What is the evidence that soundlf. 0(cm lq4hz9um1as travels as a wave?

What is the evidence that sound m-ct;0:omq if is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to t1,mgun5u, o : euvxv75f s yyl*/)bluuhe 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 cuvuyf suu,1um7u og 5l/),n*5lbe v:xyp (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passeskmhz5; hl m4*gxf51ed from air into water, do you expect the frequency or wavelength to changem 5z hh*dmxgel5 k4f;1?

What evidence can you 3:u+em: (gf;fqb t gdx38kcv igive that the speed of sound in air does not depend significa (k+mb3:gqeiv udfgcf3:;8 xt ntly on frequency?

The voice of a person who has inhaled helium1ky hzl/0mo kt5 ep(o7 sounds very high-pitched. Why?

How will the air temperature in tawo*h 27r.y1-levo c a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the a h dz8wk.i/.ho +j/mlfmplitude of sounds in various frequ lij/f8.k/+ow.hh mzd ency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog:zr3 cf5hmi wzx84b8iether as you move up the fingerboard towar8m:5 w4cii8xhf 3zrz bd the bridge?

A noisy truck approaches you from behind a building. Initiallyyuo t+p0jmss;j)5 b. q you hear it but cannot sy.5s)j sqbp+mut o0;j ee 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 11–15 on diffraction.]

Standing waves can be said trcq) lzw7 e4(1(xi fmlo be due to “interference in space,” whereas beats can be said to be due to “inter(lrcw( z)1meli xf74q ference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers w28 ix0thrz cd(4znw50q;rstaere lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togwzidhtx4;2 r00q z8t srn (5caether?

Traditional methods of protecting the hearing of people who work iniuxa k97z- ir( areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphonesz7uxkiir a9( - 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 Filqo(m6p-0 m* j(zkynig. 12–31. Each wave can be thought of as a superp(mz*-ilp(m 0yok 6qn josition 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 thhjvpi2m ( w86dpvu.-z v-rzk2e source and observer move in the same direction, with thev2 rvp 8zuk w(.hmzvp-i2 6dj- same velocity? Explain.

If a wind is blowing, will thos5nh ynlqd. 25pco(lpb;iy z1 8 r).xis alter the frequency of the sound heard by a person at roni(.5 llp5s2b;dzp)8 h.c1qnxoyy rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows va4wcn2d , nzq6krious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the groundnk6 2nc,qw zd4. 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 forgc,g *ikw- jkwob18 d8g8c(fp the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after sh8wc( dbgcw pi8gjk,*8fk-g1 oouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He s./f0k s;x4* krtctms7/e jkg s6*pgw hears the echo of the sound reflected from the oceansjt0;p7/sskew /mg*.x k fsc4kr6*tg floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength)tr :bi 9oymrvwb-d)4 s 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 aokc)s9/k2 m+joa w *xzbove a school of tuna on a foggy day. Without warning, an engine backfire occurs on/ cs+k2)mjxw zak*9oo another 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 clif/k:+ovhprdn pnk0-k. f. The splash it makes when striking the water below is heard 3.5 s later. How-k nvopk/+:k 0n drhp. high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike th;r3m j19y kvdo6y pe2me concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Ta2dk ;6 9opyve13j ymmrble 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over ont) yll q w1r1wrp/ks0+e mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temp/ls rrpk1ww +l qt0)1yerature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 d)reusxcox u0.fv9fl:8e(s 5j:df 5 keB?    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 soundqy( i xjmr6og 13(5wgo whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of*i1dznb(kg ;p 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intenski1dgn *;bp z(ities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally n: vr+i(ysqa h/oisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add( qhiyr+:avs / intensities, not dB’s.]    dB

  A cassette player is said to have x ,e8;syegzx. a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio ofye x; zs8gx.,e 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 fear5fsm( ); 7jfq v1/fdv9ey lrom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centereale)(5eqf7vyf 1; f/vsd9 mjrd 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 v4csj+0woli +v*t iso53i ufe* 3ya u: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 -..wp3 qcc ihsamplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a .h wq3cs.c i-ppoint 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 hg- wo .lwsu5znl, i02130 dB when placed 2.8 m in front of a loudspeaker ow5sh z0lg.,-2onlu w in 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 2bc 4x-qx,hoy g -/hma8.0 dB. What is the ratio of the ampl8-4,/ h-g ocx qhxymbaitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wilub ur:z rvg)q5/(rvl 8l the intensity increase? Incrur:/u (l5rg q8bv vz)rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freque0 t/aw(p+hcq kncykc/wa h(p+tq 0 of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave inml0i3c86hm6a :o ei/attql eui e0)f( air that corresponds to a displc0e0t :6uq i/mli a8hl)36 t(eo femiaacement 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 a md ql2.4 ajw3-9fwvfv100-Hz tone that h4qf3 fm vvwld-a9jw. 2as a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that ake-o1/ ile; sgf9ix5b n ear can detect when the sound level is 30 dB? (See Figexbo- f/ki;5sgl e91i. 12–6.)

