What is the evidence that sound travels as b;ibk 0j8m3;v;x nmmt a wave?

What is the evidence that s onsywfj7 5m9;ound is a form of energy?

Children sometimes play with a homemade “telephone” by attachif8i5cvqsv ;y6 ng a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, thesy8 6v5vfi ;cq 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 waterx/+v(tmoqwm (kdh 3t 6, do you expect the frequency or wavelength to change?kow+6thvx m(td/m 3( q

What evidence can you give that the speed o*sw 80jemky-eep3- tr f sound in air does not depend significantly on frequency-spr -3yee0j*t wemk8?

The voice of a person who has inhaled hecqwg9ri,fo ( ;8ng1g)fsg f( nlium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pippt,z kf q4 do+urhxwu66f3v)/es?

Explain how a tube might be used as a filter to reduce the amd ++c5q3ybny fz56f4/zz jfj(kwd *srplitude of sounds in various frequency ranges. (zn/yzfjsq5y d+d kzr4j wc3 (f+fb5*6An example is a car muffler.)

Why are the frets onihtukgd-wm+3x2* *e iujhs1, a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridts1kuh 3j uwdim,*2ge-xi* h+ge?

A noisy truck approaches you from behind a building. qkt5zkx1dx/ ;jv 0pu) Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brigh pd)1kt;kv/ zjq5 x0uxter” — 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 iylmlc97u 39 7 :h8rxs(pivj hgn space,” whereas beats can be said to be due to “interference ml v:hp97cs 8ry ju(gi 79hl3xin time.” Explain.

In Fig. 12–16, if the frequency of the speakers wuy; + s*s9ofmyaj 7sn;iltay:aop;z1yc6.: lere lowered, would the points D and C (where destructive and constructiy6;usll: .:st;;n oay7jm 9co ifa zsy1*y +pave interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who worky:eb9 z;73ain(s/jr*;med fdqy3 sv l 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 zm 3le/; yei;n ajys*v:dr(d9f3 qs7bcould adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thou )ij:xw 5gpl 7g4fgzet425bv mght 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 frequjpvgfg2lt7 )i45wxg:4z emb 5 encies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sr .h7k9 k3oaraame direction, with a.3 79aor krhkthe same velocity? Explain.

If a wind is blowing, will this alter the frequen6jt ;;c2ks ulkcy of the sound heard by a person at rest witk6 2 lsjcku;;th respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions.cnk f )4vgmnf y0fr*0 of a child in motion on a swing. 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 frequency for the sound of the whistle? Exp0 .)40k*gffnrncymvflain your reasoning.

  A hiker determines the length of a lake by listening for the echo*wa8q6gc0l k;bg l;ki( zoju1 of her shout reflected by a cliff at the far end of the lake. Shel1;q86lgg ;zko kj*au b(cw0 i 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 below the waterline ixo n5/8.xpqopu 8u h(m/tq2w. 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 p oxi /85t.mnq2u(q/ouh p 8pxwoint? 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 wavel8 2ko ,wq6byz, /zvvi6xut1vjengths 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 schoolk1s1, cn u8zlx e4xu;g of tuna on a foggy day. Without warning, an engine backfire occurs on su1,xc1xk; gzeu8n4 l 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 from79z* txz is2ib6bwf6tb5 bco. the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How higi z5zs6.owcb2ttx7 *69bibf bh is the cliff?    m

  A person, with his ear to the ground, sees a huge st:v t+(/lmaev;:uw x c,8 esiufone strike the concrete pavement. A moment later two sounds are heard from the impacix t8ml;:(efac:u v/,+evsuw t: 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 mile of dist/ ib 1l0 2-3qgyfepn,yrw c5syance by the “5-second rule” for estimating the distance from a lightning strike if the temie30 ,wn/1-ygpycyr 52slb q fperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atp)*3 h tz92zw ubowts9 the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose in+ 5seg.pq h3h gp:kh+itensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of bd9g r3y:+ pt4pln *3sde a3fg95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not spl9+g e*r 3d33agfpyndt4 b:dB’s.]    dB

