr +epp 7p r6i-x(a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1v :b 2jgqm*d 5q86dupr u eujx/i*9a+sip2i *m.80 m long is open at both ends. It resonates at two successive harmonics of frequenc q*+a i:dmj6m/evbq xugpuri*u95jp82 2s d i*ies 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 g 5jg1s(s 54e/t zbhac5;umdj$^{\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.7fs -wyiqvz4 a 2.14-m-long organ pipe at 20 w .zf4q-yis 7v$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 yg;u )ku/1ru4y )n fhka60txwcm 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. What is the rela0uh/ k 4uf1))rkytywn; g6xuationship 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 t8-- syxmb2;ow d5wdp7 3dm*zvk)nxsj rying to adjust two strings, one of which is bm5n ; s-2y7mpd*xj)-okx8z ws dd vw3sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Czqrw3u(fwaph5dpuz7+)ubq qf+9e / prr.13e (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 (brand X) operates at)sp,vo4wxv ,ri . vsq(9qf p)h 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,shp(x,)osqv,.v9rifv qwp)4 estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork jv6f;+7bcvj, 8efnjd and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string?be;f6ndjvf jc+78v,j Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequenc7 dv1b*i3mmwhwe1 fmid07*tb y, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [H**wvemi7b0it d7dmhb1fm31 w int: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mipn:ywkwtk- .7 9f l.haddle C (262 Hz), but whf - nwylat:k9. kp7.one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B h .dw77wn382psaz k5lmy gu7 xcas 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 7wn8y7 d g .5zu2lwkc3pxams7 beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m froni;c7+,d yte3r8gd wum one speaker and 3.50 m from the other3+cnu7 ,wydr;e8gti d.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hea/trg( footvilzcpqx4m;xw 61l,-;-f rs three beotx wxt;;(fpm1g zf6,q-/co4vl-r li ats 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 a1 iotqjggf (m.k ki88hfsmz,;; f * )m/f5odsuir. How many beats per seco1mdu sfoghtsj 5kq;f ,kiz)m8 mi/.( *;f8ogfnd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sqa*nk7z ./d xpbf ul:/iren is 1550 Hz when at rest. What frequency k/ f/n*a x .plqud:b7zdo you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect ; sf.ov31wm. bw wmyd/if a fire engine whose siren emits at 1550 Hz moves atsy f.mwmo . 3;v1bd/ww a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequen7 *ixf+l vq(tlcy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are thl7ftl v+qx*(i ey 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 singls6zmhyr/ x vsl 6ka04n+h5dz;;nhjf3 l p y;e9e frequency 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 frequn mlz d6/pzfn0yh;49yv; s;xj6rake3lhsh 5+ ency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends o,lq1(ki+ak1 y0 fps m)jwngq1 ut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directl li1q(jyg1p+1w m q, sk)n0kafy 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 m/s As it flies, the bat emiw l k;7d5co(xjl :7qputs an ultrasonic sound wave with frel:d lko jx 7uq5c7pw;(quency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originj g qqye4(gc*,*kb5nmal Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station agb, nqk (c**4gmq j5yet a speed of 10 m/s ?   Hz

  A Doppler flow meter u7zbt wdg7z/n/ j3hz 0vses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue i 7b/z7nwhgzd/ tv30jzs 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 waves ofyxx-1g*w a cp +fne22h 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 frequen msxnwvedz 8wgz2 - bk()/i.:h2op:xj yc3m6zcy 570 Hz. When the wind velocity is 12 m/s from the north, what:d-p3 zhv2x:.s8zyzwg b xck mno)2m(jie/6w 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 /q;x,e/cu;of z;3 1mu p cynoimoving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where v8jnkz1(fkf4the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction n jzfk(8f1k4v of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speedy7*-k cpimf g/ of sound is only abo f*p7y/ imgck-ut 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 sktxwn3nowiz7dao8(.. d: x 8xtrikes the ocean. Determine the shock wave angle it produces ..8(tk nwo7d8nxowxixd3za :
(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 +n*c*8 co bsm; 8n;4lek edbcc$/theta$ 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 above the groun-rysup2 j70njav h*7nd flying faster than the spee va-20jsunn7ph7yj r* d of sound. By the 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 sona9xns j+m7fg 4kr device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?g9xks74fm +j n    s

