What is the evidence that so2cnw0 4as xpk7und travels as a wave?

What is the evidence that sound is a formegqgk. rz 7bx8(t6f+qt e z4d5 of energy?

Children sometimes play with a homemade “telephone” zz9sn9tw s,z(+ b6u2 pjb2 93wooujnvby attaching a string to the oj99w2v b3jp+ 2tz9nb wosu(z,nu zs6 bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other 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 yo9d*fxtlmd*0 n u expect the frequency or wavelength to chan0lf9ddt **xn mge?

What evidence can you give that the speed of sound in air does not depeb4ir4apm / )iund significanti/i4)pa br4mu ly on frequency?

The voice of a persorjx,8vj 1 qf-c(3tcn un who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgru:gxo/4v/bn nm9o ui c4/a w8an pipes?

Explain how a tube might be7 j8e9l)7 xwbi gjvzmr4+ja9b used as a filter to reduce the amplitude of sounds in various frequency ranvbj899lz 7rib7+x m e j4aw)jgges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together bi:/93mu gp olas you move up the fingerboard to9 /lg: 3opibumward the bridge?

A noisy truck approaches you from behinilo 7wkux:-hbub81uz+ 4o7 ed d a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction ol iwbx7bu-7heu+ 8:udk41oz.]

Standing waves can be said to be due to “interference in s 9rz6;*o gwlxm 2fv1zspace,” whereas beats can be said to be due to “interfer1*f2 zwgvx;l 6 oz9srmence in time.” Explain.

In Fig. 12–16, if the frequency of .ohx(asd iea39nvq(d* ct 8v0 the speakers were lowered, would the points D and C (w d.3 eoc8 (qa9thd(nsvv *0iaxhere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of prote73meaun*+ vd. ee2d15 qpr kyx3qm;mecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduc3uq7xrded m anv e 5y1q*pe2k+m.;3mee 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 could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sulgbn, fy 4s-,)2q 0m/oecab wqperposition of two soun/yq) o-bawcf 02,,l4bmq egsnd waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directionxw+w4z dc uoy,0r34 zp, with w3ro4zyu+d x zw4 p,0cthe same velocity? Explain.

If a wind is blowing, wvvq-ikxd98;e 6 w tk(gill this alter the frequency of the sound heard by a person at k gtq ievkvxd;9w- 6(8rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chil2)vo pb: hc93sc fv;g yl0xf*xd in motion on a swing. A monitor is blowing a whistle in front of the child on the groundlbho fc y)s0:xvf*2vx93 c;pg . 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 ec5p s,vs n6fli; :o9r81vfwnis ho of her shout reflected by a cliff at the far end of the lake. Shw,56r f:s so 9ps;v8lnii1fnve hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hph 6l t.h edhw7;:q5p1deq2xjis ship just 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 (Table 12–1) and does not vary significantl pw1qqed 65xhhe2;j.7l d:tph y with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 203 li1xk/u06g) lmu8jpljg (ua $^{\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 kg (eu0d uhx3i8 6cnx-x e8sx5of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by 8sd5u k c-8hi 6xx0(x3ge eunxthe fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it ma+js.t4rvyxo8pnr* rpz9ch07gi t. 2 k kes when striking the water below is .j4kg2*znr+8t0 7v o pip9srrht.yxcheard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the h n9b:n,b; :82b 5vhjlpppu wgground, 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 are 1.1 s apart. How far away did the impact oc ppwbulnj pv 8:b nb59hg;,2h:cur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dmb( dy(t5 1-;+hjsue oamk 4snwsq+f3istance by the “5-second rule” for estimating the distance (qs+5wb+y-h(4e mfj13 d ass;tmk uo nfrom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sounubq.g6o0z q4;g; jn lyd at 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 whosevi--w8nog; q- 80opmvsb p7vj intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired aq/9m9-t2uz ,8jwam eb5 frstsimultaneously at a certain place, what will be the sound level if only one is explod2js/b5 9,tr 9awumeqt8fza m -ed? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpoj:,x.4cqdo ilane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if tcx.,q : 4jdoiohe captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said qn jl/53pzj5z to have a signal-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 backgroun5zzjq3l nj p/5d noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from ese jo; fjdz(zj/6ghx**6 a:ta person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly a(g;s6 *ojtdj fhzjz6:*e e/xuniformly 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 aregyp:p *du.il 2itk,w 3a 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 t4ogul 5 ci6m4nhe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn tiu 4o ml456cgno 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 74 -3dvdberwd m in front of a lo73-e drw4dbvdudspeaker 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 detect a difference in sound levblu+v.; 3de wkd eh(ggs2w,cxc* b/ -qel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by/gqcbehk 3x 2blu-ews g,d (w;vdc*+. this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave isyoq q esbz;;67 af5hf7)8 txed tripled, (a) by what factor will the intensity increase? Increase by a factor6 fqq;58obf 7yshzd7; xe)tea of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice7. sj8cvtbl p; the frequency of the other. What is the ratio o7c sl ;p8.tjbvf their intensities?   

