What is the evidence that sound tr372e18tbiz a tsfem )yavels as a wave?

What is the evidence that sound md )o xb22o4r(taq)gbx9b3n jis a form of energy?

Children sometimes play with a homem.1kv/jtg x)i uade “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).uti1vg)jxk/ . Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you7q-qma a df tzsi2+41e expect the frequency or wavelength to changez+mqia q4et-fa2s 1d 7?

What evidence can you give that the speed of sound in air does not.m fh5ehny:armlw9 -: depend significantw.r:-9ayn fm:5e mhhl ly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?p ne(faq 3/w3bl4i3 tror4h(r

How will the air temperature in a room affe 6 kp1 n2a78multqytz;ct the pitch of organ pipes?

Explain how a tube mi w.:r.d,cz3z m)8v jfghhq4isght be used as a filter to reduce the amplitude of sounds in varsz:z c )3iqrmh f4,d..hj8gv wious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move 3,xyz(5axtw d/,gpru:c0oj kup the fir0 z:xtx,5pjda y3go uc/k, w(ngerboard toward the bridge?

A noisy truck approaches you from behind a building. Ini o--a9ugo5oeu6-n+o rl0ok7rzqos*atially you hear it but cannot see it. When it emerges an gooun-ou *r6zo -a+ rae9s5l7o-oq 0kd you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats c2 3 5y8vij yikh6fngw6av6 gkj i2wnfi 85yhy63n be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin52v5(tmz9va mqtf-y ,vx d+8xnm rg*nts D and C (where destructive and constructive+- ma(mxvt 8r5 , t5v2qgmn*y9xd nfvz interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with.d 7 ,e4cmmrnu very high noise levels have consisted mainly of efforts to block or reme7dcmnu4. r, duce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sx3hrmr2ci jz v81 3qy+uperposition 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 apa3+mq2izvh8cr y xjr31rt? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same +jx oub.(yfi 2 yxmc/w /ki.r+direction, with the s.2jxwi+o(x.+f i bry ku//m ycame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pk a et,;.qqk qp+n7gb*tn9wp ob03gq c71vg7e erson at rest with respect to the source? Is 10 pp+qt.ek gc7gbn*k 9wo;qq ng ev tbqa3,77the wavelength or velocity changed?

Figure 12–32 shows various positions of a cnlq hr 47emq.lq7/3hx hild in motion on a swing. A monitor is blowing a whistle hh.7/elr 4 mlqx 7qqn3in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listenin5wb+ rgei. hze7,ewx:(owk evr :y6/yg 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 of the lwxiheryz+6gyk ,5vw er w e7:/:o.(e bake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of h9) -r:p trxgiq,uh*peis ship 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 signif-: rxe tpurp9 *)gqhi,icantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air d,gx pczn z p*:q,ro,jz wg4+9at 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 *l 5uxhbpj -nhbq+)f5tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). Hf+uj5)*b h xqhlb5-pnow much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from th/m;n ctug pc( s*rek(0f x8gi;3 8wsvve top of a cliff. The splash it makes when striking the water below is heard 3.5g8 v* (grssk(t;0;e x3wvn/c8ucifp m s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a yf apd+w tmdhk:4xc f3 8i+t-+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 m8a 3f-td:fyt4+xhd+wpc k+i, 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 on.fgi /m pr3f4xv,3xxhe mile of distance by the “5-second rule” for estimating f/3xvxr i,4pgf.h3 mx 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 lat f4p dv+ b3ktlx;y40nl8dr/ub8wp6 evel 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 irt ,cbr2 /aiw3a2+ d24jy3jxvjm1 wu untensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level o/j5 9r 9ggeerudob5ws7 e g 6rq3o7/zqf 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is o/g73odge q9wrujeb5r geq/s576z 9rexploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distc nan r/6 h0fws(v4*xdh *qcn,ance from an airplane with four equally noisy jet engines is experiencing a sound leve,4h*c0varfd(q/hs n*nx6 cw nl bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have av1/(vqfu k8 dqi-, y8)wez5fp h8siri signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of/vki(p q hriqy5z-8)ie v1wd uf ,f88s intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversloj mmh7n qzbuo n54;;n b:55pation. Use Table 12–2. Assume the sound spreads roughly uniformly over :;4jbnm ho55q ;zn o5mnulp7ba sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum 2g 1ol.r nyiuv af.51nwhose 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 ifz* .)4bbpgq9b-2 3db j.d8gdvr h vums rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibel3.d2 *bv-gdz )94v gjm u.bp8 qfbhbrds you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 p1 ,ji3d+ cyzqm in front of a loudspeaker jdqp , 1+zcy3ion 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 differe; wk w1w0gzn3i+x/s ejnce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?s1gw ix3k0wzjn/w ;+e [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intg6u yx0vh+tnuzh isc6f2o*7,ensity increase? Ii c ,u2uxyg67 ts*ofhv0z +6hnncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one cp+j jfek s*/*has twice the frequency of the other. What is thepjc/ks* *e+ jf ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corras*3yfab.y4n dowg +:esponds to baosygda+w 3 *fy4n:.a displacement amplitude of 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 7 /sdjh .f8s5qu7hl**ap qbgua 100-Hz tone that has a 50-dB sound .fj*5sa*s7hqhb8 g d/ uq lup7level? (See Fig. 12–6.)    dB

