What is the evidence that sound travels as jszwha35sfyq*d bq/;b1iw3j 9x,u,t a wave?

What is the evidence7ar**e6b cht7k:hgz y that sound is a form of energy?

Children sometimes play with a homvrhp 3 v2.peh+emade “telephone” by attaching a string to the bv +.2h 3ehpvrpottoms 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 you expect 8o;yi6cusmrg +d p( ,y6ixi9ithe frequency or wavegrmcui oix(8y;ps di 6 +6y9,ilength to change?

What evidence can you give that the spyo 077+wuet ;ttxd,rpeed of sound in air does not depend significantly on frequenewt t r 7o;d7+utx0,ypcy?

The voice of a person who has inhaled helium sounds very high-pitched. Whyj f. stm);cf3g d9e/hw?

How will the air temperature in a room affect the pitch of organ pipes?k4kh+. p *t5ybsj*pt gx pl4o*

Explain how a tube might be used as a filter to reduce the amplitude of sounds fr1 18ii; y6r4zbfdk )nym ho/za;ow.in variorn rmkh) 16fb;y4i.;a8oy/1zio fzwdus frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) 6g/yu umk/c 5(ss 2mncspaced closer together as you move up the fi 5(usu //smc6mg cnk2yngerboard toward the bridge?

A noisy truck approaches you from behind a building. Initiallyb,k*t*s ss;vq you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you heav ss*b,;qkt s*r more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inngzg w 06:knu((v(uhx terference in space,” whereas beats can be said to bn6n0((vg hugkz:(u w xe due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wou9; pg/j.lyfgtld the points D and C (where destructive and constructive f9/ptj .ygg l;interference occur) move farther apart or closer together?

Traditional methods of protecting the hearingf 2t+ys4eq0d ytb9 am- 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 tec2-d4yms0 q9bayf te+ thnology, 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 yuk8n kwrlim m4-n/-(wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whic/(8u-mnm i knlwyr- k4h 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 directif.l:r52k,-tz3 vmqvjt,6p z vlywt7mon, with the same velocity? Explail:t tqzmw2m,.76rvpv , y-j5kfv 3 tlzn.

If a wind is blowing, will this alter the frequency of th .ewaws xsp2rq2 te,fq7)p0q(e sound heard by a person at rest with respect to st fs2qp wpwxeq0q,27ae.(r ) the source? Is the wavelength or velocity changed?

Figure 12–32 shows various lj .q)cc* aa if4:7letpositions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will tejlal74 qfai.):*cc the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length ofyyjslx5*;: ev gi9z5u a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lakz:v5 l;*jy xsuge5i 9ye. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belowscjnn)9 ixp)4yy6,wgh3 bqi 7 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 specyhj)p63 )xibsy nnw94q,ig7 ed 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 atz2++ w qpagbh2e x.sb, 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 boajxbt9lh 7/g-xt is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire ocb lh- tgx/9jx7curs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whj4atu 1; q 3-gozy4ycjen striking the wa4 ut4g3z-yjo ;y1caqjter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, seesa hj 3m;ng4k shv2-wg f2x p4qq22 lucvki*j96 a huge stone strike the concrete pavement. A m 2jkux34v* kq h 6hqiw4s vmc2 f2a9n;l2-jggpoment 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 Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent er v.loq 9,pf*5u7 n8, o,ouhchfgijz0 aror made over one mile of distance by the “5-second rule” for estimating the distance from a lig p7n.zvf q j8,ohi5ua og0lo ,uch*9,fhtning 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 level odsx yf4/pvf; *1hcdh(1 oh5h5 n8z jnif 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose -z7hc :hm 3ygwintensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when lvs1e;rxg+.5o /4s+ju bqtlf fired simultaneously at a certain plac4lxo/lft+gu b 15+.vj s;qe sre, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a c 2bek 6nb *xutncp52,ah3 ygy4ertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wykbtx p5 g*b uy2,en43anch26ould this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said touad :-ig/c r;c 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 tr/a-c;igcd u:he 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 conversath) o-gyg.7g w5kb, ystion .oh , sb)t7kgyygw5g-. Use Table 12–2. Assume the sound spreads 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 ear8gck.v3q ae9 pdrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is raorhfssd8 ;*d9 ted at 40 W. (a) Estimate the sound level 8;fssho*drd9 in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when ply q3aj1l+yxy8 fkt(.b hpv *w3aced 2.8 m in front of a loudspeaker on the stage.wavtxhp3l3 1b (*yf 8kqyj y+.
(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 2y2i 8od.nk5f np9h y-whf*9zv.0 dB. What is the ratio of the amplitudes of two sou-hv i9hyyo dkn ff982 nw.*z5pnds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (ah3 j-pb5 oiy 0rsp(h7+qule 4k) by what factor will the intensity increase? Increase by a faqi sp3+70elkr4(b5phuy j- h octor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplx v/ y)*sofcql.e;vb /itudes, but one has twice the frequency of the other. What is the ratio ofbov/s ;ey/fvxl *cq). their intensities?   

