What is the evidence that sound travels as a +ax74r9 eadsn wave?

What is the evidence that so gekt txj2r4+5und is a form of energy?

Children sometimes play with a homem+yn t qwt*c23cade “telephone” by attaching a string to the bottoms of two paper* c2 wtcn+qyt3 cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect t n5q,s q ;+ou3sp+1 ;bd smg 8sqm6/fu0hzshrdhe frequency or wavelength to change? qm5+z uq b;shssmud6+sprq83,s0gdf1ho;/n

What evidence can you give that the speed of sound in air a(x3 cm6)v1php 4hwv jdoes not depend significantly on frhm vpv43 whpja(61x)cequency?

The voice of a person who has inhaled helium sounn bed+,o*.7gvy50hl ih 0yogyly3ir ,ds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ py(*4mpea 00s adk,geyipes?

Explain how a tube might be used as a filter to red tolzqx8 hcndm))+;byy: f3d2uce the amplitude of sounds in various frequency ranges. (An;nl8t)y dbmc x:q3 f2o)yz+h d example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) s4z*n 7gd:ku mjpaced closer together as you move up the f*:gmzk7j 4d uningerboard toward the bridge?

A noisy truck approaches you from kr4 pt;p5-:wckyuq 1ybehind 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 diffract: 4uyr;-pyk5p1 tk cqwion.]

Standing waves can be said to be dx-g:.b tblw kqxgq75k *er 7d/ue to “interference in space,” whereas beats can be satx r-:/q l7kgxkgwb75d. qb*eid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers )tfabf0j8dynt 9 jxz6qeo) 67 were lowered, would the points D and C (w8j6)an)t7fzefo q6 tb0xjy9 dhere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people x hm8ork u6t*6do6xd4who work in areas with very high noise levels have consisted mainly of efforts to bloctux*4h k6mod6xdro8 6k 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 could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can bep l g ijnuqu+m7s58)2d thought of as a superposition of two sound waves with slightly different frequenc jm+)i8u 5uld7gq2s npies, 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 r49 h2klu bvgammwlvx28+sj7o,)nl7 in the same direction, wisjla4lr vlw+9 2v)n,mmgx2u7k7ho8b th the same velocity? Explain.

If a wind is blowing, will this alter the frequency of tha*7* jpy,b y vaps+3kde sound heard by a person at rest with respect to the source? Is the wavelength or velocity ,yy+kda3a *7 vsbp*pjchanged?

Figure 12–32 shows various positions of a child in motion on a swing. A monitb+j3hj ju0 ch 4;xf.skor is blowing a whistle in front of the child on the ground. At which position, A through E, will+ j0ux .;fhjskj3h4cb the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length ofw tebd5 fkr *yi4n)1o( a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echtrybe1*ofnk)w 4(i 5do 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his sh oc ow52l.;y49j9k:zjp en:cylw; txx ip just below the waterline. He hears the echo of the sound reflected from the oceany w : wx9t5p cjo;y.e 4clxkjlo:2z9;n floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 3bnf3-a8 pul j$^{\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 )wixl x 5qjv o 1ydhs5;m.8g*gabove a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses beforj5l;w.y )5mdv8i1*xqhgx sgoe 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 splasy.y bx 6i*,bcjm bnlt2izt ;;o3c-v7gh it makes when striking the water belv;yz,c;bo-t6.3b7bic lym tn2*x ij g ow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground,al,r g v1w/0xd 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 othea, lvg1drx/0wr 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 distance by the “5-secondsqy,e:c nzzq+) 4uwc*1a;owq rule” for estime:yqc1zw+o )4 , qnz*usca;qwating the distance from 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 the pain levt6z k2l *9dhkfel 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 tj0d 5nvl f,o:v/p d0 y/x2eelsound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired cb2tqj5s;*bzx5j y;7yzgq;ox z ( rt3simultaneously at a certain place, what will be the sound lqjzy ;gxzt( oj5c qr b5t*;sxz3y2;7bevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a c4y/ azpg3 le7 29qe7rauryk 4iertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experienr g79yaie4eaz7 2pr/lqk 4 3yuce 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, w+pb+ce yw1uh c(p7y5lhereas for a CD player it is h7y1ey+pl(w+c5bcu p 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal ai8opn. fh b x-uy5b56conversation. Use Table 12–2. Assume the sound sfb-x yoa 8h5u.6bi5 nppreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose5-65mb rwzz tb 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 mr ewfa+)9uxenq5 b-q1odest 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 tu9qex-q )fbr1wu5 a ne+rn 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 if-z42qg+ eox dB when placed 2.8 m in front of a loudo-i xg+ef4 2qzspeaker 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 level of 2.0 dB. Whad8ix cf1v63 klt is the ratio of the amplitudes 8 3dxfik l1vc6of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, ehdkirdk u .4 z6, tipbn),h65(a) by what factor will the intensity increase? Increase by a fac,pruhhb.6e,di)6n 5 4t zikkdtor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one1i/- a5gg;vqcyi/ ywi has twice the frequency of the other. What is the ratio ofy51vggi- /ic/yw;i q a their intensities?   

