What is the evidence that-gx.m c()xnmn sound travels as a wave?

What is the evidence that sound g50a8,d4zq xl kzqc mvqi- 5y3is a form of energy?

Children sometimes play with a homemade “telephone” bye;p3r jlhi(m * attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clea* r;h m3(ijelprly how the sound wave travels from one cup to the other.

When a sound wave passerl j oayeexdpmqq- :()f46m* *s from air into water, do you expect the frequency or wavelength to cha p-a flq)yx(eor:q*4me*d m6 jnge?

What evidence can you give o22ea0kobyn jr2i 0 t(l4blm8that the speed of sound in air does not depend significantly on frequencj i k e 0b2o242r0lmloba8tyn(y?

The voice of a person who has inhaled helium op0p,o*f tz g t sbduda6kmz638o307usounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of4lcunyuhq(a/ g r7w6; organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude o8g6yl ar,sci ve47:kpf sounds in various frequency ranges. (An example is a car muffler. vsc7k8i:4 r6 aypegl,)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move l5aa. v::f8ig*cepa5vf ath+ up the fingerboard toward the bridli::vaftgac ea5 8+vphfa 5 *.ge?

A noisy truck approaches you from behind. u:m)foa) txb a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–f:umt)a.)obx 15 on diffraction.]

Standing waves can be said to be due tog0jl;v7oeu127q gbt 9bs1pizxox d 6: “interference in space,” whereas beats can be said to be due to “interfe2o opdv71lqsggb96;j:z eu 7x0i1xt brence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wehcwaz 732wazz) owqbp9s( m+0re lowered, would the points D and C (where destructive and constructive interference occur) move fartheqczh3 29bwo0 m )wa(s7p +zwazr apart or closer together?

Traditional methods of prt3* ne ggz50f aidz1h(otecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching tag*g d0(ihztf3 z n1e5he ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thougdaijhucibf.t /gp( uet4- ;fv*-q ,;qht of as a superpositij/e,* bf itf ;(ih-; p.gdtq -avuc4uqon of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the ulbgqssr 8m7r;ui*n ,5-s mi4same direction, wiqsi 4 m;rl gus-us5*m,ri8bn 7th the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heardwc:*i,b :xtpj 63yns o2zi+ /fep+eu)djw8bw by a person at rest with respect to the sonu jpw+*d y fepcw6,z3/ bw+bt2)iej8 i:o:xs urce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on) u ddbatw3/agb 2n6b5 a swing. A monitor is blowing 6u) ag2d53n dbtw/abba whistle in 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 listening for the echo of her shoutedbjlq)7zwf/ yi*-tdu v. c.) reflected by a cliff at thefqiv z)dutdj-* y .wc/7l)e.b far 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 side3moa z -u((ylm of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly buz3y (o(ml-a melow 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 297- q8f4 ljm hiypmkf+0 $^{\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 abov;7 tak o/c*eaxe a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How7;a ax/o*teck 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 cliff.cjdkv)5k mp p 9hn2+clga1e)0 The splash it makes when striking the water below is 0ag5 md2pnh)c )pl+9vec1 kjkheard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hug+z5z x ey(2sn5g ok;8 o8iayiqe 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 cgq2ie+y sozk xy o8a(z5in 8;5oncrete, 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 mile of distance by the “5-second ru8rz sv.e 0t2;olor mo8le” for estimating the distance fro0o o s2z. lvmre88t;orm a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sounpcz 2)aghv8h8w*q)t cd 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 intensic)-uq; *t-s f ;9 f1isufd f.gjdox,nyty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouiirpn, 44ulpxd1gb r ai5-9k0sly at a certain place, what will be the sound level if on i 0akug1dpi9-x r4ni5b,lp4 rly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain disaepr ,q3xutid.84:i u tance from an airplane 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 eq4aitxd83 urp: ui.,: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rati *tos0zbw .o9m8esz; q3* piwto of 58 dB, whereas for a CD player it is 95 dB. What is the otpmb*9w;w *qiez otz0.s38sratio 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 qn:h jzba/,wx6ctj f :99; t ldgk9wd+sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centdj /kx6h w b d;9ntlcfa+9 wgtz::q,9jered 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 w *7 m:a:sqvf gkbe0*jhhose 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 azclcmpr8el +i+z--8 amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connectedrlc-i mal-ce+p8z z +8 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( d ;er:z)astz2ppgf* dB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. ( );p2zrdz*esagf p: t
(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 typicalr8b ftl1g)1n(vl o rz:ly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels dif)l:rg 1ftno vblr8z(1fer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wh)52 qze 7vquqkat factor will the intensity increase? Increase by a factor ovquq)ze57q 2k f    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dig 8--(l3ql;/kcuydulqh1p pvsplacement amplitudes, but one has twice the frequency of the other. What is the ratio l( 8 13uplkd hpvqyul/qcg;--of their intensities?   

