What is the evidence that sound v 4zr5 n qwaeh30nzc:j:.7q dwtravels as a wave?

What is the evidence that sound is a form of energy b2vrge3 *yzl:+ k/ uhepws+yo0;z0 in?

Children sometimes play with a homemade “telephone” by att x lpvbr/ 9y/tyvy0e 0b8.dwwl/:8etv aching a string to the bottoms of 9pwl8/l/8ey/ y b 0xbrdvt:t.vyve0 wtwo 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 clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expe)fc r3 d41kglqct the frequency or wavelength to ch1gf3k4rcq l) dange?

What evidence can you give that the speed of sj *9i1 aoi8u6w* oouueound in air does not depend significantly o9i6uiju* oo8u 1*weao n frequency?

The voice of a person who has inhaled helium g1 w6vu jezr):sounds very high-pitched. Why?

How will the air temperature in a romg8 k *z.tfwc6ewf02r om affect the pitch of organ pipes?

Explain how a tube migh5xdq+cat,ub * t be used as a filter to reduce the amplitude of sounds in various f+ 5b adu*ct,qxrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move uiw8 dq.ccnuwa.)):vyv2 *cbt p the fingerboaycwc.da u8b.:vi cwtvq *)2n)rd toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear if rz* hn/hw2:it but cannot see it. When it emerges and you do see it, its sound is s */r z:hwi2nhfuddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference inl ) dpefb*d.xak b;-dtqkt-7* space,” whereas beats can be said to be due to “interference in time.” Explte7* kk d-l-b)b*qx ta.fdp;d ain.

In Fig. 12–16, if the frequency of the speakera 3 0 k:pwnezp*s7tym5s were lowered, would the points D ak7t*pyzs e pamn5 0w:3nd C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectix/l n+d7xy*qln.rdug hc3u2 2ng 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 coul + xunlndcy3d.r g7x22ul*/qhd adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wavbbind -yos m 7bz803r5e can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the t58d-0mz3rs iyb b7obnwo component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the5m-f+; jitlz3 4xko;qhd*d ik source and observer move in the same direction, with thxk oqi 4tl miz 3djfk-d5;h+*;e same velocity? Explain.

If a wind is blowing, will this alter the frequency of t w 1ek.u(v 40qp)qgaks* b0a3 p+xhtrqhe sound heard by a person at rest with respxa ()q03s1qea*pw+ukqgh. 0kpt rvb 4ect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a skn07 ms u,nk5b,sc ze3wing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest fn 7ssubnc mk,53ze0k, requency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of hj yp:/c0 w0ikzer shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the leiy: p0c z/j0kwngth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship juskxs 4 )- cfgtymdtp,6)smh:e)6itn 4ot below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (int6s4mc f))46edtm :hy )xgsp okt,-Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 3 4f2 n vfjkqyu.du//d$^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a dle8 ja(-r h( c3o8eio: pz9 sbjk o/p7quua16foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfir ood((k39 67puza:usac obhji81e -rlq 8jp/ee is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The n-qg;e:+ipc nrja;sp7fm8q)splash it makes when striking the water below is heard 3.5 s later. jcs7)imqanfrq-8n :;ep+g ;pHow high is the cliff?    m

  A person, with his earx7,i49 swqdba to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they ars,wdx4ia9 7 qbe 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percenb+8( gnnw1 9npv9h fxrt error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperr9xnwn(b89 1+pfnghv ature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at tu p..2ph.ehfy 3 ev qr*gdgs0xk9d6 f.he pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity 1l78qma qvt3l06yrcw is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fi.9i2 +uayo nq6:b ahdtred simultaneously at a certain place, what will be the sound level if .qynuhib2+ada9t : o6 only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally n*m0hy ewins,78g ;elu6z :zmhoisy jet engines is experiencing a sound level bordering on pain, 120 dB. What 8s;: e0gwny h7i,ml *hezu6mz sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal 0pzs qo4t)ypq91 ,b*dnra/iv-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgrou9az*qp, d ytbvi0s o14)rqnp/nd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of 4y0m5mh6 xm; m2n cumosound from a person speaking in normal conversation. Use Table 12–2x2 cn6m;u5h4mmo mm0y. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave stritz d832md;k kkr5wed/ kes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more molc794n)bfoyg z 2p kn,dest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at 2cfn94zgp,ykob7) n la point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frlw4xzw6 /ypn 6ont of a loudspeaker on the stage.6 l46wnw zxp/y
(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 abt iz74 zg s3r/zz7q (8u (1vqdk7wqva difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sect 37(sv( rkgiqzzat4z 8d7z1q7uwvbq/ion 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inrnh;s.i c6yuxe w. :b1gss18ptensitws 18ucnp xhsbs;.e6:ig1y r.y increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equ )vna;8qyqc3k s0ep 4fal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of tv c8pk ;yfq0)es4q3an heir intensities?   