  What would be the sound level (in dB) of aommn; qb uh6n88 v85mj sound wave in air that corresponds to a displacement amplitude obm8n5;u86 8n m mvjhqof vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud z453b7xro8;f eugr vxas a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.xrf78x4e ;3obr5v guz )    dB

What are the lowest and highest frequencies that an ear c 0vhj7 f6;yvtm2dk )czan detect when the sound 2v0z tjv6d;f) m h7cyklevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangvaxsepi) ekf;6 m1cxgvo *:(ux. 0;l me of sound levels. What is the ratio of highest to lowest intensitys6uge c x* m:fv0im1p)(l x;kox ae;v. 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 Hz5 :, e+as3dsi2wlkm sr- kos1h. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strs,:1slsa+id kskwor 2he m53-ing be placed?    N

  An organ pipe is 112 cm long. 8 aes3w08t zsuz sd9w;What are the fundamental and first three audible oveww388tzsesa; zd9su0 rtones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of an e0qc jqk4 bgq l*5wb*1fmpty soda bottle that is 18 cm deep, iqqb150 lb4 qg*wkf*cjf you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanningm0mvst ,*8eio the range of human hearin ,mims*t e80ovg (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 p/b(gb q5zb2v a frequency of 540 Hz as its third harmonic. What will be its fundamental fvzbb (p2gb5 /qrequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p 49rwwwj80uu4 r0e-rdwa 9 wailay E above middle C (339a0ww8 iw0 wu r-w u9rjadr44e0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (26sr+k9r: to ydqg 1:1zwe 4dbiise: c,62 Hz) when the temziw61b gsy9sk1c d o+:4,:r qie:edrtperature 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 2 cdnaj +6+/fbq0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ofe ,5k;lz d4gcu the flute in Example 12–10 should the hole be that must be uncovered to; dcg5kzelu,4 play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate al*19mqand f pgvf)+ r1t 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed aqgmvf1fnp9 * 1)d+lrpipe. ----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 enfhm m pa-2rjux9w/*7eq.zr* kds. It resonates at two successive harmonics of frequencies 275m a/wzfj . mu-79h*r p2*kxqer 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 .p f6+l-ndhym$^{\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 audi6asy/gi1l s 2ible range for a 2.14-m-long organ pipe 26ya1iss/ g ilat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lot j7i5g r a9r0ja5zz odk003zzng. It is open to the outside and 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 iz950o krg a7dirjz3ja 5z0zt0s the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust tn;- f0+,t dmp+i rvdtydh.u) fwo strings, one tyd,id - ;0u nrm+.)pf+v hftdof which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency ifvtz/5*t(yv0pu r e7f h middle 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, while anotheg pk kobyt45:zw(z7 w8r (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, estzyk 4wt 58pozwb7k(: gimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when svr gz( l/80kpsounded 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 yvp klsg8 /z(0rour reasoning.    Hz