What are the lowest anh28x r/29es+igzxuffaj2 f w)fje(- nd highest frequencies that an ear can detect when the sound leve fa w9r/ ux2ff2x2+-jez jnf s8ig()hel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate apqok. 80dz bh1 huge range of sound levels. What is the ratio of p.q0zdo b1k8hhighest 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 vi qn;8wb3r.ru; mxj: yabw9yh2olin has a fundamental frequency of 440 Hz. The length of the vibrating porqn 8yyrbm.j92h; aw r;3: ubwxtion 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 are the fundamental kcben6m2m-, +df n8tpl y+3eo and first three audible ove 68 eb+tekmpldco+ny,3-nm f2rtones 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 towc:l ap;t6 (, s5 t+toft6b/hp *kulpop of an empty soda bottle that is 18 cm deep, if you assumed it was a clbo tklt/t sp;a lfhpp6(c*u:5 +to,6 wosed 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 pipe d31fwvsi : 58sfwgi;es spanning the range of human hearing (20 Hz gsewi35s1fi w:fd ; 8vto 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harm*j;o j u.( shw8+xkucjshl- s8onic. What will be its fundamental frequen sujw8-cx. ou+h ks(h 8l;jj*scy 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 am ydy8nz:5)r middle C (dm5y:y )znr a8330 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 7 z)z(f es*7gjqy6i nworgan pipe that emits middle C (262 Hz) when y7z * ingj76fzw q(es)the 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 bn5i*d)ew6i w at 20 $^{\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 should the h ay:e f(q44wgiole be that must be uncovered to play D above middga :4e 4ywi(qfle 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 -v.,s / fvfuf0vj t*gaoqn-(+sbu/ra 264 Hz, 440 Hz, and 616 Hz, but not at any other freque -0vj/snfrba,v(fuf s a+uoqt */.v-g ncies in between. (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 resonates at two2wof+98; oy q f9ajrah successive harmonics of frequencies 275 Hz and 330 Hz. What a;9oyhwoj a2ff8rq9+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 u34iv 3hvt -ql$^{\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 arlux(h vzr7g6+q j57 nme present within the audible range for a 2.14-m-long organ pinmu + 57zvhjg rq(lx76pe 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/(gf3v egm-+tzz c z*e and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standi +gzctz/*f3ge ( zvem-ng 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 u)b.fx.i mlow. v:z9jbeat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other s9blfw.m)z. ou:.vj xitring? ±    Hz