  What would be the sound level (in dB) 8sbj bv(/ln:h(ufed *vi (b( eof a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13b:d(8 (ihe*( bn l(bjvusfev/ mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to1/kqb tqnq06gdqd* /ed rku3: seem as loud as a 100-Hz tone that has a 50-dB sound/dkq : d 6tq1*u3rqk0bd/g neq level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can de( e;/ qbh395vu tcl,fvi9zfbutect when the sound levfq9/ve9 lf uct5;zb,3u(i bh vel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accimh;se vze9-;5baw. zn;-mor i;jfy9tx*n7kommodate a huge range of sound levels. What is the ratin .;m 7bejm* on;ye x5ziraiv-t -khsf9w;;z9o of 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 violin ha u /e0lt)qz2(o) bmyans a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has oemt)qyn) 02l(bz/ uaa mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamentdtso:, v7d vbae/ /s4tal and first three audible overtones /vs4 :,osbtedavd7t/ 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 aut1b6 p:m uhv)cross the top of an empty soda bottle that is 18 cm de1h:pbm)u vt 6uep, 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 spannink -7ndxgx g;3og the range of human hearing (20 Hz to 20 kHz), what kxdgx -7n ;og3would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third h2ols) 86pediyarmonic. What will be its fundamental frequency if it is fingered at a lengtp ode8l 26ys)ih of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play; wdoe 9c7xv jvr*z)c (ls.5v kl91zcc E above middle C rd*c9;l) o1clkwxc v(s vzvc9e7 .z j5(330 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 pw1ih (6pnigla.u5 5utipe that emits middle C (262 Hz) when the temperature t1uwu a(l65ig 5. inhpis 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 a 51 5 afdpubszb4kd-)r 4a bqsn.bnu*2t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 n3 euef92ho04q7pxs *6 5rabua0dbwushould the hole be that must be uncovered to play D 5*0 e4o30 q6ad eun pu2wx 7bfrau9hbsabove 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 resonate at 26b( qzd 1g,f.js4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show (ds q1gj.z,fbwhy 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 long1c.td5x vakv:0eklrv u3d: d3 is open at both ends. It resonates at two successive harmonics r d0k3 1tc5veddx vv:3l:k au.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 *8 xi ,0pouohy,f:1wkr: fgoz$^{\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 thj ;nwchrzr, 7 j;/3.c ln*c;4en rjcile audible range for a 2.14-m-long organ pipe al7crwj,ncijjcnr; . hr3cz ;/*l ne4;t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to 7.d on7xwr2xvn7;a 1)n cgwr jthe outside and is closed at the other end by the eardrum. Estimate the frequen1wnxn.7rno77gj2 da)x;v c r wcies (in the audible range) 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 beat every 2.0 95 c(a5 o;1r k1xvziapolgn3ss when trying to adjust two strings, one of which is sounvapcr5s;ok 5( n oxg1139zai lding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 H)mkh rf6rz lm ) mz/(9(k2suzfz) 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 anothereqviu 3g)1 .)du m1ugp (brand X) operates at an unknown frequency. If neithee gm1qv)ipgd13u .u) ur 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/x 6 lzonrub0/3s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency03/ nzbxu6 orl of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension rpwgg*mtdwx0ylix* 4 ** y b,8ynb(8rin one string is then decreased by 2.0%. What will be trp0wgy nb**,*g8i 4w8y*x tmbyxdr(lhe beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identkrz5u3)xi6 rx ical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other3rkrxx56 i u)z at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B h/6s 0tx.nzxejc5 ,gw fas 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 begxw5f0zten 6/ ,scx.jat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person 0 n sgzk.*uu h5carct47*egjdq ( kv,uxw(9*mstands 3.00 m from one speaker and 3.50 m(uuuqc s 0hgj k ekm7* 5(9ncd* wtg*z4vr,a.x from 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 ar qtd)avqs7 iawg 04;g6;2vzz ie supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s whei;);tdz qzs v4gvia7 ag6w20qn 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 ofwm:x.ed nb7tq +(aok-2 uqavw4:zf. l wavelengths 2.64 m and 2.76 m in air. How many beats per sec:2qebqlmz+a47knvuf w xa .(- o.d t:wond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firz fm27psxziyv1x,+s.edg8uu v 3j, q3e engine’s siren is 1550 Hz when at rest. What frequency do you detu zi.s18vj7quz +pxxdv3f 2 3s, yegm,ect if you 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 d6e+ppw 6q (ny*r;uscvetect if a fire engine whose siren emits at 1550c e y(r6us6pn+p*w;qv Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz v+s5bdkkg(-i2 jzy 0 dsource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies ex-ijbs0g52kvzk+(d d y actly 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 frequ917 n t;hq5j e4kustt3sic4a yej h0;q-mr uk;ency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hu4iukt3 jth7tsa4;eem0q j;n9;15sr ykhcq - ears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrason+ *il;j uzy4bp vq 5c3cm+um-yic sound waves at 50.0 kHz and receives them returned from an object movi lu;jzm*-bu vcc +yiyp4m5 3+qng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall 5kt6rr;/ yl5 mf)dalt at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave witlrf/l;mkyr6 tad5)5th frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experim-21 y0w (iabootg* 3a7ofq4aez cq4d rents, 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 tht1i43* awqo 7go0-oae24fzbr ycqad(e 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 measure blood-flow s ada1,pz hpq6v+faa-8peeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in huma a,68aa1z-hpv+d aqf pn tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves m,w 2a/1wuj/ dy0xjko 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. m +zlx p2gq;q4When the wind velocity is 12 m/s from the north, what frequency will observers hear who are locate+q;4zqx lpgm 2d, 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 lanmmt5 .p-mmu 1g5ikb-9mxsjn; d 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 Maym)8, e-vp zblch 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes wi mpve,y8l)bz- th 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 planet where the speed of sound is a ahm;e2(tg-i t(ag;e2maih- only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave an+ o6d:i +diqaoe f03.rrn.gl ngle it produceson e:qgi or d.arnl3d+0.f6i+
(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 / wl kx29c+ gaiyit bye89j,mm,n24bz$/theta$ 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 exactli46hx6acy +wwxqik a2la;j8+y 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizon6qywc l 2++w8 4ixaix;ja6haktal 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 pulse* anp ty(s+a. x,jwe(ss downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulsw.na,*e p +jy(xas(tses (in fresh water)?    s

