What is the evidence that sound tny;ki ccgx,iz l3re-u 5a,: tv:mm /ymv i;1,oravels as a wave?

What is the evidence that sound is a form ob:p a9w p9(q8(v- uxqxul 5ov:;nbox af energy?

Children sometimes play with a -ykt kita -+ve4wm:( shomemade “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 th-tk w 4(a:-ykvemist+e 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 inn y74k2hyzqxx r a14.lto water, do you expect the frequency or wavelength to cql47zaxr1. 4n 2k yhxyhange?

What evidence can you give that the speed of sound in air does not depend signi*ot r/bhc)2v5j i bbe.f n(g/jfij(2 /r5 ectigh/f nb)vb. o*jbcantly on frequency?

The voice of a person who ha2w k*-(k ujojp*wyx 4ms inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect tez 4/x8qbv j4hhe pitch of organ pipes?

Explain how a tube might be used as a filter io1jjszc: f2 n3or:f8to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffleroj31c 8n2:isf o: jzrf.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together abktz6ugj+iw2tpei8 q c0 z9(axq6p ,3s you move up the finge6 9qqibzp iawptcu8 ,tj6zke2gx 03(+rboard toward the bridge?

A noisy truck approaches you from behind a bul 9o 7rw*ubk0silding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “br0u 7lbokswr9*ighter” — 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,” whe/1ah wnwhdr 82vk xo,+reas beats can be said to be due to “interference in tr18a2+ o h/d kvwnhxw,ime.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pozb 8h5+.m aatzints D and C (where destructive andh5 .bztzma 8+a constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work i. tu rx3cnj-rhb;u2h7n areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could ad nhxbutuch 3;r.-rj 72ding more noise reduce the sound levels reaching the ears?

Consider the two waveskj(p3c (9ykp 0xv i*os ptr(t* shown in Fig. 12–31. Each wave can be thought of as a superposition of two y(s 3vtp(to(ip*c jrp*90kx ksound 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 iow0iwzli q)t8d8phd + d .3n4moc09 qlf the source and observer move in the same direction, with the same vel8c0qodnpw o 8i04mwlqzl3)di+th d 9.ocity? Explain.

If a wind is blowing, will this alter the fruke 0a/+ukfw 3equency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity euk / 0u3fw+akchanged?

Figure 12–32 shows various positions of a547jotcts: 4kcbw n:s child in motion on a swing. A monitor is blowing a whistle in front of the chil t4 js bk5sct:w74oc:nd 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 listening for the echo o c; k9lpm) +fjx;co9jgf her shout reflected by a cliff at the fc)p j;mg ;jxk9o +9cflar end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the l ig jd729sf)ewaterline. 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 gse7f il 2d)9jsignificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wav17j r5v 47qyxjgs84ox1cz aitkt3zw5elengths 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 tugl,a/hb39 f;dme bv7ena on a foggy day. Without warning, an engine backfire occurs on anvd;9 el,bafme/bg3 7hother boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clif0w09oj4o, pi:i ytnz xf. The splash it makes when striking the wa0 o9i4tpz nj,wx0:ioyter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stri (v.h 9.ssy-iw)lix xlke the concrete pavementh)xll. -9sw (.vyx sii. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent e0t(gb8c(rnpw ht:jtc/p024 ta fj g -qrror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strt (n-tg0 wj/tph:g2abccj(rq4f p80t ike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sounmz 5: io)slr8;e+ihesd 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 whose intensity i.zik+/t* p-kh gnvk y0s $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce.dpfzt gq 9ewq; m68q vie4)c, a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hideqmwc6 z; 9e.fgt )4ip8qv,q nt: Add intensities, not dB’s.]    dB

  A person standing a certain distan f2 ytg-a/+gmd(mq;pe-i , pdece from an airplane with four equally noisy jet engines is experiencing a sound level bordering on2ma g d/p(;y t- dme+e-,pfgiq 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 a signal-to-noi2fmrex07+0ibvq *u yp se ratio of 58 dB, whereas for a CD*rmiuy p0efxq0b7 2 v+ player it is 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 output of gfq7onv3m0dc uj jweo2(,hzeo 8+: 7fsound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unifo(u:woezc 3dghooj7 , 8mnf f0vje 7q2+rmly 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 an faf:4e-6rnetf/x5xu (je nq t 1:ixo( eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is rai 1kaq d43, wlcptv/r1o,6skited at 40 W. (a) Estimate the sound la 4p1t,ws oqv1, kl id6r/c3kievel in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in f+ qy*co ):.fm uqf9w23smkj lzront of a loudspeaker onl2s:mzfy+w*j9kof m .3uq) q c 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 difference in sound level of 2.0 dB. mpgi*-xlq0d,3dhn xp 7yi: h(What is the ratio of the amplitudes of two souny hn*d(qxxm 307ipp, :-ighdlds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, ; a-nwl;pa+um 196y o-fphhe a(a) by what factor will the intensia ; -- wfme1uhaypl+69aopn;hty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacem/o jm;6wchb, cent amplitudes, but one has twice the frequency of the other. What is the ratij ;6h,c/mbwoco of their intensities?   

