What is the evidence that sound travevk2 :5tit t08p rtel-els as a wave?

What is the evidence tha1fwaf .u39 quj78 jedqqv ,mx+t sound is a form of energy?

Children sometimes play with a homemade “telepq./r. tvd(p5 tz4py* 9ueh osvhone” by attaching a string to the bottoms of two paper cups. When the string estrh(p*p.9d4/ q.yvu 5zvot 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 paj6jck6b**y af.-h1s t maoo7:enh o1o sses from air into water, do you expect the frequency or wavelength oe h :1tasomnk6h o* 7j1 -.c*6bfaojyto change?

What evidence can you give that the speed of sound in air does not depend signifhlg; lu8*lbhcwa -a;.icantly on frequenc*ca ;-hbl .w; glulha8y?

The voice of a person who has inhaled helium sounds b;vu 9;ungpe+ek,fyo8k)fcyymd9 46 very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pj jm s:ic4j5ld 1-m vy0(jnyn3ipes?

Explain how a tube might be used as a filter to reduce the amplitude o96 ehh9esf4r9ruvy1yf sounds in various frequency ranges. (An example is a car mu e91ue hyr s99rfv4yh6ffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togetherna *hf0k:m*ktvt 5f-f7lz dr 6zx8p-d as you move up the fingerbon-p*a 7t 5*dztkx8 l6zf- f :vhkfd0rmard toward the bridge?

A noisy truck approaches you from behind a building. Initiqwql-66e4jxr ally you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “bright q4q6xrl6e- jwer” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats cv9,d.b7fv6qki nk9:; hc pcqfan be said to be due to “interference in time.” Expl, b: vqikhfpnk6;v9cc7 9qdf.ain.

In Fig. 12–16, if the frequency of the speakers were lycw/.w kwhe1)owered, would the points D and C (where destructive and constructive interference occur) move farther apart .ckh /ye)w1w wor closer together?

Traditional methods of protecting the a btm3yxl)y ;tuaf3 ht+4rl7*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 yxat* utb3) +m4t7h3;l l yafraddition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be tho.rp, npx xw2j(ught 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 two component frequenx(p,njx w 2r.pcies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direcuh1 nql-.0-v ohq mqq6tion, with the same velocity? Expl1h-qq nqm-l6.u0v oq hain.

If a wind is blowing, will this alter the frequency of the sound he0 7z0yqgpqucvq6h6n u ;)qjqm2 .ibf ,ard by a person at rest with respect to the source? Is the wavelength or velocity cbqq;u ,).7y0zq0 6g hjc62qvqpmu in fhanged?

Figure 12–32 shows various positions of a child in motion on a swing. hgsqopv0;h-ebv s r*l6;h n0. A monitor is blowing p qv6hsgl0h;0nh;* v.r sbe -oa whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the 9qtxl1;2wu p kecho of her shout reu; 2xwqp 1kt9lflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just be ls -/.1wslnr7dpke9e low 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 seawarplk-/9e n1e wsd.s l7ter is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in z:+ of,efrzr1 c* uzd9key97dair at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. b+ky h-8ne8-i kzvvnuchu0 0vlz8 :a. Without way0c+h:b-v v l8 8eiz-zakn8h0uk nvu. rning, an engine backfire occurs on 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 cliff. The splasq/b7(b;nv ggufe 20ixh it makes when striking the water below is heard 3.5 s later. How high is the cliff?vg e/ (f;ubi27g0nbxq    m