  What would be the sound level (in dB) of a se57vp5* h w*hsbl:fjes 5pgp. 9f+wbtound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 +f9wthpevp* : 55g js *be57l bpsw.fhHz?    dB

  A 6000-Hz tone must have w ic/58h;l/b9y lxsevubo;b6 rhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound5s9/bbl;/v uo8y6hb;l er cx i level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear cxwwiqu+ 2l 0i6 7z8apyan detect when the sound level is 30 dB? (Se7y lwpxz8 u6w 0ii+2aqe Fig. 12–6.)

  Your auditory system can accommodate a huge range of sounwiri.:y c ;ihid *6u9v8fxp/nd levels. What is the ratio of highest to lowest intexy8 cu. ip: d6; ivfiihnw/9r*nsity 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 fundamojc lb;5 0x+g26djm*3pdnlfm ental frequency of 440 Hz. The length of the vibrating portion is 32 cm, cp36 jo 5g+l2 mlbmdx*jf; d0nand it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lon: (+hfe6;il9slxtiwq g. What are the fundamental and first three audible overtones wiqh9x(l+s l:eft6;iif 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 f e;r si ff6pcu 5q-(q7.7r3fna du;euorom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wauiup5uq6r7s f- o qf( f3;nr;7cd.eeas 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 n z// x0mxtml:hb9 y1vhy)c79y-gnh t with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), wh mg -h9ytt n yc9mz1b x0nh:7vy/lx)/hat would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenc7ervoa te*;uun5z.9b;+ 5;xtpwd y sly of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of on;y5ro* 5spt7wtluvz9n+a. x ;;ebue dly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and 97z:go k5)xwq gs)zenis tuned to play E above middle C (330 :7z9s) )wkexz 5ng gqoHz).
(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 m5aj w 3c;xqt 2tr0pks)iddle C (262 Hz) when the temper5w3cp ;sr jqt)ta20kx ature 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 p:htu p)to 5o8at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should tpw m.g qe(.fk0he hole be that must be uncovered to play D above mi .(0k.empqg fwddle 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 pimqzf/7gh ;*vlqtn7; ( ppkwrf 2t3w l*pe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a cl7pzf*(vq;mr7hqtl2 kpg lt3wwn f;/*osed 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 bol. 5o) hkv:zyeth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wha.o )hyl 5:kevzt 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 xljfh0b9 yn+ag0j k ta))r6 nf2* x3+rjws(bx$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long orgar 8bc/l6tm 3l2yobc:k9a rw,an pipe at blrcl r wbc: ,aa3/2mkto98 6y20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm ldm:)egj+m4*lrkth s grfc *)(ong. 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 is the relationship of your answer to the informatio ( 4gjef+*mdcmr)rkls: ) ht*gn 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 to0 g 9j tjs0itkp-1b;ca adjust two strings, one of which is sounding 440 Hz. How far off in frequency -; aj9b g1jt 00cipktsis the other string? ±    Hz

  What is the beat frequency if middle C (262 giws4b9(-yblo ns u : 58(gnki6nq u0zHz) 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) operfx g.ig);: ::bftgdfcates 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, estimate the operating fre:f c):fi:fg;t dgx.bgquency of brand X.    kHz

  A guitar string produces 4 beats/s when so swhqr )uqw.q ;3ha4goo8j2j9unded with a 350-Hz tuning fork and 9 beats/s when sounded8)h .wog h2;wruqjj9 3qq s4ao with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sawa ;6maorhhe q6 k7+(b2rd- eame frequency, 294 Hz. The tension in one string is then6h-q;+ owb7ea rka6er hma2( d decreased by 2.0%. What 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 tx; x+ft gko4*ywo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 2ykxx o+;t*f4g5.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.,gq6yh4en9 5olir* k ;gf(yz a Fork B has a frequency of 441 Hz; when A and B are sounded together, a n9r(,4 *qge5 kfh;oylzg i6yabeat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m 7 fy -,wti+tqcfrom one speaker and 3.50 m from tw qc f-,ti+7tyhe 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 vibrau s*bskr6 7xq :9;tf8da:7h bchs bf9xting at 132 Hz, but a piano tuner hears three beats eva7shxf6rbf*8d:c 9u ;hssx qt: k7 9bbery 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 and 2.76 m in air. How many beats p6e9m0a gu0eq2 xcilz1er secondc2im1 gxzq96el0aeu 0 will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire hde 2x:; ;wtvaengine’s siren is 1550 Hz when at rest. Whdawhv;2xe : t;at 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. Wtn1f6wodrn4 a(n0p v2 hat frequency do you detect if a fire engine whose siren empn4wnfo1n 2t r6a v(0dits 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 ivhc5u/ y;qhi. f 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 yvi;u5h.ch /qthey 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 equippe v5h7u.y cy90l6 qfssud with the same single frequency horn. When one is at rest and the other is moving toward the 0yuvsl y6f .su7qc h59first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at8f vv y 8;9j+oz*vqqfs 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frf;8 zs y*j +89vqoqfvvequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits 9 qt4kzcx3np )7e i2lxan ultraso9iz4nk2cpe 7)xxt3ql nic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experihjoyvv:yt39.s i n6 .cments, 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 res9 3:.vtyci hv n.yosj6t in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Sfvg7c 4z7k tj3 g sk1::5ispdwuppose the device emits sound at 3w4 cgjk: f775:v1k td3spzgsi.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 usi(k+ y)gqod9lwt2 2c pqng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequen ; go09yoa+ttpl :k9imcy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obgmpo :o;ta9y9+k l 0tiservers 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 +nopkn5v1 (ir,msd4a moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sou14(x5 p:uqb zknkwez /k:- re*wmnvm*nd is 310 m/s (a) What is the angle the shock wave makes5n -(uk nqv m:krkzwwm/*be*: e zx41p 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 where the sp;s h/lb5ve tqcec h;8 3y)l2teeed of sound is only about;53bt;q e es 8cel/h2hvyl)ct 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. Determi7sq;-3-yzh lrss/ egyne the shock wave angle it produzsyr-e/ 37 y;lqsghs-ces
(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 p ql)qrwe4a3d 4onmy-f;kf,-$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground c26zhl6/m t9zdt;q 8u :keen hflying faster than the speed of sound. By tecmz96h8 t/t:keqz dn6lh 2u;he 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 than yn.julmri+y+/b/: ct sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth iy/r+ bnl:u/ n+ycjm.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 there in the humanca;z; i3qb6 yhi6ur,a audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has r*/22n bwxyuna display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. /wy2x*b nrnu2
(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 close to the thresyq,,0kt ttl,g hold of human hearing (k,0gltyttq, , 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-dBea 84 d4d6ih(gii(j.kryg sv- sound are heard simultane4(6ihgr .eiya4 sikv-8jd( dgously?    dB

