What is the evidence that sound travels as xf1fl ro9:z1oa wave?

What is the evidence t:k-zsdy,;b)wqm jn )c4n os 1vhat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string45ha e ez:g9.zhv p4wp to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the ph:gw 94 va4eh.zezp5other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes6) i4z;o3)j na b5srvk9wxnb r from air into water, do you expect the frequency or wavelength to cha))vkib;64rwnj3 z n b9 r5oaxsnge?

What evidence can you give that the-*fihlm z u,b1rd;t+;nlwguq22mhu 8 speed of sound in air does not depend significantly on *,m+f zt2hudmq blh;8l1;ug2 iurn- wfrequency?

The voice of a person who has inhaled heliuzz ogs:wbr4ob0o)),gcpt;yzp- k)r *m sounds very high-pitched. Why?

How will the air temperature in a room af4jmaa 3: xoym3fect the pitch of organ pipes?

Explain how a tube might be u,-ef(her/g -9cwsl bj sed as a filter to reduce the amplitude of sounds in various frequency rang -r9eelcj s(fwg- b/h,es. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced cl0aeqppcyb/* om8 adb cut68hwe8(/l1oser together as you move up the fingerboard toward p8lhc0eu/aabc8 d8yq *pwtem/ (1ob 6the bridge?

A noisy truck approaches you from behind a buiir::hk 0zach8(d 6vpz lding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you he :h0 k8czr6v( :iadzphar more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherea-e8;:f*wpj mj0bhr dks beats can be said to be due to “interference inmj0e b jfh:-;pwd r8*k time.” Explain.

In Fig. 12–16, if the frequency of the speaker+n k o262vslwgl)tiv3 s were lowered, would the points D and C (whesvl 6w 2kl3)2t+vgoin re destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearitf/qxmme2:7 ;ylx0ndng of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, at:m l emxn d;qx720/fy 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 swy zs0w + )b4w8vilzo0uperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. o v8zsw04yibwz+w) 0lIn 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 t q7gn6r zkwke76c9tr*he source and observer move in the same direction, with gq* zcr ewn7 69k6k7trthe same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by mt /bcl5wn:z l0eo 01fa person at rest with respect to the source? Is the omlnl0 btz1:e wf/ c50wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion o q;b- t,gasz+9vo5zud faaah(2x -:ny n 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 hig- ;a onqh9zyb vta2u+-,:fg a (za5dxshest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake bygch+ (.v/loycdhr 8x 5 listening for the echo of her shout refrghh c8 cvlxo+/d5.y (lected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echpxe9y/r30nx m v50oj ho 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 (Thyevxxo/ 09 njr35m0 pable 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths +zk, z-sm7gnc 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 above4aw6q , e0ay na44crob a school of tuna on a foggy day. Without warning, an engine backfire occurs on another bb44roancwa, 4ea 6yq0 oat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking gk (gja0 3v f:*1dirhjthe water below is heard 3.5 s later13kgijd0f v :* (jagrh. How high is the cliff?    m

  A person, with his ear to the grou1 czo00dz z.z8 fxg+vtnd, 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 occur? See cz8z1 0 g .tzfxov+dz0Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-a.(yej0h i0ncmcy9x -7qcg5 nsecond rule” for estimaja yi.g 9h7cy5x0(nn ec cm-0qting 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 pa-mztv1qbr/f *7 :nix.m0bi ; aww5yugin 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 whgo/2e, c ucnjbevk)*0/ u(mr hose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simmwbou8fs k1yy,j2v 3-wt(:a.o pp +x iultaneously at a certain place, what will be the sound level if only one is expwto. k:p 81b u+xfyvpm(j2,w a3iy s-oloded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eqd- ) ainu9bn2xually noisy jet engines is experiencing a sound levbu-2i)n dn xa9el bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hhe13n3ak.ym -akd* ihave 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 sigh3iaea1hm*. 3y-kdk nnal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output om ccpj 5(qu+x)f sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly un qp) xc(cm+uj5iformly 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 str,hv;*pjf-tuqi 5du. sikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modeste 174:,shlnnfn5orcl 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 5 c:f4,n 7nlnslro1heconnected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in fr4d cnzu m1n69tont of a loudzn n9cmt41du6 speaker 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 typically9q* cvi w8,4k7y wyeux.bf3i v detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of ti9vq *8 .3b,ycv7ey wwfukix 4wo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triplediww-ylp.,6 00ada kys, (a) by what factor will the intensity increase? Increase by a factop sa.k,waiy w-y6 0dl0r of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaceew w+:(m(gj) egtssy(ment amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitie+w sysj)( (wg(emgt :es?   