  A person, with his ear to the ground, sees a huge stone strike a-.kpri-i(fvpkt4i 43 a4 jrc the concrete pavement. A moment later two sounds are heard from3(4fpap .i4a kiirjr v-4tk-c the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one )ts vkhfr + t)g69lyc(mile of distance by the “5-second rule” for estimating the distance krl tv ()9ts +gc6yf)hfrom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thesh4cim3f-ni vg c -m8 nvbdm5.lnt 0*7 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 tom qr-1p 5ihh/9e2r ais $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levetk/5x6g m(m/zmkiju9v :.aoll of 95 dB when fired simultaneously at a certain place, what will be the sound /mtzx v akjk(.m9l:u/o 5gmi6level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance frt pj c65hobe eaq/o58k4i falz:j5 4b7om an airplane with four equally noisy jet engin4 h bzl4jo/ akjftiep75 ab6e55 oq8c:es 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 intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas fojj; 1 s(.hcpicr a CD player it is 95 dB. What is the ratio hi(j1pj cs ;c.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 from a pk5o k.ca,i, gxerson speaking in normal conversation. Use Table 12–2. Assume the sound spreads rougag i.ok5,c kx,hly 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 strikes an eardrumhs: 0+nrr cats /zvk*xl*x21 n 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 amplifie+ywi(4;xgx ux r B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from uwi+g;y4 (xx xa 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 ioj 3 bk;oj/x1j .ffrm8fzab1)n front of a l kf8.j/j3bx bz oo)mf1jraf ;1oudspeaker on 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 dete-hi4j7wsz9i t ct a difference in sound level of 2.0 dB. What is the ratio of the amplitudwz-7h jits49 ies 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 will the5-hnf )2 fvxaxd d*6yr intensity increase? Increas xy*rdxf-vdn 5 h6)2fae by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but onm06t.df p9yl7rzs 5u me has twice the frequency of the other. What is the ratio of their intensitir pls.y69df05 m zu7mtes?   