  What would be the sound level (in dB) oets 0p, bz9k0 8dv0dea*een4bf a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm ebne4t0p0d s*,0ek9ezbv d8aat 300 Hz?    dB

  A 6000-Hz tone must have what sound le1q4041cpc.e8wwbse cq jc0 s mvel to seem as loud as a 100-Hz tone that has a ewc14 p.e4wbc1cj80qsc0 qs m50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soun0d-y3z ooqs (yd level is 30 dB? (See Fig. qooyd(zs 0- y312–6.)

  Your auditory system can accommodate a huge range of solr ,8km) ycu68.f tgcpund levels. What is the ratio of highest to lowest intensity m r8cuc. )fptlk68gy, at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 4g,ad 6xmn2axie6 :dbq)7n : uh40 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tens g ,hun 7bqaxaed6m6:d)2:ixnion must the string be placed?    N

  An organ pipe is 112 cm long. What arepr+bgb 1 u5k )xf4 46kurvgkh9 the fundamental and first three audible overtones if the pipe is xh ub+ 6rk)k p4 grku5g49bvf1
(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 wouldorg mjk64:y8n you expect from blowing across the top of an empty soda bottle that is 18 cm deep, :y8 6jomr nk4gif 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 pipes spanning t:9ff5cbjvx(mu- 6(xg xrn 7kdhe range of human hearing (20 Hz to 20 kHz), what wouldrx(vmu 9(56cgnxfj :x7 f k-bd 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 klwi95ojflqy35;- 5-nu eilias its third harmonic. What will be its fundamental frequency ;3ow5k j inyl- l9q5-fi5lieuif 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 tupc9nnf 1 *)g6/f rqyayned to play E above middle C (330 Hz). )9cn/fprg* 6nqyy af1
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that eopig7; vzul*e.qj* uquy8 u9 /mits middle C (262 Hz) when the t u78/e *zuy .;u* oqglq9ijvpuemperature 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 2c7 gq c5 ku,hu,q.rcu,fuvz(:0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of7lp ns- i77zoz the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C 7zs on iz-p77lat 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz,a )f;0dv tk)oy but not at any other frequencies in between. (a)dv ya)oft; 0k) 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 ;rmhiila1a p2 (1sw0eresonates at two successive harmonics of frequenci 1;hr lpes1m2w0a( iiaes 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 vz7ix s5fp8(d$^{\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 wtwmdrf) v95 v(6ty bw; aiw58for a 2.14-m-long organ pip56;fvwibww5 89dmyv)rt atw( e 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 opeayi4va (8f 1c)o;gi han 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. Wog; ha8(a cfa)i1iv 4yhat 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 adju (vs7j5y4p szzst two strings, one of which is sounding 440 Hz. How v7zy5s(p z4j sfar off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzry3z/6v kk4eh ) 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)r6b*h0a 3c gc3qcpz. g,;l5yarojac kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when theh0y *5a3bg6l)3rj,a. ;c zcqrcocagpy are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when snh:8rfcub) h k95tmq;ounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What 8n): hkhmq f95utrbc; is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 22fzkmf b m0.3a94 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when thefa b2fm.k 0m3z two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard ouc7; q/ ohnd4*k,)b 2qveu ivif two identical flutes each try to play middle C (262 Hz), but oncdb/4nuv ei2*qqh k )7uo; ov,e 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 has a frequency of 441 Hz; whenq+g yjx9zfh74 A and B are sounded together, a beat frequency of 3 H+gj7z hx4fqy9 z is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one)q w l9c+ve53nqjc s3gr-wnlk-b ou2 ) speaker and 3.50 m from v n3s-glwqcou2qw5ck3)9 j) b+rl -ne 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 suppo6cav dv 1p8db2sed to be vibrating at 132 Hz, but a piano tuner hears three d16vp28v dcabbeats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How mfcb p8 8jp3ye*bqj.x( j.l8bxany beats per second will be heard? (Assume T 3* (by8c bj.jjqxl8ppb f e8.x= 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire*8g wnfnybp/*igw(s wwy;;p(n9j z4iv7)tau engine’s siren is 1550 Hz when at rest. What frequency do you detect if you yivg*y)8*wz j gu7annwn4(/ p 9;ts; bw(pifwmove 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 dbl(o 2v5uekm*)oq/b)tq qqg; etect if a fire engine whose sireq;()mv )bq q/5ktol *eugoqb2n emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you :t w,u/pb9 iqpz*9gslat 15 m/s versus you*zb,gi:swlu p t9pq 9/ 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 single frequency horn. Wkpj1q 3a5d.x 8xu uej,hen one is at restux, 3ujkd 58a.pe 1jxq and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wakk() ubt zu,o0*w1-(znspk rbves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency?0(n,wt 1kzukupzbs )obkr* -(    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emitsf ehe-a/lpf v3: 21uni an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear -2:1fa/pevi3he funl in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppljx8+qy9tl)eevp ;w 2ner 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 stetw9 ;2l+jen8p v) xyqation. 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 speeds. Suppk/ 5 34njw0kptgfwai(ose 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 lang/wj 45 ptkwa0 ki(f3rge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi/nrz n4vtj,o9t : q;cnng ultrasonic 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 frequency 570 Hz. e l5 )cah vqu+ sx(i9 hb241kl)h5zfcsWhen the wind velocity is 12 m/sf c(il1s5hx 2c+4 zq)uk5bs l9h vahe) from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed k-wsj9hj + z25t6wsi1xko u3bat 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/1fw wzmf.l*m*s (a) What is the angle the shock wave makes with the direction of the airplane’s motion? f*w.zfwml*m 1   $^{\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 thmr un+)rw b20ww2g*rue thin atmosphere of a planet where the speed of sound is onlm2rrw gwu 2bruw)*0+ny 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 shock wqqp owu 4af*c-dhtkog 3/ s33+ave angle it p4*3 f/o 3-p oqds +3ghqkcatuwroduces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle h+ih ,xt jhk+l :dxg793a3rk r$/theta$ 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 ground fly,s q uvub:alt6 lbub1d,x 5)l7ing faster than the speed of sound. By the time you hear the sonic boom, the blubux5 l,7d s:bq),6v tlu1aplane 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 20,000-Hz sound9z28j4.xahm0j(qrc ici*g gl pulses downward from the bottom of the boat, and then 9ih( jlxzj8r*c 0qgim4.2 acgdetects 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 maen/d:ec/fge -qvqk 9z tf-;h. ny octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pi3/tmjl8 1m tmgpe symphony. It consists of many plastic pipes of various lenl8 tg1/mjmm t3gths, 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 ez;;q ti8qv0 6csa2nra sound close to the threshold of human hearing (0 dB). What willt8e ciz 2;0q6;nq vars be the sound level of 1000 such mosquitoes?    dB