  A person standing a certain distance from an airplane wit8) wn5yp9 c1 rw-tdkdkh four equally noisy jet engines is experiencing a sound level bordering on pain rc ykwtk85n9pwd)1d- , 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, whe4 p7tzxd b5+ xukg py-saw7g+jww 6:f5reas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devi5w k 4p: 6xx+yd7s-+w gwtfa bp5ugj7zce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output ofa9zx7* h-(h u u lu7(znzm obwd57qw5x sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rou5*h 7 (ubzz(dw57xa xz-l9hqnmuow 7ughly 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 eardrum whose ar4.wsj,dt1hkdb / pl m 4,c mk)*y*-wc8zlnjvqea 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 mel7f,h1l a)f yodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeakl l,hf7)afe1yer 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 plwz77z k+0d .ulznd;qjv5 x r5laced 2.8 m in front of a loudspeaker on the stage. l5duqk0v;d7 5l rj.wzx7n+ zz
(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 typical ,f,cev2;f6 (d iey0jjn, adjlly detect a difference in sound level of 2.0 dB. What is the ratio ofdj,j;2yndej a f ( e,vl06,icf the amplitudes 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 factoes+;qst: -k wur will the intensity increasests +w e;uk:q-? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hc* 1* ww5jrhrki vibjk**-j v3as twice the frequency of the other. What is the ratio of their int jiw*h*vkwr i-j3j 5c* vrk*1bensities?   

  What would be the sound level (in dB) of a soundx* zzv3xv3 k6o6 zqof4 d53dqo wave in air that corresponds to a displacement amplitude of vibrating air molecules 3qdz v4ko ox*5f6qoxd3v63z zof 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone)tzde 7d/cl7nll f4 )si.v+xw that has a 50-dB sound level? (See Fig. 12–6.) 4l )+.7/dcsi)dv7e wztxnlfl    dB