  What would be the sound level (in dB) of / hyk1rj j3bczs16 e+thry;,ma sound wave in air that corresponds to a displacementej1;ys1yj 6rh/+b,z hct3rm k amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see / p*do 9hjj:nya/dup0m as loud as a 100-Hz tone that has a 50-dB sound leve pyu0p:ho* d//a n9jjdl? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can det7d0bxsmb k;o*3vf4 ejg 7gt r9ect when the sound level is 30 dB? (S 937;fmo7gbregdvtjxsb 4 k0*ee Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lq9r ;0m9ed9 izvt3eo gevels. What is the ratio of higheem ;vgz3t9q e i0od9r9st 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 violin has a fundamental frequency of 440 Hz. The length of tob/ih vtp) j:8he vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wha /ibt) hpvoj:8t tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three aud:aq8)hcz,j.,snu kds ible ov 8,hs .,)aczjs d:ukqnertones 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 acroafa54y) yi wa62hba7kss the top of an empty soda ba7ay4k5 wfb h )iay62aottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes swvgmbyr,:ez+ pe 074fpanning the range of human hearing (20 Hz to 20 kHz), what w ve:7fwz+p4r emy0 b,gould 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 th.frpbi zg;bfm(a2r :8g-z/boird harmonic. What will be its fundamental freq( -azz bgfb/gimr.;f r:b2op8uency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar strin+uzw0wt, 31agg, xaj v0 a5kqng is 0.73 m long and is tuned to play E above middle C (333 a,w+0n5 ax1gjkwqzat0 gvu,0 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 *3zq2-pi c. jdpu4 fknpipe that emits middle C (262 Hz) when the tnd3- kfz2pj *4qip.uc emperature 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 2 a3*pb5gdqf:z /ozl:im.g 5zj0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fl0os5 gd,efdh8 rq8df2ute in Example 12–10 should the hole be that must be uncovered to play D d5 d8d,28 g0rfsofhqe 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 piplfyaj4r3+(xyh kxc e9 - o:u++umjx/grcv z50e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show fy 9ua 4 +xgo / 3:xkj- cyjz+e0(cxrlurv5mh+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 two sup a,2uk7g 6nc6 jo an))lx:.xlsi n2ltccessive u626)laxxn,l:a 2 p t7g)nc.jnk olis harmonics 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 1ck r8k,j)xva$^{\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 p59zazr.snbd 6*x( scfv;6lr 2.14-m-long organ pipe at 20 z s6(n p;*s6bxrzf9r a.5ldvc $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatja a o ./nv.p(s9j sku+x4(jpwely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of thj sav 4uo.+jj(xps./pa9(n k we 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 jfnp2m 44)wwbbeat every 2.0 s when trying to adjust two strings, one o4 j)m w2pb4fnwf which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency lul91zg/a:n2zi q) wv2nyg 5f if 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, while another (brand X) kufi7jr)xw5 +operates at an unknown freqifj 75)x+ku wruency. 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 a1- kl8qwjj3m 6:jci sn 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your rea 3cjl:6w8q1kj -msjni soning.    Hz

  Two violin strings are tuned to ourz r7 31 z*idnh)jo2the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequn*u rzo1ir)3z 2oh7jd ency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes s9 y+p(qlt; eo -6drp,ur+kpl each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0k losd rl;,ep(r-yp+q69p +ut $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzjb hs3ispljp6 9 r u:n(uus5f;8 dp.3o; 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 jr ( u.hinl5; ss:39 fjpudp3o6supb8Hz. 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 mni b*baw; ah0- from one speaker and 3.50 m from thbn0;a-wb * ahie 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 1 q0m8zz4 5z0z,3g yjln(gp.qjxn( emx32 Hz, but a piano tuner hears 0e0x5 j q.4qzz(pz3mgnzglmx(, 8yjn three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many bl2r oso0bi //ym6 *gyceats per seco/cm2i6lbryy /o0og* snd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginr,d28rjer(1zvg(u *y suvee1h ; 4gmce’s siren is 1550 Hz when at rest. Wgmh;u1 2r4ezc(eu(1* jv ,yesgd r8vr hat frequency 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 stillcjtyg -sozq3aen7:8d388za aw wp9u5 . What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at o8aun7wjs3zy :8 5gwzcda93 pq e-a8ta speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a v4fr .qfw 8mv3c80ygbc3- y fh2000-Hz source is moving toward you at 15 m/s versus yry-43f yg83 m.f0qw8vbhcfcv ou 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 tu-i-+k ))1 wq4jzemzsk piwj(: -tiaqhe same single 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 the horns zqiks)t+ aj: q upizj)4iwm-1wk(--eemit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasz e:jmlx1svc4tf :i1.;4vd ufonic sound waves at 50.0 kHz and receives them returned fro 4.usvzf e1m dlfjt:1;4c:i xvm an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emitw)il*tm56ff d zs x:7ns an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave? :fzi s6wt5 f)7m*nxld   $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a ydl.*(ooccg1l bmsv bj84v+5 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 y4smlv g8vbdb+ c 15(olcoj*. 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 measurtncimx8z 8 yj*c5tita2j-+)u:y .dcte blood-flow 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 away from xii cyz: *j8uta85m2 ty -t)d jcc.+ntthe sound source?   Hz