  What is the resultant slb7x-u-t sf6:ni2(pbvg/d bi )zt1fsound level when an 82-dB sound and an 87-dB sound are heard simul1n-l2bsfu/67v t:)ibbftxgzdps-i (taneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wh sjdr3*:f) nc+t.vubrat is the acoustic power output (W) of the speaker, assuming it radiates equally )r:un b cvtds3jr f*.+in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powc-abqf r8vu--er output drops by 10 dB at 15 kHz. What is the power outpu8c a q-ruv-b-ft in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earszb29us z0-jts. 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 j09zs-zu 2s btairplane engine?    W

  In audio and communications systeh n (d5bgq2u-2axs 1orms, 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 violinw 9bloz0:ort; 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 fv0e m;p c,jv+zixed points with a fundamental frequency of 440 Hz and a mass per unit length m+e cj;vp0 vz,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 abov gznggo2)sfi6 +j kz.,e a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air o g6gzgsj ,nzf+i) 2k.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 stringkcv1il- 65s ir of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tensio csirkl6v1i- 5n should 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 lnryjbtsvqc+ s2o5vbm)5h66pa-/ xd3 oop ($\frac{1}{2}\lambda$) 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 theh.gulg /n96;wnwt m6 n 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the per ;l6gn m.n96nguwt/w hson 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 staoy2q3 6 a0imyitionary. The conductor on the stationary train hears a 3.0-Hz beat frey 0ao qmiy623iquency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a s r8sn,(yqtb;7zx:fi wteam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured aszwy b ti:rs q(n,8x;7f 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to s 7hzydpo zeh7::cy) +the difference in pitch of the engine noisehe)7 :zoh:+7 psycyzd between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundijm*:xs (j au6vng together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How longj(:ju6msva x* is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mo ed6xbeu 3q2+l:yx9jxoh4 l4bves 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 jl49o h+6yex:2lb xb 4e3qd uxbeat 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 bea8 xk : qph861mxnuv8ydt frequency would you expect if 5.50-MHz ultrasound wauhyx18dpx:mn6 vk8q 8ves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the bl.enso,s o5 f.at at speed 5 m/s The bat emits a sound wave of 51.3s,eo fon sl5..5 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frhl d u -b1;jq(aq 93wmbbhcs(/equency 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 mob1mu(bbaq hd-c;q3w/(lj s9h th 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 fr g*9n;suib 2guom 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 bl*g9n gs2 b;uuiown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo lis34ko ccycf/ i*pmt t,0tening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a livtky0i/,m3t* p o cc4cfing 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 “c,y3bo* hn*gs*mt ( jvhl/pk/singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringn*k(h,g *c/t hyjlm3vsp/o *b ing 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 (g pecbk p-6;hoe5mf+wl(j p6human ear at a frequency of abo jo5eph(lb k(-cfp+ w6;gpme6ut 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 the ground heo (5 52afjzymox.r u+aars the sonic boom 1.5 min after the plane passes directly oveua5yf.rx jo o52(m+zarhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 )2,1l8t(pryu 9i t4kgkzsstt $^{\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