  The sound level 12.0 m fromskaor5 t. ff+6 a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output+s t.okf f5ar6 (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 output drops0laq 9yc cwy5 )x*h3lutp7n r/ by 1w03xlryh9ycln t c u p*)a/q750 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aguvfb8dm.7cc)a 1w: aircraft typically wear protective devices over their ears. Assume that the sound level of a jet airplaw u a8adg f7:b1cc).vmne 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 communications systems, the gainx (dkft;59mhb *xfi:x-c)x ef, $\beta$ 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 frequendgc*d-f njr:w5b c,)ncy 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 violieifw 6s-ck. :s/aaj: dn is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a md/faej6 : .i wk-assc:ass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fille2:e *l.t8wxe+j hbem,neu f w/d 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 0.395 m. What is the e+unltwf,eewmh. j2:x8b* e/frequency of the tuning fork?   Hz

  A 75-cm-long guitar string ci+zw f* f7qy 3)n3b)ce ony5dof mass 2.10 g is near 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 bffi o+3ccnq)y z7de3n 5)wy* its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop 9 0wqhv(qkpt g+l :e+p($\frac{1}{2}\lambda$) 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 500–100k 9mc0m 6kv9l lc9*wjypow x/y7+q ,fkh 2t,jf0-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 person moves about and finds that the sound level is minimal at a point 0.34 m farther from one sourcym wjktwo796ch x 9+y,m/lf lq90,p 2v* fkjkce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One trai k5ki7l3x1q4s0g ekh in is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other trainiqg s k1kihkx l4075e3 approaches. What is the speed of the moving train?   m/s

  The frequency of a steam/ys:c8q hb h23 bma:cm train whistle 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/bbyam3c: hsh2m8q:c velocity)?    m/s

  At a race track, you can estimate the speed of cars just by k-nj+g* 59gp:kaot.5 drb rfzlistening to the difference in pitch of the engine noise between approaching and receding cars. Suppose t5par +tz jrgbokkg:f-n.59d *he sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding 6:t l(2x0)aqlla)(bwb5ol xl aev;tp together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Howwtalt 6lx(a5; bl(o2ba l)0 qel)x pv: long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as i0j0i j(ok (ktfzsac67qy t7t0wbdr21 t 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 frba0 c6y0of 0kqtr2i((sk 7zj7t jw1t dequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beat tou;j) *q,6hdb9y qnv-f; or.uuu. c uhh0/sgfrequency would you c*hhj/)h b6q; .g.u-; odvq,ru ftu90snyu uoexpect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the mothxaq b*;e. ;fzo is flying toward the bat at speed 5 m/s 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? xozb.;;qa *fe   kHz

  A bat emits a series of high frequencvk5cg f4xd03by sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart3 k0fdg5 xb4vc, 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 to send signals from one Alpine vil rdgn6*ffw b/8lage 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 overnfd 6/w8bg*frtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pre*,5 w,vogzb dvsence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a liz w5d,bo, vgv*ving 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,u*k2ng:ual1f iow z6in/x 4q) called “singing 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 l /un fw:o42)xaki6u*q in1zgpractice, 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 hearinky519noz6h e gg for the human ear at a frequency of abou1 yz5eonh69kg t 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on tb/g(9x5ee9bhe zs1w bhe ground hears the sonic boom 1.5 min after the plane passes directlwx/eebhe 95b1zb s9g(y overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat p-j6 d eqw 4l.kqe-uh0is 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