  Your auditory system can accom 9u7 g 2isbexl*ayhk,2modate a huge range of sound levels. What is the ratio ok ug92,alb y7xe*s h2if highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a vioe,7dwh * m1vwclin has a fundamental frequency of 440 Hz. The length of the vibrating *dme w7v, w1chportion 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 fu10*z,vsgy ve yx9c 8u s1+tcrondamental and first three audible overtones if the pipe issc9tg8 ,z*+o 1y 10 vyxrvcues
(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 fj1 on;1x/jdtwrom blowing across the top of an empty soda bottle that is 18 cm d;j 1dowjn1 /xteep, 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 spanning the range yx sq zsx5r9hn70 qx;t6*k et6of human hearing (20 Hz to 20 kHz), what would be the range of then0e*r576h t tx6 xxqq;sky9 sz lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freque z fm4/kdt1*l1q)jogrncy of 540 Hz as its third harmonic. What will be ik*d gt41j qmr/)z1 folts fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned wcqc975k:ln/efkb r/ to play E above middle C (330 Hz). f59 /k7c/:r ecnlwqb k
(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 lengma lf jd;dxig )z9(j4(th of an open organ pipe that emits middle C (262 Hz) when the temperature is 2lj i ()zgda(4 jm9;fxd1 $^{\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 atpn:xk :o)j5b8je0 yiv 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fldduwwjn( w 749ute in Example 12–10 should the hole be that must4jnduw 9w(dw7 be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can reso 5o9buxn vbp+,nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betwen9, bu5p vbxo+en. (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 two suca2n6dobef u 6+ ut+7pvcessive harmonics of frequencies 275 Hz dt 6u726fno uv+b+eap 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 rx8yz: 5nkltgti / h:1dguu. cw0 a0-x$^{\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 pr +wk 2: (xf+3spebxeiiesent within the audible range for a 2.14-m-long organ pipe at 20e(2k b:xw++fex pi3si $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approx ;b+0nt iq2ypximately 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 the standing waves in the ear canal. What2 bnip +0;qxty 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 evefazw 3*/g blv2ry 2.0 s when trying to adjust two strings, one of which is sof/ lba* vz2gw3unding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and ,/i-y3prs.l+ rqp t3jllsqt ($C^＃$ (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.b87 g8bbnfsh( u b(1ud.r9xad 5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when u raf.b9n17bdbsgxu(8b dh(8played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunin0ma5y ) g2hs.fj dnlcyich084g fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasonijc)hm80c5sy0 ia.n fy g4lh2 dng.    Hz

  Two violin strings are tuned to the s+e9u, l62 owbesi-.ozbznv2name frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togethb.nsio+b 2,zow u-l6vz e92e ner? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutejk v;yo3,esr*o: z tvpp1yf92 ne,f a m2g)p8bs each try to play middle C (262 Hz), but one is at 5.0°C and the othn s32e;pt 2op f91y:em o rby8v,*z)jvf,pgk aer at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning ;e2nde/y 9cy3le.,nuz9 rumsforks, 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 2ym9scd e u,yeu ;enn.l9zr3/ 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 fro 9usnw ta,m+0.yc 3njym one speaker and 3.50 m frys30 jcmn 9.wtn au+,yom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner h*z9qyl(wpd jh).d0k nears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the l. dn)j h9q(*ykpw 0zdfrequency 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 vce0 3sbyip-a b 5b q9,y7s/main air. How many beats per second will be heard? aq,7sbcbb5my0e39- yaip vs/ (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whx-kqr 7qu1ktnmmo-kd( ktd2)x0+*s4tlvo e6en at rest. What frequency do you detect if you move witu)*tm-q7qoen (s-4r0 1xkx vl2tdotkk6+k dmh a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequen(*cixsccs , .bcy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3(sc x .scb,c*i2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source isib* f9g2xfu6p moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exact*9ubxgf 2 pf6ily 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 sqf7 4mwgnx9s:-uch y (8 :uoasingle 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 emit? Ass:sy9(nm a74 xuu-hog wsf q:c8ume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives t+ yk09wzjfa 0 e0beb)yhem returned from an object moving directly away from it a+ bbawz00ye 0kj9y fe)t 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a r:qmq+00k:gf , wx xbgspeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear ifk:q,ggrm x xbq0w+:0n the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was ppenano5 t:+r 0oe8w7yi/,1 iyw v5x balayed 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 ra w 1e85vobt:y0/oyena7ina rpw+,i x5ilway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo-p/lr 3mwm i2x:g lj gok:gz82d-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 bloo xz:wl:g3mp 2ojg -lgik8 rm2/d is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wav9lze glz34fym4 ktg h*rz/; vcbi2,0ves 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. When the wind velocitynh5pe p0jk k,5 is 12 m/s from the north, w n,5k0hj 5pkpehat 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 is7gg/s r4t/n my dm/8of 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 atyre d 7.,rzw5k Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the . 5reyd kz,rw7shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a pt 1n3 ww4l6 ntcp;efopk;aj4: lanet where the speed of sound is only aboj;;6nptk: ep twwafcn44 o1l3ut 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 8507wz7xtz:4r2lgy8z w,woe 4 z74mgmlh 0 m/s strikes the ocean. Determine the shock wave angle it produces zr 2o7w 7ztz:y lgwzm84wx,el4m4g7h
(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 gg w1ht vc,.y .dp6/2, a7 .6jjpw:jneymsmkv $/theta$ 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 *y.x1ostrn) wf41zgn d*t;ne ground flying faster than the speed of sound. xz.y*fntesrn;gno11 d w*4)t 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 pulsesxwwp17jrr u-s9kz, 6m 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, wuj7-zx6r rw mk ,s9p1what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human aue0 2sh vw,*dtodible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a d g *nks.*v:-qpgl)kqdisplay called a sewer pipe symphony. It consists of many plastic pipes opgql*kns*q-)v: gd .k f various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from )8pl, r5gq vg 4vshj1,q(v*i zt3cfdi1vhp 8pa person makes a sound close to the threshold of humanpfs,p(t 814vz8* 5jlcvqih3hv qd i)g,vgpr1 hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soed+ *ao(uo-z yund and an 87-dB sound are heard simulte+zyudo(a o-*aneously?    dB