  What would be the sound level (in dB) of a sound wave in air that corresponds l.wr yd*fo-ss vc .tg)y1:; jve5 lc,sto a displacement amplitude of vibrating air molecules of 0.13 mm at 30s;5* jycg r-.dvl1v.l)t: osf cew,sy 0 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud wryb *mp ; jtm,..2mjlas a 100-Hz tone that has;lt.m jjym .b,*2wmrp a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soun4t .b.tv,noob 5:ft)z8e.xx u s(efbyd level.to:ob,8bt vb y)ex( 5n.s4 x.tfez uf is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangg8 m7lt(beuf,e of sound levels. What is the ratio of highest to lowest m(, eufl7bg8t intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a oj( f)keb 1y2rfundamental frequency of 440 Hz. The length of the vibrating portion isre2ob y1jkf( ) 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 l nf 71cmazz94mong. What are the fundamental and first three audible overtones if the pipe is na 4 fmzc7m1z9
(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 fr)nts50pxa r,com blowing across the top of an empty soda bopa n0t)cr5 x,sttle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ withk9ay7r ut im6 )0gjmf3 open-tube pipes spanning the range of human3 i g6 kaymjmt9)ur07f hearing (20 Hz to 20 kHz), what would 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(c(ai20ajo8 en4i 1 q.ulxrhb its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengia i 8j 4b(.hxr( u0oqn2e1aclth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E aab;mmx0 z1h;p bove middle C (330 Hz). b;;hzma0mp 1 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 open organ pipe that emits middl6 fxxsj8vxl,0d/tc t3e C (262 Hz) when the tempfvx60l/ j8xtsxd,3t cerature 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 at9ke0( el/ie4eg 2+jrze piq4a 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 should the h0shm q*,t/ s(nz sxa-aole be that must be uncovered to play D aans ms*t-sh /az,q x0(bove 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 264 Hz, 440 Hztk+e5ogrt-)q :c it+ f, and 616 Hz, but not at any other frr-gf:)i oct+5ekt+qt equencies in between. (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 rwp ipg(d;c vk6zohqgn4.wa+4 p a/e)5esonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whagp( wkd.pozg;4)eq/ n 45hc 6+ avwpait 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 wee,lx j*;b1svjly(yn8rn* .. s0 lfh$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for ai3rie76 gj9c) c4zaxn 2.14-m-long organ pipe acc6zgi) rna 934ex7jit 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 the outside y 13+oazkre; ;2d 1vdsvqz3hqand is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the dys;1qo zr e132dva; +vkhq3 zgraph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, + hmv:yo(k4y tone of which is sounding 4+ymkhyo (v :t440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middlf 91eae ypt10(5rixede C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whigqlx+/dy8iinnj0 xu . p; 89tfle another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, bqu.gi8d0/p n+fxl8 9jt niyx;ut 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-Hzn 7bg9v)y6(x9rfuf2oe uvt2j tuning fork and 9 beats/s eruvyf9ot 2n bfj(96 x7)g u2vwhen sounded with a 355-Hz tuning 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 le(2jgi,;daa uie4.pda a o)qe0xh*9tension in one string is then decreased by 2.0%. What will be the beat frequency heard p i.aex 0a2 l9a4 qg e,j*ho;dde)aiu(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 play zng6p afb,i2/gdjj(c*hzu- ngo( s/ywr:f9*middle C (262 Hz), but one is at 5.0°C and the other at 25.bfz,*c 2 j/( 6gr*(n-dws9gz g:juipofa/yn h0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and ol3/+/mj8hvjn a fnt9 f;0o4tjikn-.a6 cd wqC. Fork B has a frequency of 441 Hz; when A and B are sounded together, aitn-lq kjam/an/ 8ft n4f d.o3wh+jjv6c0; 9 o 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. +i/jn4q f+ f8azwjz:kA person stands 3.00 m from one speaker and 3.50f :8nq+z jjfik /+zaw4 m 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 are supposed to be vibratinw,b39 0 go(ei xlumbp4g at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratgmp9 e(u wo 4blb03xi,ing 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 wavelengthf0ee-(kds(8 yv0k 7skzxp+ ahs 2.64 m and 2.76 m in air. How many beats per second wil (+ fkxsy 80sk(pd7v0ae-kh zel be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s b pr/z ;s7;g,qjra(ut siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 (bsra;, ;zut7q pjrg /m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect izu3s3en4y6 k8 h w 8gjvgxuf6+f a fire engine whose siren emits at 1550 Hz moves at a spee8h34vs 8n6z6j +ufegxy w3kugd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving to),j3 eq(zoqd xward you at 15(qz )qd,3 exoj m/s versus 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 thf pm5cz qez/2)e same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency ezpm cf2 z5q/)the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soufml +-n(4tw0-h/ 6tqea3pvldefe)ro nd waves at 50.0 kHz and receives them returned from an object moving directly away from oeh/ e4t)dl-06pe-n v trq a fflwm(3+it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ui2f4;m-81xa o. wl-ny alsm cbltrasonic sound wave with frequency 30.0 kHz. Wh2ms 8 mfwlnix.ya-4lb;1co- aat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played o 4b/0ec plc u-n8tckv-n a moving flat train car at a frequency of 75 Hz, and a second i-c bn4-lk cp/8e0c uvtdentical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bo7l2dto i8 iu7lood-flow speeds. Suppose the deviitu 277dlo o8ice emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonicej6x()t/v ggc)8jdy g) bl-ox waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocit*xpwq mp1.:e y13ycqa y is 12 m/s from the north, what frequency will e1a q1q wxc y.3mypp:*observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 20 h34*b; hnhgko $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s;cvmisb0x 2i4 (a) What is the angle the shock wave makes with the direction ofb 04cixi;svm 2 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 at5 62fz89wyj-j5 vdg2etwfym :8om juu mosphere of a planet where the speed of sound is only about w 92vdtojwufj8fuyjg5 8 e-2z5:mym635 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 ocr(rnk (:f3lg+w+zez eean. Determine the shock wave angle it prode w+zk(grl: re(nf z3+uces
(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 wzpz8q(- ; nl8uk;mz t$/theta$ 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 v.vnn)2 ya7w* ig5btuufe87 u flyintvu)agb* 2v757nfuy we8 nui. g faster 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 sends 20,000-Hz sound puls;xv3 tj8x/ etues 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 minimut8 3/jvuxx et;m time between pulses (in fresh water)?    s