  What would be the sound level (in dB) of a sound wave in air that corresponds t gf0 xju3)(adno a displacement amplitude of vibrating airna)f(xu 0dgj3 molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz trz tn :j2z/29u b5pqdeone that has a 50-dB92r/ ed u5:nzpbqztj 2 sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can de vw+4j h4ax8fbtect when the soundx4w jb8a+v4 fh level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge,fnjid je* mt.x3:9jwmc(/r i range of sound levels. What is the ratio of highest to lowjd:iewt9mfc x,3( rm n*i/j .jest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The len qo b ap zsw+3t0ks280vrpc7)dgth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensi)za p3 r0+vq0c t 278spboskwdon must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first tzfsw9pp2/ na3 oes: .nhree audible overtones if the pip ppo: nzw29ss.ae fn/3e 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 toh7zy+hif 9; evf.rwsi t49j 1 ctkwg9.p of an empty soda bottle that is 18 cm deep, if you assu e4sj19tgif f r 99.hh+k;czwiy.v7twmed 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 sp- xeht1jpm1x/anning the range of human hearing (20 Hz to 20 kHz), what would be the range of the l-x jt hmex11/pengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a/z6n-a ) kgutp frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length o/-ntz k6gpa) uf only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above (tm vdxbvupfb4jb6:u+n7,8q middle C (vvu 6 bm4 (7uqj:b fx8d,btpn+330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an opeh.qe6 kgwf dhqh, u19 6(al2vt ow87qin organ pipe that emits middle C (262 Hz) when the temperaturv,wh( qu87q 6 lfhhoti2w 9q.ed1kag6e 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 v6ehxnl14mq 00 $^{\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 bm04 4jl4vfjuee that must be uncovered to play D abof vujl0j4e4 4mve 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, 4ez qzy9f,;kc-+ jzgl040 Hz, and 616 Hz, but not at any other fk ;z,9g+lzc -ezjq0yfrequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at t bdsjk7 vzroft(.:o 3;wo successive harmonics of frequencieb.j;vsz7:ook(t rd3 f s 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 tc 4on ctf z:e1p8. r .)81o6psxzjlbe$^{\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 pres. +(a 8x)igjq;0zgvzpatk exi(nd(s1ent within the audible range for a 2.14-m-long organ i (1s0dg.azinz tx gxpk (( +8;)jaeqvpipe at 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.sy g2g3hqb:,10uw xzigc*lx the outside and ishyg0xqg :l gb*uz1wxs2.3ic , closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the 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 tryin/tt a/t7no u;sg to adjust two strings, one of which is sounding 440 Hz. How far off in fret s/7tu; /onatquency is the other string? ±    Hz

  What is the beat frequenc fxout,. p2os28dg s7;fe .iezy if 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 anoe . x jhdkv-c;s1f:ow2ther (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of fefdk1o xv:; cw js.h-2requency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9o vn/mihi: ;uh3e) a3r beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Ev /ah3m io:he3ui;r)nxplain your reasoning.    Hz

  Two violin strings are tuned to the same frequeni;/+7mj edg h pfdq:/ncy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 1d/pqgd;e i7jfmh+ /:n1–13.]    Hz

  How many beats will be heard if two identical flutes each try tov 9j5a ce;0i1jsam 0eab)kipazx z f gj+42l+0 play middle C (262 Hz), but one is at 5.0°C anxe0 s)00v 4g jzpkaeiz a2a51i+amcjj+ f 9l;bd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A4zd4 lwsm+x )n, B, and C. Fork B has 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 frequency is 4 Hz. What are the pos44wxls d+z mn)sible 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 stands 3.00 m b 6ih us/.+,-szdgq kgfrom one speaker and 3.50 m from the u d6+q.-i shkb/g zsg,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 supposa- t)j bs5w;h9bens0ced to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played togethewn)sh; bsat-5 09bjcer. (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 4 .qulxw:i(it eay0fxh.m((gof wavelengths 2.64 m and 2.76 m in air. How many beats per sehix mqw.(tu4(( axi.0yg l: efcond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hkq 4bv- /nf3j,vf55 y0uvtywbz when at rest. What frequency do you detect if you move with a spee3 bf qvk 5-nbywu/t4f5yv0jv, d 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 f(q cea: gj.ze/w 5i/fdire engine whose siren emits at 1550 Hz moves at a speed of 32(:jq f /ia/ ge.zwecd5 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequenq91 hwqi7cka- cy if a 2000-Hz source is moving toward you at 15 m/s versus you mov a-i71hkq qc9wing toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When on.dd-fo)xyj fff9 *m 2g ypsl/0ich1w d /1fm:fe is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T d.yi01c1j*oflwgmh 2fmd/ f/f:fx9y)f -p sd= 20 $^{\circ} $C    Hz

