What is the evidence that sound tr ,pu *kuy+ /-nj mdxg(,aiua45e wtrku+5mxs8avels as a wave?

What is the evidence jher f8 op(n6bd 95sit0 6ft.othat sound is a form of energy?

Children sometimes play with a homemadcd*x*or +t6 ujqvd5+ we “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 b+ dd jrvq*o txuc6w5*+e 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 frequency orv/ e- 8u*xxf2gw3fx5 yr:gogc wavelength t3oxgx2:xf-5 ue /vfgw8cgyr *o change?

What evidence can you give dloj(ml;/)zwkjx e- rs8/ i5wthat the speed of sound in air does not depend significantly on frequency?e;x8/d w(il/ 5 kj-jr)oz mlsw

The voice of a person who has inhaled helium sounds very kwzc g6,h e r9*h5j7nlhigh-pitched. Why?

How will the air temperature in a room affect the pitch of o m491ew.-bphgvfk z*hq5dp /jrgan pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds iiby ob /;mwf ;09,nkvdn various frequency ranges. (An example is a c;0yvkb;n m/f ,w id9boar muffler.)

Why are the frets on a guital ibb)l 2-x6lzr (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bri )l b6zilx2-bldge?

A noisy truck approaches you from behind a building. Initially you hear i +d-b7uk:qzjp2 tl)wrt but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter”qw7: +- 2ptd)ujlrkb z — 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 *w2 tgk,nvped.y:u; t“interference in space,” whereas beats can be said to be du; *pvt:teyw u.g2dn k,e to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the k9y*)obvc6klpoints D and C (where destructive and construct) bvcl9yo*6 kkive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work xwzr,l yoc6 ;of+)+keac :)kuin areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With alo)efao) wzc kxkry:c;,++ 6u 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 o o)8e: o7tjysshown 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), ar)y7o8o:jt soee 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 daz4 *dv oa2sy+irection, with the same velocity? Explaiya ovaz2+ sd*4n.

If a wind is blowing, will this alter the frequency of the sound heard by a pamb , oiv*ro q3(ej)9ej(uxa 4erson at rest with rr3ab)aq(miov4 9, je(exou*jespect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor r 1x:it fxp3) ,:0j3 xc8mms nqnhrr9qis blowing a whistle in front of the child on the ground. At which position, A through E, will the child trr3xix3 1,8)mr s09pqn mh nq::fxcjhear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengxy gfof3j m.g:;qzi. ucz0.b)th of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s xy0 f3uogq ..z:.;)mgjiz bfcafter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below t j,hu2cweka l9;d4y 1yhe waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the oa dl 21eyc;w4jyu9k, hcean 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 wavelengths in 8,kz (lhjiy+jea 11luair 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 +;znz plt g:kb/-9vcyg5xl4se g.7m 2 iufxk- 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 befo/tyig25eng z.-csmk7 lg-4 pl9v f+x:;ku zxbre 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 iv,7 sj f; mm :+pbanff8jrc ueam/+2 yxu4g2s7t makes when striking the water below is heard 3.5 s later. How high is the f ymuucfpmbfasvn7j m g/+j r4se8,:+x2a;27cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concretd:fs v1wh1r5ye pavement. A moment later two sounds are heard from the im:yf 511s wrhvdpact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one milevva+xh0 elj 9d 7df:o; of distance by the “5-second rule” for estimating the distance from a lightning str7 +vddjflo: 0;hea v9xike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound ud,5b:thyw /xuv zzvr7(u53v at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound dfvag g1sq b6 3.i6yx1whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired qg:xqy jiuh+60 o o7pomp)u4 9simultaneously at a certain py +omu ij)6qoo uq4g:hx07p9p lace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpla;xdg rqpf:vpo,ey :3,ne with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not d v,eo:qpgf3d:x rpy;,B’s.]    dB

  A cassette player is said to hd 3xt76n1*+ol e zmrlz4tka3 lave a signal-to-noise ratio of 58 dB, whereas for a CD player it io t+dzer37k4ml3l 1zxn6*l ats 95 dB. What 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 oua/ -k4 e jx4t erqcria(6iu5+lr(xy, wtput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sph4( tax6 a4lir, -rw5yx(j +e icr/kqueere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose ar/4u jf;1 isaeyx+,gbhea 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 at5bds xen+mwfbwd:sd0 )x(q:0t*,j og 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 f*(+)e0d5,: bd xgdwnwx0o tq:smj sbf rom 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 5shin 4r 1yux2in front of a loudspeaker on the stnxuh5ri 1s2 4yage.
(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 gsw + q(*g/jy)pb ,iqja difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds w jgyigp s b()/j*,w+qqhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavenn-1vwr6fhe z*x* i. +q cjk5h is tripled, (a) by what factor will the intensity increase? Increas +1hqxwc *v-e6nf n*5hik.zjre by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displac z4;sd eyur+ju(s2bj2xl 42k tement amplitudes, but one has twice the frequency of the other. What is the ratio of thsut+ yljjku ;rb 2z4ex4d2(2 seir intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspufhgn0,)l/ lbonds to a displacement amplitude of vibr/uflh,) ln0 bgating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hwq gh1djp:vi j//6;naave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) 1vgw/qj;/6ahpi :jnd    dB