  Approximately how many ocdp;2x2yd-h h9v n2 z (wj-1qxrzra;a x ltp:u2taves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symp mwmydeil45-*i j.x zptto0-8hony. It consists of many plastic pipes of various lengths, which are open oji- mxlw 05it8.* o meydt-z4pn both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of hu d c *pt-)ufnj*n08fqts*1k cqman he*f8q -cn1 t*0p*q fsnj) ucdtkaring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound);eya8w b/r5fhacbgl,bki 8qg6bi. , are heard simu/gibfq i5l8wk) ,bb y 6eag,c.8hbr;altaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whz0 ra;3r 5*dklxpv(.2agwqg zat is the acoustic power output (W) of the zg0.kx w r *adgq;(2 zlr53pvaspeaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ou(vrqa ,wksh: 9tput drops by 10 dB at 15 kHz. What is the power outpuhqs:v(kw,r 9a t in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protex(0uss, xvip6n .hwew7 9df0 ictive devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unp6i0x(e.s xi w nw,shupv0df 97rotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicationsu xvq28g xi)v: 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 fq5oqb-iq( * kwu96vn duya7 )m vez)o)requency 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 fundamenta)-hak; r/ xpmsl frequency oax/phr m-s );kf 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 with wat ,x+xr eoaa2(a 9hwob+dl 5z:xer (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 opening to the water level is 0.125 m and again at 0.395 m. What is the frequency ofxhzo+x w5al( x:do a ,bra9e2+ the tuning fork?   Hz

  A 75-cm-long guitar string opnytq+ z90m3x* v 2ozr a4tahg,he:0pf mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to pr0rpma ,qg3*p v:z90zx o4n2ea th+htyoduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to re sxj 84l (:s6luoupbc/sonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range com0r4; z )nxhizxnxeb 2mwuwgu0 * pb8-1jmu4s4ing from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what x)n u48 ;esgnu*z0bp1i4mzwwru xb4j0xm -2h 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 whistu*xvze)j6-d oles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequencejz d-6xv) uo*y 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 538hj)rs(z zb6 rd:1uu i1 Hz. After it passes you, its frequency is measured as 486 Hz. How fuju1 6b :d)is1zhr(zrast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to +e vxhc+s:t.h4a+z6q h j xdh/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 hdth+zsehx6+x+hv4.j: qc /a by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11edox p5)3. chjtzo0fa3a *,r mpidx( 7 Hz. The shorter one is 2.40 miept7jr5hxfd33(.xpa)z o d0 mc*a, o long. How long is the other?    m

Two loudspeakers are at opposite ends of t d.*lam5o,ts:p:xg wa 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 the position A, in front of the car, (b) he is between the spoalxg5. ::s*,md t wtpeakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beato1kr 0w4)a, 4 h zv0;xvpwwqqq frequency would you expect if 5.50-MHz ultrasound waves were directed a0o) wh;r4 qkv,xq w 1pzwqva04long 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 m4x:( tlun r)ms/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 )t4nul m rsx(:of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. b 1kc y6xx ))*yobxypvxgk55+The pulses are approximately 70.0c*py5y b+)k1x6ovx 5b gxyk x) ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vil.jcv3e;dqkw l*m:s) qlage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequencws q dcj).v;:l q*kem3y 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 presencxuy ,vh*7a w2py4tnf .e of standing waves, which can cause acoustic “dead spots” at.*x2y vwft7 ,yhu4an p the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumi3doqsegals+e o c 1*9ml8li9g, bp*-ynum rod held in thgs *y1,sdq aib*99-+8 o pleolgm3 lcee hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the thresho5.uv1 odt xmz)2 :h jkc.b.ehwld of hearing for the human ear at a frequency of aboh. .md.w1 b :vxjzko tu2eh5c)ut 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 t5,12*aezijb g(wzc ethe ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is ti* bj5,cgzazee 2(t1whe plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15tjxkf3jp+ +2qx q4g*f $^{\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