  The sound level 12.0 m from a loudspeakeywy39us(xi vv 0,wy-w r, placed in the open, is 105 dB. What is the acouvs9 ,wv3u(y-y0wy wxistic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power on))ky-hgh)ao utput drops by 10 dB at 15 kHz. What is the power output hkahngo )))y-in watts at 15 kHz?    dB

  Workers around jet ai:*ee9n1q:5.b.lo ljakn n cpzz qu/4urcraft typically wear protective devices over their ears. Assneuq:4l k. na/ j lozuc*bpne9q.5z: 1ume 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 airplane engine?    W

  In audio and communications sy 8/y eo3qe5lerstems, 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 frequencyp8t/n 9e xzk2snwkfw b sm*pwj45 *7c9 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 /y u, -dlavu8v l1pg3zbetween fixed points with a fundamental frequency of 44l1z-p 3v 8gu,u/avydl 0 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 5 axdingquvju 6riixjw+7) o4m1 o:* /vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from thwro*5n:+ ujjx6omq/7 ig41dii )x vuae 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 stringnw,i(; .d,nz)ecbwj wfe6l8i of mass 2.10 g is near a tube that is open at one end and al;)nj6dz bwe.iwe(ic l ,w8f,n so 75 cm long. How much tension 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 tok2ott.;9kpt 6p7hng 5 )g hfnf resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–14 v8qyn*x7vbjq -1wz,kotzm1000-Hz range coming from two sources. The sound is loudest at points equidistant om8 b w4z 7xvk1*jvqz-t1 yn,qfrom the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. -g8p9khnq )zeOne train is stationary. The conductor on the stat8ze)g-9h pnq kionary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it app (s0 nd myhee9vii42c.roaches you is 538 Hz. After it passm(4.hn9 0e2ii ey vdcses you, its frequency is measured as 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 ldksug )l7.h0m6,ii di nf1uc*mki7 ( qistening to the difference in pit nu7u, di1ik0q *lmd76)msi(ick gf .hch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a4t)sw/b+gtpby: tdy z6 k5f-1j yf/w z beat frequency of 11 Hz. The shorter one is 2.40 m long. Howb/f/:) dg-1sfyy p wwz5 tt4+b6tyjkz long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statielx -3qnu4k, s *)evs ja+it5vonary observer at 10 m/s as shown in Fig. 12–3u4-kx )slv e+,5 aj t*esiv3qn7. 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 passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.bpay;fp9t j/ 532 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that a9bp/ft 5 yp;jthe 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 isg,w 36c bvlf8o flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of cg, wbv l6o83fthe 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 approacheszf( w,,u *3m6mqkktr o a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected kf mu*,km6r,w3tqoz(by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig/ +cb7dt/c jhm. 12–38) was once used 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 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 chc+ t7mjd /b/which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presede.gpi//(j5 y rkwec9 nce of standing waves, which can cause ac 5(ygkc 9r.je/eiw/pdoustic “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,” ix tgh,jz 9gs7 wgop5:.nvolves 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 “sin .,h7gzg9p jw g:otsx5g,” 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 xzur9l*m+ ha5 threshold of hearing for the human ear at a frequency of about 5*mzhulr9x+ a 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 Mn.v2mtb0 ah;hach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly avn t0b.m2hh;overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i7 gllu p.zi7)aawb3n/7r d(rjs 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