What are the lowest and bmun ;2y:)n+n7vpf2hr* tsg m highest frequencies that an ear can detect when the sound level is 30 dB? (Sevtg+* h m2 fpns)n2 b;rny:m7ue Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the vv 3py1laes) bb;m 0v4ratio of highest to lowest is 1ma4vl bv3be;yp )0vntensity 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 fundamentazkm cv6b*w (7p :ooie7l frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g.ci(p v7k wme76o: *zbo Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fi3bt6 8iu 7ojilpvd:j ,rst three audible overtones, j8dpltv6u: jb3io7i if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the t6cmp8paxl )fxn2.:z dop of an empty soda bottle that is 18 cm dec 2m.lx)8: zn fa6pdpxep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipisc 8m2bdoj) t,k(4rt lmxn: xv;*.dtes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of n:; jold)mivrk*bx 8xs(4 dtm.2t tc,pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmoq-hfxrkl k)0;po/7z l1ej q s:6xjfx5 nic. What will be its fundamental frequency if it is fingered at a length ;z 6ox)rl/ pl7jx0kjq-skfhqf x1:5e of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mizly ;p8qng5sm2f/ *or ddle Cs 5l2;n ymzpq*/ro gf8 (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pip(ekpx 64 mynq9e that emits middle C (262 Hz) when tmeyk69 q4nx(p he temperature 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 . o9ipc2j6m kx20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the v9y-k*ll)kma:v bs3zflute in Example 12–10 should the hole be that must be uncovered to plazvm3kay- )l9:* s kvbly 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 Hzq a hs5,u75:3erubcmm ijr,2u, 440 Hz, and 616 Hz, but not at any other frequencies in betw2ir m7ma,uuc q:,jbsh3u e5r5 een. (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 1.80 m long is open at both ends. It resona b)mdyp)v7 h7qtes at two successive harm7dhb7 pv)qym )onics of frequencies 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 lj5 k qi:7 kgd3q:q6fb$^{\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 2.14-m-long orgauy neh+ b, 42cyrvqude-4g65 rn pipg6+b5ce44,yu-r2uehn y vdq re at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside y4+vgo yo 9bl7h; c)7eh2vxwt and is closyhl xcw7ybho;)+ v t vo4eg279ed 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 relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust vbez:mt b*0lg) 4 nkt0two strings, one of which is sounding 440 Hz. How far off in frequency is the o:tz0 lbt*)k0 ne 4gbvmther string? ±    Hz

  What is the beat frequency if middle C (h z+oe qm +yo*mmq z;(zg:1g;y262 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, nn d5; l866jvh*ah boiwhile another (brand X) operates at an unknown fdlh;n 8*oj6a6 h5bni vrequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a v ( f:ppw;. iuns7so8m350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning foip o(w8su;pf:nmv s7 .rk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The te8b-p0t d-by o fik4x3bnsion in one string is then decreased by 2.0%. What will be the bek4b-idf 3by8tb xp0o-at frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be ycdhhai6 v: sn,+s+d7d mfl- 1heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 26d- dncdy,hl7:sh vs+ +a1ifm5.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has : 9ixyqevbb3+o1d33rzf xh0 ja 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 th0o :f3 yxb1hb3i ezvx+j 3rq9de 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 apar.qm*5pj2fzk3 nyn;wk-a y/t lt. A person stands 3.00 m from one speaker and 3.50 ak5.kjp/-m l;y2fn*wzn3 qty m 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 vibrating at 132 Hz, but0 c(+8 misnupn+wjwca n3 2r.d a piano tuner hears three beats every 2.0 s when they are played together. (a) If w2mn d.i(r8 jaw3c+n c0snup+ 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 , ao evo--huzs i26c2zof wavelengths 2.64 m and 2.76 m in air. How many beats per second will be hez a-zo2ehic,u vs6-o2ard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 18alukhcl* g+xb3p +(u imni13550 Hz when at rest. What freque kup*+8mxnc b3+ il(alg3ui 1hncy do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a firea m((ej9: l -v0q6z xwebe(los engine whose siren emits at 1550 Hz moves at a speed of 3xebvm((sq loa 9ezwe6j(0 :-l2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving qd owoa fns ;/ bt1nx88./ftr;yb7t0otoward you at 15 m/s ved; 0t1w8 a ott fbob /.;xnofsqy8nr7/rsus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same sinw.2qk x.2 x;ctryu)odt m- sx5gle 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 frequency of 5.5 Hz. What is the frequency-c w rx).q.x5ym2uktd xt ;so2 the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50ybb 7u65.0myhckp d: u.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receiy.m5ckhy 7:b0bup 6duved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at)sz5( ve2 lmiu.qase0;pl4zx a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency .e05sv4 ) ;xsmia ep(lzu2l qz30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original D kk fz l1h:( ::2sxbkg:ad-8pm2 ,j+zr yswvkfoppler experiments, a tuba was played on a moving flat tbsy h8zl+:mz2,j:-g1fsv (dka wprxk:fk k2:rain 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow n:.hdy rx:jk; speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly awa xr;hd yj:n.:ky from the sound source?   Hz