  What would be the sound level (in dB) of a sca (osrq0-ux 9qes4x )ound wave in air that corresponds to a displacement amplitude ofs que4xro0xa9- (c )sq vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whag cih0r*rf;55 o dpn9bt sound level to seem as loud as a 100-Hz tone that has a 50dc09p5o* 5ig;rnfh r b-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detec 6fug7)9jw m-b z;n*zcp,mdkmt when the sound leve zmd,p-u6m zg n)mk;cwb9*f7j l is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommoqty2ow1.qq klr4 4g/p date a huge range of sound levels. What is the ratio of highest to lowest inteo /tpk. r 42qlqg1wq4ynsity 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 fundamental frequency of 440 Hz. The length of j u2g 28)6 qou7isjjlkthe vibrating portion is 32 cm, and it has a mass of 0.35 g. Under 8guqj k 67i2u jl2os)jwhat tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible hk o6w6c5fout4ey2+uhm j9u) overtones if the pipe is 6j hwu6 +hoou5futmk e94c)2 y
(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+-fzpl 0 k6( jveohi-z across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tuveh+6p-ikzz- jlf0 (obe?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pip o9ky8pcqj)*t -g/u u:bffax+e organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the u+ojb- )qff :k u8/a 9*tcgpyxlengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz ashwhzjmj c(.lrj1 )1r4*.pd-g jzv)q t its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of itstqrc.p j-r w zvm(1h.)gj*jldj z4h) 1 original length?   Hz

  An unfingered guitar string is 0.73 m rlm ;/7/ jqezif+mx, tlivn4 -long and is tuned to play E above middle C (330 4mqj,v zn;t/mex -r lii/7+lfHz).
(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 middle C 2s.(wv p*ct kpqv3e9 p(262 Hz) when the s2 qtcwp9vv(pk *. e3ptemperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 l6bua xq*9 .of$^{\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 hole .os)ax6ql m j+be that must be uncovered to play D above middle C at 294 jqs.o6 xml)a+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 p23, je /ajy0mkljc9zdipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other f m3jjkjdy/,ae9z0c l 2requencies 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.fstq/ 2zg8: 2j8xaukd It resonates at two successive harmonics of frequencies 275 Hz and 330 xfas2d/j 2qz :tu8g8kHz. 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 rt1 7grgbd/6 l$^{\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 auy4lx8)w: 8w6ula1;zxvb temo dible range for a 2.14-m-long organ pipe at owxawxv ;z e)ly:681t4ub8 lm 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:3 xrgv+b( 5 4koaezrr the outside and is closed at the other end byv 45rzrg3+ xer:kaob( 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 graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears e jn8vx 2sp49fk cub*i,3 ,krdone beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequekj rbc xe*,4,s2vu nfk8dpi 93ncy is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz0rkcrnbd; f g4urv0 h)7oqg y163u6r h7/pwgf) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operateieg rn)ic4 wff,7g/e 0s 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, estiwe4 ic n,f0gg e)fr/7imate the operating frequency of brand X.    kHz

  A guitar string produces 4 b9,w 22k sai;znmxrdm8 eats/s when 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? Explain,n2ixmarzd m8kw;9s 2 your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The teofnx-,h *vzclhu)t 09 wp1,a m)mf.oansion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two str,t c9a0hpl*m xo)h -mv.waf,uz1n f)oings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will 3 .cvd,x.xa pxbe heard if two identical flutes each try to play middle C (262 Hz.x,a vdxc. 3xp), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequenx*nbbuyj z-a 0 zf8z3.cy 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 possixz-ba. 3fzuby8zj0 n*ble when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m frod.z/a x1 zcev)m one speaker and 3. zz.ev )dx1c/a50 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 supq,cqjw5zj/ja+k7)l4 hz twio d64un3 . qg8qsposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibzau8q+ j6cqzq5 7ws). o i,nqg4j3 tj/4dklwhrating 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 wavelengths 2.64 m ap;p*6 2utlvgw4,g0p kslwqw) nd 2.76 m in air. How many beats per second will be heard? (0l w*4wpp slt)kw qpg,6g2u;vAssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ofd2g: a*m; edqwkdzc0ksf 86r97;q zes a certain fire engine’s siren is 1550 Hz when at rest. What freque* wg6cz02msd9s 7; ed:az8qqk;df rek ncy do you detect 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 y jxcdv/x lld bj8*1q65ou detect if a fire engine whose siren emits at 1550 Hz moves at85lvd1jb xl j*cqd/ 6x a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency ifkv,o4 1w7p; ped*zqjo a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are the4jppek;*q 1 v,od7ozw y 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. When one is f59(s s eg)ojlat 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. Whaslgf(oe j)5s 9t 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*c99 wpn)cqmn m6 mok,0ujzoj d7l ,;a receives them returned from an objn6pu m7l,d ;)zo qjc0ommnj,kc9wa*9 ect moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fl) a+5/ikghb wvvt55c fies, the bat emits an ultrasonic sound wave with chi va/t+gb5fkw 55)vfrequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was ) eudu t*t8b 9m(x;rqtplayed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s )q buttte*u9rx ;(d8m?   Hz