  A bat at rest sends out ultsymd 2 7b,; q;; vpiiag,c ssskq+z7m-rasonic sound waves at 50.0 kHz and receives them returned from an ob 7mzpqis,; s, m+da-q2v;ib7;yc ksgsject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a w e*k3avg2 me-s )ql0tkall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does t03 eq)kk*2 gmtvs a-elhe bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was t w0 7,-xcf s4;.saobyyv5jyaplayed 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 thcv yj.5ab7ws;a,y t0yx-4ofse 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-hlc) uqcx5 b9qcl5v/c.nrz2/5jm z; gflow speeds. Suppose the device emits sound at 3.5 MHz, and the speec. 5;qmnjc cqzlcrguv5z9 2/h x5b) /ld 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 ) ef6qcc*ulh6of 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 veloctb yq-/7otnd 9ity is 12 m/s from the north, what frequency will observers hear 9y dnobq -tt7/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 itu, (5 c7qlprqlh.07* pei f m-qgsxeu+s 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 Machihpas7ij xz ,a;a 5;g2lbo 0pr*c x3i- 2.3 where the speed of sound is 310 m/s (a) What is ,2;sa*3pji r 57 lh-gbzp;coxi0xai athe angle the shock 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 entersmce m4u7jy/t/-d;q; d*5s;y fayj ohx the thin atmosphere of a planet where the speed of sound is only about 35 o ya/mt-4chsdd ue;7;f* xqyy /;jm5j 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.bmycy3jj4z 53 Determine the shock wave angle it p y4jc3j53z bmyroduces
(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 h:z ua, af g;xk0 p*ti2,/tia8ebly08r n*dny$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and seens n;y 7dxsp812rg b)m a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance osx8;ngn1 rpyd)b s7 m2f 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 thatr1 ifo6mee 2m(cz6/br sends 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 pulses (in 1(cb2er6mie 6/frzomfresh water)?    s

  Approximately how many octaves are there in the hnpl-ye-v ;2hw*zoq ku( *vg +ouman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mapng6p4x9.i fub : chc8ny plastic pipes of various lengths, which are open on both endsp8 96f:ph.ucg cn4i bx.
(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 sx9 dn9w / z0i(pzpi,xicbk; -lound close to the threshold of huma c-x p;d(z90wpiizn,ib/xk9ln hearing (0 dB). What 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 sou7:h8qta nu6tf5pz5ft3h h0 rqnd are heard ah nfqtpf75 85rhh6tu:0 t3qzsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whatsxe9shf7vokmo 64yzh)dv6lo 68;r( e is the acoustic power output (W) of the speaker, assuming it radiates equally 7k z69 ex(emo64os h)6fr;sd lvyho8vin all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drop1-abyj7 j x6,yuua*s ddf)p+ rs by 10 dB at 15 kHz. What is the power outpudrs,ax 6df7yu)b*jjy 1- +p aut in watts at 15 kHz?    dB

  Workers around jet aircraft typic9gs-/3nfx1sf z:(+f pupitl9t q;qulally wear protective devices over their ears. Assume that l/z nq t1luqf- ufsp +pf9x3 ;9gs(it:the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatib6bu)66km ld+iel+ dn5:g wbions 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 frequency 1v l(:4bdoabn8d3v j,g$\frac{1}{2}$ 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 3o( 3yqoo3j9vzyq.bw :wu hr9a fundamental frequency of 440 Hz and a:uwqy3q9(r93vow bj ozy. h 3o 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 aun,r;q kpt+ d1bove a 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 tuning fork when the distance from the tube opening to the water level is 0.125 m and again at r+ nt;k ud,p1q0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that iur3g: o*2nwg +cy nx+rs open at one end and also 75 cm long. How much tension s: xr+nwcn*rgo ug 3+2yhould 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 tom 9 w8uyd0.mfb4;y6hm,;acezv w,w kq 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 500–1l+p,s*2gmen54sk ,wl hssz e1c r9b n0000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determir n4e bzs*sgh59s 2+mepl0l ncw, ks1,ne exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statio71 qfybu qgn7,nary. The conductor on the statign 77b qyq1u,fonary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you ir;.t.tns kg(j s 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fa; gt .kjr.tsn(st was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate 3 rfnj7-xm 0vssd jl) wv74l7athe 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 (f l7w-jfn3jm7dra7 l4ss0vx )vrequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together,c+2f 4jcx8gm8dju y7q produce a beat frequency of 11 Hz. The shorter onejyc28 uc4g +f8x q7djm is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastq9h2hpn c(kls/4 ax2p 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 speak42a(hhks nlp2 9/cpxqers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood f(nkdm6hphyngf :-r);0qpni s*k w,w8 low 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 thphwgqr0- pwi,dms (fn8k6nyh nk *;:)at the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a msvf/ izzvu4o w5j46 /toth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/ fvzzsi5o4u w //tjv46s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sousw: b*fwl g cnc(5ud2;nd pulses as it approaches a moth. The pulses are approximatelycn gd;c (2wusb5 w*:fl 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used fz8pmrk2;hx .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 sharp (or G flat) horn. What is the fundamental frequency of this horn, and which ohk;mp fr82z x.vertone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be comprl s n7r v(.crts 5f8ngbiee8,(omised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressub(ngtsir n 8v .5e7r l,(cf8esre 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 r(v5xkaf1eq)k)v 2 xpiods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. W)exi xva512kf p)( vqkith 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 for ;+z/3ypn5q6q 6lm xg( garywjthe human ear at a frequency of about 10+6 pznq;/ xmgy6 gyaqwlj3r(500 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.de )ywquu;;d: 0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directlw;;yd qu:) eudy overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo:pk* 2(j0p 7ujdhanha at 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