What is the evidence thaha1y 9jtaf,/-tad(uuelh8* ( cjr0d mt sound travels as a wave?

What is the evidence that sound is a formwyjn 9aueww,z.2- 0.m1n k dre of energy?

Children sometimes play */1zsnkv m*n awith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretm/zk*nna*1 vs ched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fredrg kh00 c2*.cf ,tjlj+qjax-quency or wavelength to chang+l,gjd r0tjcc02 fh.*k ajqx-e?

What evidence can you give that the spe5dyw u+ qku 4d-36jcxqed of sound in air does not depend signif wu-k5xqyd4u3 cdjq6+icantly on frequency?

The voice of a person who has inhal4x2 ) ere54c uwgkyfzo54/ewzed helium sounds very high-pitched. Why?

How will the air temperature in a room aff/30i0 pshmg 41 sxffx4(exu vr ta16dxect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce thcfta ge:-i2neq- bypa5g1m 1 9e amplitude of sounds in 5f :e19-qpa at2 n1ggmib-ycevarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move ln237ux )thilup the fingerboard toward the brin3 ltxl )ihu27dge?

A noisy truck approaches you from behind a building. Initially you hear it buvd i s-bfor+.2t 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 .srdv+oib2f - Section 11–15 on diffraction.]

Standing waves can be said to bex;br ;7jkb) zl due to “interference in space,” whereas beats can be said to be due to “interference7)bz;brl kj;x in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poi 73zubzvn0qcajb y3 v )edlg3ex3):*dnts D and C (where destructive and constructive inter 3n)cv3eubve)d: z0gy 3jdaxzbl37q* ference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in aujs /54l4twigreas 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 d4li w4/ t5sjguevice 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 wavebiykgy(1 45n es shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with n4 (1egi yykb5slightly 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 observe+rq-f)ckxevq+ g; zw6 r move in the same direction, with 6ger-kq x;)fv+ zwcq +the same velocity? Explain.

If a wind is blowing, will this alter the frex6tfoyi4,b //w qpu)n;kp,heq ko51fquency of the sound heard by a person at rest with repoekfw;)xif/6u/h n4t bko y1q ,pq5,spect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various p5pa+j 9z5 38jteyhrc cositions of a child in motion on a swing. A monitor is blowing a whistle in front8aec3p559 rtc+y hjzj 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 forfun773 38uxr*g nlrao 5oan3e the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouenau on3 o35ur7 *fg8 nx3r7alting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the i no o0xsdg.z00ft ,bkaj*0t6waterline. He hears the echo of the 0 .0b6i0zd kfgo saxj*0otnt ,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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavel f7, +cr,d ll-0bpwig93qhlmha7 *p tcengths 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 schoolp py 1 p/czvnk+vd s/pc8e.tm-d-8p1mp,wcl 7 of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (lc8z 7-mk1p 1t,n+cps8 vvw-/ cd /ep.y mpppda) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makesx sozq *8;:qrdvqi q- d*p-s)l when striking the water below is heard 3.5 s later. How high is the cliff? xspv;:zqls8qq** )- di-qd ro   m

  A person, with his ear to the ground, sees a huge stone strike the concreteuqkwk;i :::x+ mjal +w pavement. A moment later two sounds are heard from the impact: onakx: wjwml+ u;q+:k :ie travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error m) l dxszww4*m3ade over one mile of distance by the “5-second rule” for estimating the distance from a lightning strikw3zdm) s*4w xle if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lqwgn*.b0+n8nd 4 js5+ qitntgevel 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 levelp ;a+zxyga sa zg34n*+ of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level ot-rr8dd v7e(t 0a /g9z q6fqwbf 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s-r/at08 qf9zg(tv dbrew6qd7.]    dB

  A person standing a certain distance from an airplane with four equal kbvhu2+42vslok4(r dly 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? [ k(h2v 44kl uv2sro+bdHint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noidamzb 2y;kz9 9 /nr)gzse ratio of 58 dB, whereas for a CD player it is 95 zmnda)rzyb;29k z /9g 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 sound fromcm22;ea 7 kt.q.4ne5 upbw8:rk rlsym a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cey2knk.;48w c apuml72ree .rqmsb:t 5ntered 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 eardrumm yt 9zvlwy,4ss vd*() 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 i:cv.mest3a9bv c1 b c8s rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m b:seb 3.vtc8m a9ccv1from 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,dlx+kyt 1i4) girp8a meter registered 130 dB when placed 2.8 m in front of a loudspeaker on thl k4 i)a drgxi+1,8ytpe 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 soawy0(v0 x5i zzund level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectiz(w0z0ya 5vx ion 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what p; xn6j lj4)-twe*wg gfactor will the intensity increase? Increase byje*g jg-lt6)wpx;4w n 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 th 2gkeduw5wozd-:tvkt2ba o5 uk1 +1(ce frequency of the other. What is th2bd1 5 oc(-gud+a1tv2k:twk ueok z w5e ratio of their intensities?   

