What is the evidence thatfbwrb4 9 k/as 3)lqtcl *,3w;qoatsx1 sound travels as a wave?

What is the evidence im;1fqrn* *z/ i8bi a*5j8au-wo ump ithat sound is a form of energy?

Children sometimes play with a homemade “telephone” by at) 6,ppu2: hi urbfh*kmtaching a string to the bottoms bi*2hu krufpp,6:hm)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 intkowxu* .+pzi ,o water, do you expect the frequency or wavelength to change?.z*wpk+,oui x

What evidence can you give that the speed of sound * +42siplte*oqmg6 5l/wbnxzin air does not depend significantly on frequw m6eb*lznlx2g+q stpi /*45oency?

The voice of a person who has inhaled helium sounds very high-pitched. Why*x)r8-vyg zia?

How will the air temperature in a room affect t 31rbtty,wy,h he pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude oxx 2sj yhrp6)l0 .)nnkf sounds in various freq .x6)lr xjh sp2kn)yn0uency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fis(shl;w; + 9xmvu hce:g. 12–30) spaced closer together as you move up the fingerboard toward the le9s(s;; +: uhcm wvhxbridge?

A noisy truck approaches you from behind a buiojez nz;/0 g+j ,,srwsua,y7slding. 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 diffractr ;z,+e7 a/jsy,uoszjn sg0,wion.]

Standing waves can be said to be duht b7 pt/yg/2te to “interference in space,” whereas beats can be said to be 7t h2/ptyb/gtdue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of thqb h9 la0b5b.je speakers were lowered, would the points D and C (where destructive and constructive interference occur) move far b.50qhb9lja bther apart or closer together?

Traditional methods of protecting the hearing of people wy9 jytr:x.mh r 4j6uj6ho 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, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambtjym u:ryjx9hr 4 6.j6ient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two wavvg pw;c glf2:c1 9by4kes shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with sliglbyv:k;fc 4g wgc192p htly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move ti-n;i0 fi e2sin the same direction, with the fs i; iti-en02same velocity? Explain.

If a wind is blowing, will this alter the frequency of the soup cd-o,w 0y,n maupqyyy0(p(2nd heard by a person at rest with r (,ndp2m(yy0puapoqy0w,- y c espect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chio5y)d ; / :rtugphye(4kiks1yst(4 ny ld in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the (t5yg ;yhtn( srk:i4o1yyd p s)ek/u4child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake * hgit+sq6t5c- w9jae by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hearstg 5*c-e w6+qh itsja9 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 jusdi0q:-0dnxwzp u ,xd /t below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the spwdxdp/,: q0d- xuzin 0eed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtsw/sh sh;jh9p3 -nqm d4 hc*7w7 ecdk7b sa5q)hs in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy5baiz);3 ubh k:neft6 day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). Hob3afi6;5 zntb ehuk): w 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 striki;ppl+)nrh yn *t /owq3ng the ww t +pq/oh *;rnl)3pnyater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ea1 ;z ujgcn 6usf;i.)lvr to the ground, 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 co i1uzvs6cuj;l;f) g. nncrete, 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 mile1prx:s rm:9lzppj0:q of distance by the “5-second rule” for estimrzps: p9jl:r pxm0q1:ating 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 sou,qy3wgnfzwr43nmo 4c )it-p2c5 de+und at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound wyj+pw. dt3 w p*3-2rl nja8tlzhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneous w9b-1*vvuapu e/cd8jly at a certain place, what w*e uucv -jb/1dw9v8 paill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wit cmt3z.gyn7i3tmb3 / bh four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shutcby. giz3 t7n/ m3bm3t 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, whereas) pw y;m7b4 ksayb /5afxn7wn. for a CD player it is 95 dB. What .7/b7yws f5nw ab4 yk);xmnpa 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 0 o7rc.p +n2w1;xmfi:bstqmj a+bf 2tsound from a person speaking in normal conversation. Use Table 12–n+qwmxo fi j0 2:fb1t;+ prac.7t2b ms2. 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 eardru7g(xs:rtwss 4 /67w rxgxmxn5 m 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 2k ;w (6m)cqkgb*pe pyrwwyb o1n::/w)50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to eaq ypy:bkw6)/r:w p1wgo km()en*wbc ;ch 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 whejzk34o/* yj 7aki a zz*u*l6toawk5v*tt2g 3un placed 2.8 m in front of a loudspeaker at7k3at u2 ay5 6lzg*w*k3*zz vtj/joio u* 4kon 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 t jp(awqx 6;,qlevel of 2.0 dB. What is the ratio of the amplit6xp wqa q;,(jtudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave iseh1nh pj6pd/+.0f ja j vcz)nljt4i w :ju3m;9 tripled, (a) by what factor will the intensity ;djevjnmuj6p:pwin / 0 c)aj4 l3h1.fhz9j+ t increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tg0(0idqq,m6jt meu:4- fz ct hwice the frequency of tu(0gzt4mf iq 6 0 t:qmj,dc-hehe other. What is the ratio of their intensities?   