  What is the beat frequency n7 zbibu6/j72g:gkcdif middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, w 4ujv3y1 uv7inhile 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 5000 Hz occurs when they are played simul u3iv1nj y4vu7taneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundeb-jqh6 l.lt(6q kg/yn d with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What k6(-l.qgb qj6 lyh/tnis the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensiok5o+p-oyv jl -n in one string is then decreased by 2.0%. What will o lko+yv j--p5be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will v/)dfcky 5 8hebe heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and thd8kch)5y e/f ve other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,j 34jodwj j:/w A, B, and 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 p jdj 3:wo4jjw/ossible 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 from one speake wxqr(3klan(96 o l m;1ljm;tkr and 3.50 m from the other. a96w(ljm31t ;xl ( qknol rm;k
(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 vibratingz y v9t.k*bd q/6 +u fmhunrfsu1w 3sc2niw714 at 132 Hz, but a piano tuner hears three b qdw4cruzv+hkm/nbf171us 2u3yi*f9. w6stneats 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 *t 5;tjd50 dmyc5*2h8nyrzoepo7o lgand 2.76 m in air. How many beats per second will be heard? t yo5jgldt7 y25r*5 meh;dn z8coo*p0(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency o8atekrvc ofo )y(sbh+0+ e)x/f a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect r/h)+ bef()0so t + 8aveyckoxif you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Whaxuzbr7gd:s9dix7 (gzkw h) ; +t frequency do you detect if a fire engine whose siren emits at 1550 Hz moves atzd 7b:9dgriszxg;) xh7(+kwu 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.xw 8a 7txfw1v 4*dyqg 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 t*y.8wgwaqx17 ft xv4dhey 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 frequencvv zc3m.7kxh5 7t hpl:y 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. k3.v h5:c7ltz7 x hpvmWhat is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic b4e:b44bqayx 6di2 yh jr bh7i*4*qqpsound waves at 50.0 kHz and receives them returned from an object moving directly ahbj264:r44iaxqeh**qbb pyi 7qy d 4bway 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 emits an u.t:a t: /rtn5:qdx v:e.tr lqlltrasonic sound wave with frequency 30.0 kHz. What frequency dn:l edarqtqr/ t t:.t: :.l5xvoes the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played oidy6*kmltd *m* wgm+5 n a moving flat train car at a frequency of 75 Hz, and a mdl+* dmwy 6*ikmt*5gsecond 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 wave6 q9ahylx g7l.s to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed oa 9qy7.gh 6lxlf sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic j0 f.g 0yseh1wwaves 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 freqb ubg sbohr)xu1x4z07h;z3t/uency 570 Hz. When the wind velocity is 12 m/s from 0;7b )gxt4z hshu1 /oxbr3ubzthe north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spee uk+p*46yhdlf d 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 nzovc+/s .qw8 *mvm1 athe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the dizao1csmw* vq v+/m.n8rection 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 o0 rgc kf)e4 k 1 2kfcoj)tzok,:zq9bp.f a planet where the speed of sound is onl) 92fcre )zf kbz0t:q,o.1kk4kp cogj y 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 ocean. Determine the ioid./+ orw2z4 pj7gr shock wave angle it produces/jr2 d ri4pi+.7oo zgw
(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 vhap) o d:ug2 9e9fu) 7euuyz3$/theta$ 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 ex,5fln 8fpr0t vb 7kts3actly 1.5 km above the ground flying faster than the speefk8 p,lvt0r3n5sfb t 7d 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 sonar device 8k bde5zp* -p+yd5yx0+xmdjk 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 -ym+ 5jky8k pez+bdpx5 *d x0dfresh water)?    s