  Two violin strings are tuned to the same freque-;b 6la9m ij7,xhn,h k1ayjzu ncy, 294 Hz. The tension in one string is then decreased by 2.0%. Wk juajl-9z,ib1xa h,h76;ny mhat will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eacz1(r,n3gcfa3 4i; q ytcygo8q h try to play middle C (262 Hz), but one is ytc34g, q1qc3;(r8gozna if yat 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 odn1u8 uv.-ddi/w8byu .c8v ec4di+ e a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frbncu.81viee-o d +8cwdd4v/ui8d yu.equency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stw.36q wt dz72rky 51wagwc 1szands 3.00 m from one speaker and 3wckyz 3r1qd 1zw 7a w6s2gwt5..50 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 vibrating at 132 Hz,0,0iq(yd 9gx uwnuk d+ but a piano tuner hears threeiy00xndu dku q(g, +9w beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m an pr)z-hg+ ain2d 2.76 m in air. How many beats per second will be heard? (Assume -2rgi+)np hz aT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cedbokanghim ;9(;3ozfel - )l4rtain fire engine’s siren is 1550 Hz when at res4i9l (e;- onmzdb a )f3ho;glkt. What frequency 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 you detect if a fire engi any8(-d- q: v1ch2buwpw6 qvrne whose siren emit- :(ndcawwbvurq 8 12q6yv-hps at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if axl): 5jioim )x qs2laeg/ h. s80 nf*+ujckjv9 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 samevkqlxssueh )a 5c8fm+j*o) :i . 02n i9jxlj/g? 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 samenq0 ,:h r-2m*8x rlijx8wpq wr 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 j pxnlm:r0-q 8q2*w,wx8ri rhbeat 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 an qt6ls)5h / (s*xgvnxid receives them returned from an object moving dv6(5*gx )nshliqxs t/ irectly 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/3fkj+cez8w zjp5 k6oa u z(z9 3t+as8ts As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequu +8 w5t9ejoz8ta6 (kczf+3p kjza3szency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expe 3y e-zcxud m(sw1nq g2+x,3urriments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a u 1y,sr +-(e xunw3zcd3xg2mqspeed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mm;q s2(u nfq2i7,wpf; z xch3peasure blood-flow speeds. Suppose (u3q2sphmzpif ;n;wq2 cf, 7x 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/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves nv1dz fh, 3kh/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 emo*boqx.f 5 wbzs l qeq/k6k0a632c*ikits sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obsebfe bqzq2. oi3kq5lkca 6/ x6os*0w *krvers 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: yaqxrs 9;:ueezg; ; gbk+b6k 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 wher ko+vrqk i,e ,h-izx11x fkrxi; 4d/j;3x3isne the speed of sound is 310 m/s (a) What is the angle the shocv;x +;iorki13qij,kz/1rxehk f, x4x n3-id sk wave 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 atmosphere of a planet jup*p 8,6q kq dab7vt(wygqa,*8)ijz where the speed of sound is only about q ka,6ajwgdj*)qtuiy q,b7 pp*v88( z35 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 ocesut; 2 4go/d;d0rf aoaan. Determine the shock wave angle it producesu2 do; df4 astro/;g0a
(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 b8 (pu;ghv vl3$/theta$ 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 td q2y89s f0f.xyin;l khe ground flying faster than the speed of sound. By9xly8dfi fskn;y 2 0.q 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 soun pf-+ 7orcu9l(.gy bnar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maxin+u.rbg-fc7 (9 ly oupmum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are theret )3kvv .l)zkpgg/)mb3kx 7zo 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 ok zjmgk10)9l nw-2dbf f many plastic pipes of variom-2kwbdk1)j lg 09 nzfus lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound clos pjp25u b21yyze to the threshold of human hearing (0 dB). What will be the sound level of 1000 sucpz5 p1uyy22jbh mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an +vmoia l,t+,yd p5 x 57trw0hd87-dB sound are heard siriwdth d5tmx0oy , ++av5,l7 pmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opxs8+,pwdmaz 8en, is 105 dB. What isw,8xd8 z+pmas the acoustic power 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 ffwl /skr: ,bl-dmk u.hi* *;ioutput drops by 10 dB at 15 kHz. What is th*d :-ihls ukb; ,fm*wf .rlik/e power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their sgzt9tb 4)cl:ay q0/ad a3ct. ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, a gtab ct czlad4s9/ty0q.:3)is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, h5u,x0vo es+p 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 ajtl 2b2 j2gt9m 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 violild0; hydm.1nh n is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass h.hn l1;d0 dymper 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 yj;s0mp nd5m8a, . g x:jaz*jia vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tunin j*jyz ;m8gm ajanp:xis0,5.dg 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 a tuc 3gro.wshq,iz9 +mt /be 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 fu3s/zi m ,r+.gowth q9cndamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass w u6 4obpqmj,f9as observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1 i-2a*a mjhv4r000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the pers 4arh*v2ai j-mon 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-Hlvhtmdqo,+c o/) 3* ifz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What iso t3om *i, fcqv+hl/d) the speed of the moving train?   m/s

  The frequency of a steam train whistle as ivvc/*gl*m 1)fva*fm rt approaches you is 538 Hz. After it passes you, its frequm1f)vgc* a r*/l*vmvf ency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you /:vc8lrn(dfa8ds6h pp 3n.smcan estimate the speed of cars just by listening 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 (.afc l3n8/ m8:6vp shdrdpnsby on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of v clay,ljfjt)/;2n+ a 11 Hz. The shorac2,fyl/; + jv tlajn)ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of .ltkh5a ian6+8xi-9 xg+b zlva railroad car as 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 betwa +xbgt aikhx.l96 i5lv- +zn8een the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood f3 u.f 21r6emhiil 5qxhdua0a28gm(sklow 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 th 05fusx .g2 m hea a18(2u6lqrdm3kiihe 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 while the hnd7xujy7izv(ls5 * 2moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the freque d(hzvjnl7*7 yx2 u5isncy 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 app9mt fds(4g 6cdz miw:0roaches 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 re69 f:mi(w04d tgsdcm zturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was omgs lg 0/f5h5knce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sfhl0/sg5gm k5 harp (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 stereo listening can be compromised by the presed ws6sc(s3.mi):j0l:xr xhplakis . +nce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamentala x3xc .r.mhdil0s6i(:ss:)sj wk+ lp frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slenderh552zj. q i rgg747ole z6+gxcgot c.a aluminum rod held in tzoah z7tg7+cq 6g5 .c.lro2xg5 jg4iehe 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 threshold of hearing forn8 q2;yn9st cm the human ear at a frequency of about 1000 Hz t my nn8c92sq;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*hsq 6wd-8:h 2ayjynf g)aehwnl+ e)3. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly ovn a) 3nlh a62ewyg *8+h-fe):hjwydsqerhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbl5 3.8gzafmi0em we i,oat is 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