  What would be the sound leveq h 4 h-sxs1v+6hrq7h+ 777b r,m0tbqk opefefl (in dB) of a sound wave in air that corresponds to a displacement x k77bf7,+tfqh -sh4+bmhe1 q0o6qshpr er7 vamplitude 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 1:kz m tfg fkldfz/8017)hwoqa 100-Hz tone that has al8d kfozz) wt1/: f1k07fqh mg 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencxq23y bxfgmz7:3 /1 xksg rvc.8jo:cuies that an ear can detect when the sound level is 30 dB? (See Fig. 12–: o ygcqrjz128cxk:f/u3xgb3xm sv. 76.)

  Your auditory system can accommodate a huge range of sound levels. What is a*lbj/xi pb q7,rr gby(zz5: 0the ratio of highest to loyz (5rbp7bjbri l:/0x*gq,za west intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin-juvsgd-, nn2 has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and iv-u,j ng2snd- t 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 fundae(p v*hd+ lr5imental and first three audible overtones ifed(i+5r vphl* the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top ofw: u kfu.l-f5r an empty soda bottle that is 18 cm deep, if you assu:5w-kurfl .ufmed 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 py/ ya ;ktwdskx3gb .fv*o 2/5spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pi;/3bwg / dy2yaf okxsv.p5k t*pes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as :9li.sab0 i,;tepe vf its third harmonic. What will be its fundamental frequency if it is fingered at a length o9v e,.is0ilf:bte ;p af only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunedc; pgxi)9ue/ uwv/tk7 z 7g7mn to play E above middle C (330 Hz). 7w 9p;g gm)ei7vuz//7ntuk c x
(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 oxblazx0c4 )j6.j ey4 kpen organ pipe that emits middle C (262 Hz) when the tempezx)4y 4ebxjj0 .kla6crature 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 20 hfpf8 r m:sg8+tyy.*v $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthzajya x2j.tl2h9*/ fk piece of the flute in Example 12–10 should the hole be that must be uncovereyx/a. 9jlzatk fj2h 2*d 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 resonak+jvn8cd8 a4xhdlopr (6n,w ,te at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a), n8jp,w+d 4ncadk8 (xv6holr 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.7rlx fw3w, (ij7q--3u rozrdb It resonates at two succx( biq,uw-l-3j fzwrd37r7or essive 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 :0.yw qz.igygnxk21/h: e vyh$^{\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 a37qyb:ux bk k0re present within the audible range for a 2.14-m-long organ pipe bbkx 7:3uk0yqat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It iw27yzqon6 7im wkdtb -cx )sn*ol* 3d;s open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible robqn;- 3m2c*) yk6wstoz7dil * dx 7wnange) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one bea3./cxm *bbrphp89 x 3kvr6az wt every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the othem/8.9pr3p c bz xrbx v3w*hak6r string? ±    Hz

  What is the beat frequency if middle C (262xtqa v 18vnha;./rk*w 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) m eb,a)ljl,edsc 3v-; operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency e)3- vcj adbes;l,ml,5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces c wmne :rn(h(d1 v+4ol4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tr1h+mwel n:4((vocdn uning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensiot 5y-odjxu5td48gz ; xn in one string is then decreasejxo d5 tdzx5-8uy4;g td by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to p pi,nuyl7ct8 98e h3z/mzdmb7lay middle C (262 Hz), but one i8m,9yz8ep l hi/377zbndtum c s 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 nj (p)- om8mxfa frequency of 441 Hz; when A and B are sounded togetjmo )pnmx (f-8her, a beat frequency of 3 Hz 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. Ah6 pd5 nq 5)ye.enqrut,3-mcq person stands 3.00 m from one speaker and 3.50 m from the other. cd tn.q,q)e npy35erqh-m6u 5
(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 vibratiy; us-4r*q;jy h-ya 2 la0opldng at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) Il--ja *0o;q2s u4 ;lpyhay ydrf 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 wavelength.hvv) j0cwhn 2s 2.64 m and 2.76 m in air. How many beats per second will be he )whc0vj vn2.hard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency pw2jby n5ojef7o h.3 -of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if yo .jy 2wbjp37n-hoo5 feu move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire e ,efjw6m :uu y**qi;qlngine whose siren emits at 1550 Hz moves at a speed oe;wm iy6*lqu*,jf :quf 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movinu 1i8/y7hq lhg0su8zm g toward you at 15 m/s ve uqhgh7i u0/18sy8zml rsus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single freqwyf (2 pavl7;c1 //ul)ecsg)pitqv o5uency 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 hornsw vyte(p2a/og;fv7lcsl / cu))1 p q5i emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out +p,,x* * 9 d-dg,fhc *ux2gbkvydjcfpultrasonic sound waves at 50.0 kHz and receives them returnccpgdhdk g + x*bu,,p2 jx-,dv*yf9*f ed from 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 byk 7zm1zisro s1qi: g) 1s/ef;at emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat s 7/esmrk gz1:qsy1fio ;zi)1hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originw v3phw/.ia+lb u85 jial Doppler 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 station. What beat frequency was heard /3iiapwl8ub+j5 hv.wif the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure,a 8hl9tfuw*0d:mk1siwuez - 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 Wh:l* dh wsiau 0,m9uwt1 -8kefzat is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fo9rk:d1ehi-3 x(od vt requency $2.25 \times10^{ 6}$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 tf t/(8lewhl;2wljr8::r zolc he wind velocity is 12 m/s from the north, what frequency will l j: h/ lrl l8:fzr2;t8oewwc(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 sperub7 imbi(-/;suvd4r ed 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 mljf. 1h vx/ywyq)xicc-0p 5g3/s (a) What is the angle the shock wave makes with the direction of the airplyfpj/h.c3xgl 5 wx-vi y)c q01ane’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 -clkkv84t( m tof a planet where the speed of sound is o(t4 l 8-kcmktvnly 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 ocejd .w1g 3/cuof 5*;y39nlieu1 tycjctan. Determine the shock wave angle it produce duc.o1j; it1 *n3yglj5ftw39 ccyu/es
(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 -qkgo+d/ g4fv$/theta$ 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 f0*mwc dy.hbzrj;:oq3 0 f;igm lying fastec;f:wmj*iz. 0o3m qyg0 ;dhbrr than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that s z bm*p2:ga:o1y 2coxuends 20,000-Hz sound pulses downward from t c2b:2 z1mouay:o*pxg he bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are tdfdcb*np. 0k81w3gpthere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of man4 7i8clh 2ou /hhq(fstwfq1,sy plastic pipes of variolqs,s4hh7 8w1 hfc( iqof2t/uus lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threspj(rppwrs12dyq* jk6 z/: io)hold of human hearing (0 dB). Wha1spqjkpo *ziwd /2):6yjrp r( t will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87ke 8d1n-eal6i -dB sound are heard simultaneously? ik8 - l1neade6   dB