  Approximately how many octaves are there in the hum 8nrcm4jrz-7 qan audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipea7kf-h 2fl -ab;iuy16buumj 3, 0 xjkf symphony. It consists of many plastic pipes of various lengths, which arekfa7-ujlf263h0 u x;buyif mk-bj1,a open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the touq/iuc : 133zx ;3pb8bkm acxhreshold of human hearing (0 dB). What will be the sound 8uazcbuci3;q3opmb1k x x/3: level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB m;cidi,.qpbn51le h -2xe 9ilsound and an 87-dB sound are heard simultaneous e.libp1chiixe, 9 2-ld5qm;nly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 n pfkh2 scu94/1navu 2dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all 9 n2uuv2a/hk pcn4 sf1directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hx o: , dd)0qw 4uf9qvxd,+ey3ujy.4 ih7yq pqcz. The power output drops by 10 dB at 15 kHz. What is the power .dicxu3yvx7yq 9h:jefpdq, d0y,+ u qqw4o4) output in watts at 15 kHz?    dB

  Workers around jet aircraft typizxawun3,oa:fm v xr)cw,1 2; rcally wear 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 airpl r za1c;2,:oravu xx) ,wfw3nmane engine?    W

  In audio and communications systen xl7a-;r+ a;sr pa+bpp* z: awx-y1soms, 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 fre0-vp6qw, fx*udqj ur6quency 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 longwc c6tu3tn0/*0v ebzl2fq*q s between fixed points with a fundamental frequency of 44w 2n fc/03qq*t euzvb0stl *c60 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 v1 5fykdfmb y(4ibration above a vertical open tube filled with water (Fig. 12–35).byd1yk fm4(f5 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 of the tuning fork?   Hz

  A 75-cm-long guitar string of mas2.twys 8i/p ohj:zyk2s 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 produce resonance (in its fund.iywzoht2/8sjkp 2 :yamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fullme j x-:7bnwqbuumh p6frf)b3)w-*a4 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 jo)tterj mc26o*8br 2 yo0bc6coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the f8 moybc) ot*2 jbort06jr26e crequency of the sound?   Hz

  Two trains emit 424-Hz whistles.m-7w 8 .iyi5szuljr5n One train is stationary. The conductor on the stationary train hears a 3.0 yw 8ziilmnu .5-s75jr-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam h g qhw x.6* -gf9aeuewp+s4z2train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocieq2hg 9zeu-+sx w g. w6afp4h*ty)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thih73:ixpe t3a e 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)3:pitx7ieha 3 as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produnhw 0ym. dmtkj0j) m9,ce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lm0,dn 9k jwy0.t mj)hmong is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it m01q o/hhvo,+rg-*j zxnrce, ioves 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 hq-/vjic,o1erh,x0zo*rn+ gbeat 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 0.32 m/s what beyh j(h ur*q)tlo5 tfa, xteo18xw1b0 3at frequency would you expect if 5.50-MHz ultrasound waves were directed along the fh (,r1ot* fe83l5qt)xh1wx0tao jb uylow 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/s while theaxcqz9mlo,05 bm 2 pe7 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 w,zl29pcx 7mbmae 0o5 qave 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 mkfzxqrn27 9c7fm(y-punl2 sfa(k1d :u9 ibb6oth. 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 is em6b x-u : 1dnf(a(i9b29kfr27fqcmlnuzs p k y7itted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals fromz;vyn3kv 9*un 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 th3nkv;* v nz9uyat only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by thervg 5qbk:4 ttm3h*wveddy:8 e ;l7um2 presence of standingy 27q tmb8lvhvd :uk*:gedmw; 5t3e4r waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental 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, slens; lbwk(isc ;ve2bp2 ba8wk5* der aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a lib(2ib ew2lvs b;5;*8cska kpwttle 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 twg;yl+t d9of f1vazb2nr ,.o,hreshold of hearing for the human ear at a frequency of ab nof b1davg9+wo.y;z, t2rl f,out 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 atj0l 5 )gudds7fmuk w.vq(d /:q Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directlvm : (luq0/jd)7 5qfdk.sdwug y overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo6:1; 0qzatzi+xhipp eat is 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