  The Doppler effect using ultrasonic waves o-qtyv7ar4,0 w4:u4a6dr +slvlur behf 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. When the wind velocity is 12hm qa1tp;a .h)mr)i3j m/s from the north, what frequency will observers hear ; h)t13j.a imapmh)r qwho 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 m- iaxhi1tch .g1( 6hnzoving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 7 ,iyffwh*.zp m/s (a) What is the angle the shock wave makes with the direction of the airpif zy7f,wp .h*lane’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 ar-uuo d ;/:7hfq zun4k planet where the speed of sound is only about 35 m/h-rqdo 4f7nkuu: /;uz 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 u1fdd*b6k*nb z1/tswocean. Determine the shock wave angle it produw/ts6u b f*zdd*bnk11ces
(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 ,q4+z /5zsfvap0r u ag$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and s 37mvh6* 2,stst js w*a,rq9i-qltlw xee a plane exactly 1.5 km above the ground flying faster than the speed of soun ,l s-q26 m viqhtsax9twt*r3 swjl*,7d. 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 that sends 20,000-Hz sound y+ 8 hbue/t8f 8cn0vlxpulses downward from the bottom of the boat, and then detects echoes. If th8n f 8cut h80y/bve+xle 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 octaves are there in the8:gji*e bgyk6 human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pimy 9wmoes/ x3 f *tkfi,a/w)d)pe symphony. It consists of many plastic pipes of various lengths, which are open 9m)xm3steaw k/fydo*)/,wfi 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 pers/g 7kjqqjcc1pjc1 x hdt,+u497dls 5f on makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such m+j gd lpqthu17 f9c 5,7dsqjcjk4x/ c1osquitoes?    dB

  What is the resultant so z66vo u .rp zyd.e6.wqo5m9grund level when an 82-dB sound and an 87-dB sound are heard.zpem..9d vr6uo gq6o5yzr6w simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, iyv - tq.w,l 36ml /gtp(7fmfxps 105 dB. What is the acoustic power output (W) of the splpv.f (g qt37m/w 6y-tm,fxlpeaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hzj5 :eri5hxh c-7 hqai5. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? 5xr-5 ci hj57qahi: eh   dB

  Workers around jet aircra,cs1grn+f 7vnft typically 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 ufgnr7+vns1 ,c nprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systedm+y,i(viszg/ : s:mcms, 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 yd n8n25g )ypa-wyp 6 djx(o,kfrequency 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 b vf b5xaua;m1yc4sgm0 x (a /.r. l,or4uvxe2uetween fixed points with a fundamental frequency of 4afr loy/u1vu.augvc,2 x;r e5xxasm0 44m.(b40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with wc v(wnm*f :j2uater (Fig. 12–35). The water level is allowed to nu (jv c2:fw*mdrop 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 mass 2.10 g is near a tube that is open at one (yfnqp:-g(b)iex94k vfk mb/end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) kix( -f embvq/(9): gbpynk4f with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate l :fmw a6-wm-+g-os 3a)pazihas one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure cz. g v;kw+q2q(6acdl9up57 ixg/yyhtone in the 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 person moves about and finds that the sound level is minimal at a point 0.34 m farther9h+gqag(cd;zw/ x 5 lk 6 ivq7cuyy.p2 from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz wm6 jv p:np:vv1histles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is nv m:j6 ppv1v:the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. c*:c z* :-4idege i bs5qqvd4tAfter it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity*4-bdiq5qe c4 *:st gvedizc:)?    m/s

  At a race track, you can estimate the speed of cara:* thq7b9j qls just by listening to the difference in pitch of the engine noise between approaching and *bq:l7a hqj9t 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, sounding together bno5cwjr.w x56/sc 7i, produce a beat frequency of 11 Hz. The iw57ro 5 bc 6./xwcsjnshorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are phwc1yrkm3h a4l)s0, at opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed3syap) rhh4l0w,mk1 c him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bea1e0fp i,,qmg et 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 waves trag eeq, f,ip0m1vel 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 tjft +te:6.8ok)q oqv ioward the bat at speed 5 m/s T ioftv:.8eqk +6 o)jqthe bat emits a sound wave of 51.35 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 frequency sound pulses as it approaches a moth. Theqd7n- lsy7w ekqa 95; zz4izh1 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 a97dy5s;1 ziezh7lkzn 4-w qq emitted?    m

The “alpenhorn” (Fig. 12–38) was once v+dw4px.qh : hw/ l,rdused to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of tqv , 4w.wx+lr dhpd:h/he 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 b))z4txf 2/16 nr u+jksnefsz py the presence of standing 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 standingnez /p6xjffzrknu 14t)s+)2 s waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slende,r wzpu -9j8vfr aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little pra pfzu8-9 ,wvrjctice, 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 thresho:ln pz+mk59vak10 n w.h .3eqk pmm(wmld of hearing for the human ear at a frequency of about m a eqk3+lz5 nknk9vwm.1:p. wmh0mp(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 ob)xkzim 1zk9,o server on the ground hears the sonic boom 1.5 min afte)zmx1,9ik ozkr the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 0r,tb dksvc,3w7u v( :pi svmn*g7.xeis 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