  A Doppler flow meter uses ultrasounj3po) /efri6- t;:kaexxwq0hd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/re6/qfko3);h0xj:wtx e -a i ps directly away from the sound source?   Hz

  The Doppler effect using ul noe/.mm vnr.:trasonic 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 veloc+sawyj 1dsf; 9ity is 12 m/s from the north, what frequency will observers hear who are locaw;ay9 f+ssj1 dted, 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 lapn,v..nji/ew nd 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 sound is 310 yl7cga-+,gmc-7v c4 lfe ist9mf61jzm/s (a) What is the angle the shock wavei7l yt9g+z1l6fmceg- sf jm 7,c4va-c makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosoq;jlf/eyhne5 (u;k7 phere of a planet where the speed of sound is only about/7e5(ylek foq ;nju; h 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 t j: ,uns7blsf5he shock wave angle it prod sjfs75nlub,: 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 k5 9o-o4jha /9gq hmnnny(8 go3zb0ov $/theta$ 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 groun )khd2lh y6c4ld flying faster than the speed of sound. By t kl62ch)l4dh yhe 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 sen ul (wz-j/g0aj0(aeau ds 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 wau0la-j(gzau0j/e ( m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many o zf7br9lf js9yq )6ka+ctaves 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 consistsi fh, *5lercc6vuco:( of many pu5,o: ecifl c6hr( *vclastic pipes 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 makes wkkw: +,pp.hb;g9f x i1ecn .ta sound close to the threshold of human hefg xh:cwe,wn9;b.+ikt 1pp. karing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant/ gss 8-bvn8orj 0it4m sound level when an 82-dB sound and an 87-dB sound are heard siv8s jtbgn/smo48 ri 0-multaneously?    dB

  The sound level 12.0 m from a loudspeaki6kbyt.r jb:0*dex lejswn, u*9h4.g er, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, ass0euixbwrlkg..dybnt 6jh*j,4*e s 9:uming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ouw;muxfoi ev*;wp)x2c76 6hwh em3r/htput drops by 10 dB at 15 kHz. What is the2hcheup6);v/fi em*36woh xw7x ;mw r power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over tw6kt f.kpb)1 iu2h au;heir 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 radf)i.t6k;2h a wpuukb1ius 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 communicatio0ygkp5 4/dg d +zhj5fmns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a f:q+* gltrb vp.ggab y1)7:nyprequency 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 with a fqn-x: td/3evjtmu4 u0undamental frequency of 440 Hz and a mass per unit uxqt-d3/veu mn4t j:0length 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 vertical open y* l p0auy-s77s l:efstube 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 s-lys7:pua lye *f s70resonate 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 n.-,y76sdww zkh ;cj saq7yo i-ear a tube that is open at one end and also 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 tdyca7oijw.k6w7;-yhq ,s z -s he tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r)pt -4p4h hycdesonate 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 m+ph xlb; rb7+in the 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 hb; m lbxp++r7is, 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 stas utkki ;/,- dzw /7vms4wl-kltionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?/dt; m,sks / vwi--lzl7k kw4u   m/s

  The frequency of a steam train whistl 6ujj5pq+zp)cd0z3 l je as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant v6q30pj5pudl+jzzc) j elocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to h nge/ e)skc)hs/6g,)jnj;ey 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. How fast is it going;ysh )kejnges) )/g,je6nh/ c?    m/s

  Two open organ pipes, sounding toh + 3vfub(sw y,nk6e*cgether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?(scuf6hb3kvy+*,wen    m

Two loudspeakers are at opposite ends of a railroad car as it mo 5jemqn4q-ax t*swf-oad8 *0vuzeh*zyu9 ,(t ves 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 z*8 e05,-n (-*tfa94d vzqhj*a ymseoq wuuxtthe 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 blpu rgp(6doi .mmr(y 8/1 al7qrood 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 8pao y(q ui6r m(p.d7gr1/mlr the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at spji+oyt 49.49pkxox mreed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frxo 99xjk+4.ymi tr4 opequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches d55yr*x nceea y9s/(lbz(vz,se9i 3 za moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 maz5(en/x sze sc9d3i* ery5zb l (9vy,s 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 Al3w2-t (-b-utplfisa ppine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequencyptw 2tlf( p--3us-iba of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pres+rgt2wfih) o 6d lv cg4 5+nr+6:tis9gof.bmr ence of standing waves, which can cidtrv+m5ho6 :rs.+o )9 gn6rf+f2gtwi4c g lbause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singin bw*v7pqkf+ s(r 5er xe9iuu/;g rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, 5r iwbqxe/; 9*rp7sueu+(vfk 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 threshold of hearing fofhz-;p;2 +3g wmgdekr kp s;; a-5kxevr the human ear at a frequency of about 1000 Hz fsg; e+p-;r kx-zk53vpe;ha mg;wkd2is $I_0$ = $1 \times10^{12 } W / m^2$ 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 hears thmfoi6 b 8-9wfse sonic boom 1.5 min after the plane passessf m-wb8o6f9i directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is wpr)vzy-l-3j 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