  Approximately how many octaves are there in the human au*1.xupy4sg rgdible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It conswe mlv.r 1aw06ists of many plastic pipemwa vrw 16el0.s of 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 a person ma07p 8sdmb,pxt( z4mtqkes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitx(p m 8,zbt4 dpmt7q0soes?    dB

  What is the resultant sound leveli fu63p ms3as/ef:*v p when an 82-dB sound and an 87-dB sound are heard simultaneoesf / m6:*uvfp33psia usly?    dB

  The sound level 12.0 m from a loudspeldfqx *ec);0amp90hdqbf2 d: aker, placed in the open, is 105 dB. What is the acoustic power output (W) of th*9dqf qd l fpx;a:m hcdbe2)00e speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dy/ws. iciaf5jkak3+bf evw t0x0). j+rops by 10 dBfw5+yt ic..v0+k i0asxj aj w) 3kbf/e at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically vuv4w yke qw/ v,jjcy:*9tf4 -er+sv;wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 rq4t9:u/; , jvvwsjv4 + wekvey*c-yf 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 0m(.p,nfo w9k apo/ unng( 7-ymz4ol wsystems, 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 (yh4qwm6ezz ;bje+7om )xq2 ztuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points wij ;jc:k ,sk6jnth a fundamental frequency of 440 Hz and a mass per unit lengs 6jnk:;jk c,jth 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 verticlw/if,**styz3ttmra l.4y s3 al 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 ag4 yil lyaz.sw * f3sr3mt,t/*tain 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 a1jvd8 pf i(xag)oa1l7rp1+sdt one end and also 75 cm long. How much tension should bpldr 7 +8os ja1gaip1f(1xdv)e 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 waoy5odecek(.v 0yv* z(s observed 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(ucs ;9 tyexn-9wx oj5 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 farther from one sourx9sutw5o(e; xc -y jn9ce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. .h:0liv4gj kbalvw 51 3e7i3*h cg5prh1vzgnOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat freba.h7 * lrl34 0vh1gckhg1nji5weziv :35 gvp quency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 53852+fgk( lm- mh(6pwc.h 0po k qtztvn( Hz. After it passes you,ck(o+ g - l(w6m52vp(m khhp.nztfqt0 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 listening toukn-xfkq(xy-0p3 2d o the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes3o d0x-fky k2- xu(npq by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 1vun:a9la ,9obpr8 b z-1 Hz. The shorteaup8v,-n b ob:z 9l9arr one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a r a*m j81l 2jqzdbkb558uh8a toailroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sojd2bb8hk*oz5 a8t 8 5 1lujmaqund 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 bloo ogp smr*jdjkm:ehyb9m o:0m9:9ofl;* rw 3z(d flow in the aorta is normally about 0.32 m/s what beat frequency wjmw:e3 :kyjo s9r (9; mzp9dmhlg fm*r* ob:o0ould you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 5 aff /ng,ha9km/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 thengaa9f/h ,fk 5 frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freqkzkgcp4q.3( q il (rc5uency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms4q3.iqkpzgc( (lcr5k 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 emitted?    m

The “alpenhorn” (Fig. 12–38) wa 0 8pl) znmh(vm )3b0gdofrm2ps 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 f(pm ldp 02nzoghv)0m3r8mb) 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 st.i lir 5uwisq9p9 l(t)ereo listening can be compromised by 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 hq)9ii .w u9spl 5li(rtigh. 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,”6 ldq 9xp:cn5 j(hsy:,-mxiqu-w 6cgf involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod canf9-s, q5nculm6i(y xwp 6:-cj:q hdg x 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 eaw +j scg(9nhmh/6h; lzr at a frequency of about 1000 Hz ilm 9h+jsw g;/hh(6cnzs $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hearjmw; -ja/7 lwrs the sonic boom 1.5 min after the plane passes d j malw;/r-7jwirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 71 zm:euqw,bq 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