  Approximately how many octaves +i mf0zx1n e9f5t.zmn are there 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 manpq c7sy6sab 0(*-8duk 4jaycyy plastic pipes of various lengths, which are0s4*a cyuy7k cd-8pa sjb6q(y 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.nx.m jw29wa m 6/5ovov0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 sx5 mowmvw.n2o j/a9v6uch mosquitoes?    dB

  What is the resultan.4 1anms7 q52s5yi* agf iegxot sound level when an 82-dB sound and an 87-dB sound are heard simultaaa n24x*o1 em5qi75ssf. igg yneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What ,ae av,-mefb:a9 9qpw is the acoustic power output (W) of the speaker, assuming it ,ea:p, 9-qaf waemvb9 radiates equally in all directions?    W

  A stereo amplifier is ratfll;3o.u v c 0r+jtijn 0grv3(ed at 150 W output at 1000 Hz. The power output drops by.0g c 30(r t; 3l+unfrvjljvio 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectizf fwjooc )i90m4 42bsve devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted cbzfi2 s90wf44o ojm) by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, t 7,30ch*-uw w trodjmphe 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 tg)ouw, 8tf1b ,yvp9 npo 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 csmt.ibu)f v (3m long between fixed points with a fundamental fr.fubv() 3mtis equency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a verticayjh4j87-pcf kl 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 f7hyp-c4jj k8f ork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tu pqp)55 g z9n02t6cngremnp*t be that is open at one end and also 75 cm long. How much tension should bt96 mpngnp2 nq5rce0)*g5z tpe in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fulp 42c tsop3v6;lx2 lpcl+f8 uil 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-+*,pwh9y jo)v bouha +Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, woy9+ o+* hb)uapjhv,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. One train is stxqcmby +b61,*4xgruw ationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train awgxb qu6x, *cyr4b 1m+pproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train 0abk9 s/ihp4am8 ny i4whistle as it approaches you is 538 Hz. After it passes you, its f aa0i4n8b9/ i4 mspkhyrequency 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 (4a:yh74f 1xkxpb e ynlistening to the difference in pitch of the e:h7 xfa1y4(yk 4bx pnengine 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 a beat frequency of 11 Hz. T 2cwz.+6 y7,zl(px9;y.j5pt qt b nq kdvqio,fhe shorter one is 2.40 m long. How long f 6ky,v.,bj7qon2y+q9tx dw(c.q 5;ppzzli t is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves p; 7svu w1gxk,nast a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they havek;w vs1xg7,n u passed him, at C?

  If the velocity of b/zz0e kk:1 pfii 1wg-llood flow in the aorta 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 wavekzzk0 1f-1iwpi:/ gles travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward thej edkd, 2aiu:: bat at speed 5 m/s The bat d:ik:,e duj 2aemits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sou54rfu ghfks3,h (wq+z0zyl. hnd pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before tz,hgw( zys k.3q4 ufrh5l+ fh0he next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sen-8-1/.b iaedh elt rfgd 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 blo.efl1a e8g-h i/d-tb rwn in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for sterb83q2f-c,bj*k gue ;)dub mgd eo 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 wi,u 8q-b3dfue gbb;2gjk)c* d mde, 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 “sing;6,33yc g8qwbz cv pcling rods,” involves a long, slender aluminum roc ,y3p vgcw 63;b8lzqcd held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, 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 threib m9j*5;x.zh i)ty awshold of hearing for the human ear at a frequency of about 15bh. ty xami9)wj*z;i000 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 tuxqj-fk tqcpe , o24z:du0s3 )he ground hears the sonic boom 1.5 min after the plane passes directly overhead. What i4j)uzxpe2o u k:sqd -tq,f3 c0s the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i.wp3 . )fuprips 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