What are the lowest and highest frequencies that an ear can detect wh0pmuy,9* 9oofl.i9f gmbd 0av9 d l4tzen the sound level is 30 dB? bi9pa4d l9 tg0vz .9 m*ym0fofd9,uol(See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels.na3e( idhw pv4fla9 .7 What is the ratio of highest to lowest intensity aphnv7 ewa4d 3.lif a(9t
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin ky 2yimagn6xi 3o f5,3has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a m3yk,mi5a3gy2i of6 xn ass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three aukc)frk; 9ak 6ldible overc9;6)akkflr ktones 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 exp:vxgw2kt94 lor6o0w cect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wag69 w wl:2x0roctok4v s 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 or,y c.z3d bj 2xaa6(ryggan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would bay3cb xr(d6ga ,y. 2zje 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 54) uuuw eb68x1qi- ,,gpuzryi0 0 Hz as its third harmonic. What will be its fundamental frequency if it yqxue)i r 6bi80 , ugu1uwz,-pis fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is.0h-lq d(ontgj.cfh( 0.73 m long and is tuned to play E above middle C (3 0cg-((loq .hh jt.fnd30 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 o crg/ tabsmbn 0)e,+hmfs14,zf an open organ pipe that emits middle C (262 Hz) when the n,c/4m bz t1msrgba+h)ef,0s temperature 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 atcrcths 87 ;jhd2 hex9+ 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutec/l /m t6 e kx.oeg9r,nr:haw) in Example 12–10 should the hole be that must be uncovered to play D ab ,ceklogmwr r.th6:ea9x )//nove 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 Hz, and 616 Hz, butgg(z- s9xt. eg8ag*t8v2qec z not at any other frequencies in between. (a) Show why this is an open or a closedz9. -et gae8(8cgggzxq*s v 2t pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates aixn7s0 );d1asvn cx3c15govgsb+ q uk1y3i i1t two succes73c1xd50bg+) vs3sk1qyoun1;xi s 1inga icvsive 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 8z/g6x u1i7qay r wndgp;ew/1$^{\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 witlnsyp--hc31.lffa j1 hin the audible range for a 2.14-m-long organ pipe at 21-f31hljya.-pc f nls0 $^{\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 outside7nz8v,ob4c hru2d1b e and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the stan,vb ez287n rhc ou41dbding 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 beavq +.,iw, c.-zza.gf;;hy0p e nopzwlt every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. Ho-. gz.wvzyna clq,hopf+e,;.w z0;piw far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 a e+xgn 83ob n*ls)w1lHz) 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 kHzjg18b pl1ut3jjd+r hytqy4hz w:u5 4a 0d8yc- , while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estg3y+ jqaptd 8:u1y 1wrh 0u8 4bjdt-4hjyc5lzimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s wc -;. yr 3)gfb7fqiqvdhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Expl qvi ffg3b-7qrd y.)c;ain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Thnhh5ew k7v:5op9py,z- d p4mye tension in one string is then decreased by 2.0%. What will be the beat fre wd z9vpo, yph4-:p 5ke7nmh5yquency 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 play middlelv 2+tcx,7,rh,ec fikwf- -c6riqd t; C (262 Hz), but one is at 5.0°C and the other afhcew;,v- 2q kl,-xcr dri+6fctit7 ,t 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a vo18 +zsk 1 c.+cvsvntfrequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when c1v vno.ss8 tz1c+vk+ A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker ac n, n9e;l zc0n+u m5p(ilhm8pnd 3.50 m fr mml(9nuei +c,h;p5pl nczn08om the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner e90v dbnxsh** hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mustxh 9 *dev0b*sn be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats pemr:g7 +n vb*gg8pxxbpr/: r8 kr second will be heard? (Assum:/ :nb x8rggkv*bprr p+xmg87e T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s pnz6c. h(: rdesiren is 1550 Hz when at rest. What frequency do you detern p(d h.c:ez6ct 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 detect i(p0k((f xbq b/r vts jcv/-d1zf a fire engine whose siren emits at 1550 Hz movvdc (0xb-1t(q kbsjp ( /z/rfves 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 source is moving toward .ncr /ktwn)l:; t a6kz)mz au6you at 15 m/s versus you moving toward it at 15 m/s Are ktwzann6: u.zlak t)6mr);c/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 frequency horn. j21fre2zfc (3 0 frrlfWhen one is at rest and the fer2 jz (3 20fflrrfc1other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rece;jmumw *4hdu7+ l 3ce0e qoejr.(z2tbives them returned from an object moving directly away from it at 25 m/s 0.*mzoc23wb du7 huelj r;q4+jt m (eeWhat is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 iz x3wa25 .h8 bqz/ojmowt4x. m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0ito 5ha4z/q w ..j3mxz2bx8wo kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mo 7)wpp7 y cobqq/,;eymving flat trai 7 y7m)ywqpeco;pbq/,n 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 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-nb 4/e/ 3guxusflow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sounu3xb uen/gs/4d 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(i0 q4 1/pvvvwrpo9 oy ultrasonic 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 frequencyns4 /w;wdn9x/t5k hz j 570 Hz. When the wind velocity is 12 m/s from the north, 9/ n;kxj wwntzs4d/ h5what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving77vswhbu *0h b on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sounk52lyuif-v54f q iry(d is 310 m/s (a) What is the angle the shock wave makes with t-r(2if yy5kiu4v qf5lhe 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 atmospii:*+er.. s2 srmdk * tbtra)bhere of a planet where the speed of sound is only aboutskr+bti2rmdi *.*es)ab r. :t 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 kf3np usk,2fch/2 o7 jangle it hsuof7cfj3/kk 2 p,n2produces
(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 .x3-pbzi0o zw/gx f .o$/theta$ 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 lr2c /-ya1oxlsh,w x5 ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane hassyhow-r2 ,1c/lxxl 5 a 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 v ocwp+x7;yzn y6,l(x 20,000-Hz sound pulses 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 pullo7 ywx,zvpy+n(c ;6xses (in fresh water)?    s