  The sound level 12.0 m from a loudspeaker, placed in mt4zz95 rfd. 6xxrnn tz n+s7.the open, is 105 dB. What is the acoustic power output (W) of the speaker6nztzn r+dzx.s5 .47mtf x9nr, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outp7 iof1wikuu,rufcol0x+ff9 ;1zk1.x ut at 1000 Hz. The power output drops by 10 dB at 15 kHz. Wz k1. ; xrkfoii9+cl u1f,1uf7fou 0xwhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircrafk vqwc*db cg)ck l6z.+w9 zcfz5j:0q(t 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 wou*g.q+ zwwbqc)j:0(6zflzdcc ckkv5 9ld be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systemsopsk*l, c*5a t, 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 freq ymiw)wc79np9uency 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 be,cz- n pcxtw +x/fij) c9fxk7.tween fixed points with a fundamental frequency of 440 Hxfwj-.c9)p+tz x/cf ,7i cxknz 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 vib (: lupyryl6s:ration 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 the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency y:(y lrpsl u6:of the tuning fork?   Hz

  A 75-cm-long guitar string of m 39 /zjwz;8s jnkt-vnvass 2.10 g is near a tube that is open at one end and also 75 cm long. How much3 w/z;tvj8nn sj k-v9z 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 mlg3h5cc2hl21qcz 7pobserved to 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 500–1000-Hz range coming from twirot 4iv0fkj)7y 92 ngo 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 t92r)ti vjn0o 7gyikf4he 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 stationary. The conducto dmvllgw4o.;ex-o1 -grn o- s.r on the stationary train hears a 3.0-Hz beat frequency when the other tr 1 e;o-rvxldg o-.ngw4.loms-ain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afterrs2*lwha) 5pvb y3d(d it passes you, its frequency is measured avhsld dbpr35y2wa)( * s 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed 8pk rk gm,7 qcst,t7,ok.u0lwof cars just by listening to the difference in pitch of the engine noise between approaching and receding ca.,qku,kktr7,plo m gts80 cw7rs. 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,f(z *kgoioy7 / sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long io*zgokyf(/7 . How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statidu(d1,)w + ihvar)vhp onary 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 )1)a dvpiu+ wd h(hv,rpassed him, at C?

  If the velocity of blood flow in the aortaatv82 +rh3ws j is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the tvj3ws ar+28hwaves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed i*ii /,zdhk n.6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after t. i d*zi/hn,ikhat wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches al z( o)bh8jbw,wu+e o6 moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emittuhz le)+,w6o (b owj8bed?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpin1ys :x le7 mqp2p)bg r)g-,goce 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 thi y7gc:1 -rb,) pmpq ogxsgel)2s 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 jtu,r *6obr2 gcompromised by the presence of standing waves, which can otuj b,r2rg6*cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing(dp7s /fk h37w c-fngu 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 d7ghc( nf/3uk-7sf wp rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency offs)va 2;tb jv1 about ;v12 )jtbsavf 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 grounrs upy ,s8b1,td hears the sonic boom 1.5 min after the plane passes directls8pst ,uy1r, by overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is gdw*shs7, v ;( hkm /kygmj35m15 $^{\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