  The Doppler effect using ultrasonicxf /*a 3w2mppwfr wf44 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 of frequenb d:8h6b zrs,cyq*m0t cy 570 Hz. When the wind velocity is 12 m/s from the no: bq8t*6r0hmbc, s dyzrth, 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 lan+ sngj1x7q4v4 s lf0vgd 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) W*+g2qzeig + xrhat is the angle the gq *2z+r+ xegishock wave makes with the direction 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 whce /cz(n w0ui5ere the speed of sound is only aboie(nc5cuz w 0/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 strikes the vx:2i1iw gq5r ocean. Determine the shock wave angle it produc 12 qriix:5gvwes
(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 -k gq *rx6go k(pn(h;u$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead:b pmv.g 1gu8z*jn enq)o t)7l and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic b. ol 8u)pb zg j*v:n1m)7ngeqtoom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 2 u3i-c)oxmhbcll+f3y0 n n +o80,000-Hz sound pulses downward from the b nco30l+n-yxcu8 m+oif)b3lhottom 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)?    s

  Approximately how many octavesd8+ljmc7 ui/*z hg fex87/b22wvoxu w are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a se 8eq9. obqmf.aub)2 ,ktjwp-b wer pipe symphony. It consists of many plastic pipes of vario,92 wfm8b e.ab-. o)qpukbqtjus 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 person makes a k6il 3rbi0p5e )qjm/5u lpk*wsound close to the threshold of human h/5m3)50qi juk i*k pwel6brlpearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an9 ;- hij(tvyjn 82-dB sound and an 87-dB sound are heard simultaneouslytyi n(j;j9 v-h?    dB

  The sound level 12.0 m from ) s5da x; x-jgoh01ircl9f3fvqgx+-ut) e ;b qa loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally i1)h-etvq 3 uc9;dqj x;rlgf-xi5g0)s+ ba fxo n all directions?    W

  A stereo amplifier is rated at 150 ts8r jy8-tb+yl/1ue/ 2y aie yW output at 1000 Hz. The power output drops by 10 dB a/ bsirj2y+8ty /t-eela8y 1yut 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically weari9ku-pbj c:a. protective 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 unprotected ear at a distance of 30 m from a jet airpk: j.9 cuabip-lane engine?    W

  In audio and communications systems7g q9(qe)z0z)67d.vfy sh zz eyfgq)v, 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 lsd3 gj0znyv ;lnyb,(fzms,fo n5* 4-is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed po9 e;tjuo,s7 kq5ei e.fints with a fundamental frequency of 440 Hz and a mass per f7 i9,5eeejq u.ok;stunit 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 vertisx8b11m hb* pwcal open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water lembb18 wp1*xs hvel 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 tz)x *aqpwrm/7dxm 7eab1 5p3eube that is open at one end and also 75 cm long. How much tension shoam*/7r xeedm5 w qz3 p)7ab1xpuld be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full(up1lnc :s :xu 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 coming froipv4c xbo el7j1:) yl,m two sources. The sound is loudest at points equidistan v,xcllpo j71i)ye:b4t 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 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationarya unwdyfx g+3v3n+)946arq p f. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traipr+ fnaw43xydfau)+vq n69g3n?   m/s

  The frequency of a steam train whistle as it approaches zw- 7lvr* wgr2you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fasr -lzv2gw*r7w t was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to i2roe6d))ejmc-o pq:ski 2;c the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octav6)2c2):e-iqoc;s pmik eojr de (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produc*ynkmi*65qh )n.xy 0qqqm( une a beat frequency of 11 Hz. The shorter one is 2.40 unmy6x0 myn*h*qkq n q 5(q).im long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past;dbi9rr7e5fex in 6e* a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 7i5 rdin6ef9;x er b*eHz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.3pyd vlmi5u-: 42 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 wavep45ul i m-yv:ds travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying t icw;6kpkaz44oward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave refle;zik6k4c ap4wcts off the moth?    kHz

  A bat emits a series of hilery8r0vsv0 4k *ob 2egh frequency sound pulses 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 one chirp returns before the next chirp iel*0bvs2r 80k r oe4vys emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals fr; ctc/b,qd 7a2j yk m70os7ylfom 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 thatoj/t ,y7 fb2cs ;d7lcqm7yak0 only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can3xya mr0 js-o :,t0ayz be compromised by the presence of standing waves, which can cause acoustic “dead jm0r, as0zyoy3x:-a tspots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invol4tjaj); klltv)wr jr qy9c:53b0k 0xgves a long, slender aluminum rod held in the hand a9w0k5 ktg cl4tjl:j q rb)3vy ;0x)rjnear 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 :h*.s4v bzpax4;)gv lzywcx) human ear at a frequency of about . : v;w*sbxvpxz )y4 4zh)clag1000 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.og g1ixf):*( ohm )nna An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the pl*n)oh1)m:gaf( g ox inane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat p.f (t0 j*3hen*tna ynis 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