  Approximately how many octaves are there in the human q0i --bnakld o9xr 0jf,j xu8xm9ezzc xt2952 audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewo +o ;sr(eyo4wer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bows( eo4;yr oo+th 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 closedblv- 5)oy4nh to the threshold of human hearing (0 dB). )n 4b5hy-od lvWhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound o d-dl)pkmztt;1c 6aio; 83br are heard simultaneously 8io6tdb3k ;lo -;m cr1)zdatp?    dB

  The sound level 12.0 m from a loudspeaker, *m laj*d:q)kd placed in the open, is 105 dB. What is the acoustic pl *dkj* m):dqaower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpc/3zf0y7v9zk ko 2za q48mqxout drops by 10 dB at 15 kHz. What is the poxcyaqm0z4q 2 /z3oz8ofvk 9k 7wer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear pr(4nmnal; jq lep+;ol,otective 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 intercep4qm ,nl(nol;ljp ;e+ated by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the f2oa7.z5 8(x eutupojgain, $\beta$ 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 frequencyh2 g5aulu5 /ld v;:ept 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 z+4 i,p1t,zp j7*vikd*m aqfgtween fixed points with a fundamental frequency of 440 Hz and di*zpig,mzjp a4q ,7k +f t*1va 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 abon7,pi) jmkf;hi6grw0ve a vertical open tube filled with water (Fig. 1jni,imfh;r 0g 7wk 6p)2–35). 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 of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near h 1cl:+oo q;k ;o1erola tube that is open at one end and alsooorlechl o ; 11oqk;+: 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed +ezi vv 3kjgm lmb;:((y,x,vhto 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 two sourl rau*hi;uxm*ntlxe7p4 k+0o5gj r..ces. The sound is loudest at points equidistant from the two sources. To determine exactly what t tgp.in+* ka hel o4umlx57u0;j* xrr.he frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hu-o mj+1xgy5x3zja *gz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is tgoa1m+ xjg-y* j35z uxhe speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. A )iclva+9+ f1,vgh tcnjvbl(j0db/* kfter it passes you, its frequency is measured asvn*l91vvg(0b lkc bjci, +d+f )a/thj 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 listeni;f z)yran)ry n;ifnl ix )bc,t.j7-q3ng to 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 goes by on the straightaway. Ho.37cy) ;f,)biaril yjtnnxr; )zqn-fw fast is it going?    m/s

  Two open organ pipes, soundieec+ lc: /e.kf5igr+c, ut xf/. w3cahng together, produce a beat frequency of 11 Hz. The s f 5/e +lh3cwiuck/cg,.fr.x:ea+ ctehorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as yquxt q/u*zf:s.pk 23 it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (y . u:3/szft qxqku2*pc) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s w+dnv1cnvs61 5)bc nsrhat beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume t5nnnvr )+ 1b16vss cdchat 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 m/s whill d7nl b:m7gg:u i-vdh0al*- ke the moth is flying toward the bat at speed 5 m/s The bat emits a soum:*7l--ikdl70lb v a dngh u:gnd 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 hig+s3.s)cv c e3h2dgfsoh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and eac.3gc3osse+dhsc2 v f)h 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) was once used to send signals from one Alpine vil) u*pz;rmw yb(2xwt0dlage 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 alpenho*btx;ywp(wu )m0rzd2rn 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 sq 8fp3dtc5dn+j9wv;1qg o q7ltereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots t fqjg;3dpvq98+qw7l 5ncd1o” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involma 27:hd2 q)+rw6vql g*fb oeives a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-longebg+h 6 q)al7*v iwfdm22:orq 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 thresh:yh y;(+qjl n b)ntg5fold of hearing for the human ear at a frequency of about 1000 Hz);lbyq :hgt5jn yn (f+ 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 ground heax quo 4( e;,wgayvr)+ers the sonic boom 1.5 min after the plane passes directly overhead. What is;erya4u we)+ovg(, qx the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1jpytc*r*i3 o a5pao 535 $^{\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