  What would be the sound lodohe4bs, j u s iwvz/s/6y+(2evel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrw4/osi( zv+oj,h usyb 6/eds 2ating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must 8i( 9 iu+aweilhave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–uial9( ii8w +e6.)    dB

What are the lowest and highest frequencies w(sp7l n.*vyf4kg/yethat an ear can detect when the sound level is 30 4lnkpes.v*wy/7 f (y gdB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What 3a+n(n cko5wp *,dp+bgni7ri is the ratio of highest (k7n ab+ c idwp5rnp*n 3,io+gto lowest 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 fundamets4 syms-;; mlp u+u0:l, mxpsntal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under w+l0 yltm mup ssp;usm,-x:4s;hat tension must the string be placed?    N

  An organ pipe is 112 c,k 0lxljql8 q j;z1qd*m long. What are the fundamental and first three audible overtones if the pipe isd *zjlkq ,1 x8;ljlqq0
(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 1v o:iu2ldh d3the top of an empty soda u1ldiv:2d 3 ohbottle that is 18 cm deep, if 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 7c/:bz v azb 7(:xv s beluyp2:y1ccr:pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would /1z(:vpsb y 7r a :l2 bb:zv7ceyx:ccube the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hasa23ynx5t9nz*o4t rzb4-v mr a a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origixzo 4rz3-tbam5r 4n2*9t avnynal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above(k.s*mo g2ekx zfwzn3 ) d/xwn0)w/ ok middle C (330 Hz). ) f(*)oon 3k . //exkdzz2k0w gmswxwn
(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 m rwax1ytvn/ n)i; dwd:4vr4o 0iddle C (262 Hz) when the temperatn/r4ndo vytwd10x4av:wr i ;)ure 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 maj)p.n+d,hkz *r hld8 *htp7at 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 .u yc(pdv ks6+ po5(wnExample 12–10 should the hole be that+w 5p(ov ksucd(.6n yp must be uncovered to 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 ca ccqd7e8xv4 e1n resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in bedq 1vx8e7 cc4etween. (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 5j5sbo0wlw7y //0cz:r s k k hpqo4i1eresonates at two successive harmonics of frequencies 275 Hz and 330 Hz:hs1y be0s4 k0r/wjkc/7lq5oipw5oz. 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 eln 52:ezdksj9 xwch -+--l ss$^{\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 rc-pnt7.ryo7 lc 3x2 pn 3d6hx (9uabypresent within the audible range for a 2.14-m-long organ -37p 3yxhnc.dr yr6xa (l2u7 nb9tcpo pipe 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 is1 ,mtez4yo5ze6l1w myv) m 1qy 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 t156myzom e1y y,t) vle4zqm1w he 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,: xpc ,vgsw*w trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? wpg,sw: *x ,vc±    Hz

  What is the beat frequency i1 (6m: eohrhjkf 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 another (brand X) opedul55fw / pr0drates 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 ar/ 5udrdpl0w5 fe played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produce(od2hsvl8x l /s 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational /os2x 8(hl dvlfrequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. a pres2io:7o:The tension in one string is then decreased by 2.0%. What will be the beat frequency heardaoeo: 2sp7i: r when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if twoswt4w;*ir1cv94q r n k identical flutes each try to play middle C (262tw4 s9;rqcnirk4*v 1w Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, 4-zk*f fasc 6tyx d)7*roc:qp 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 possible frequencies of A and C? What befa*t f4s)7o:k*d6pccx rz qy-at 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.h3jiqfg(w 86)wdm b.z80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the othez(j).qwh86 dmg iwf b3r.
(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 1st 5jkv)yfy (032 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) 0kt)5jyvf s y(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 ;p:sa)3r),czt b75pe2xsxowzqa y 2cm in air. How many beats per second wz7:s 2c )w ca3 sy2pp,xxezqtboa;r 5)ill 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 Hzvb-+ti ybr7pb3. oge7 when at rest. What frequency do.b+ g7yeo pirbvt7-b3 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 fireweu)0tw fvmn30 +k )f cshi7bo3-o uz) engine whose siren emitf3we)o3+ b7c n om)0wtk hzi)0uusv -fs 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 a 2000-Hz source is mo, 9yti5 ed6jtczg6jj-ving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two6 izjt9j5dct,6ge y-j 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 one is ot uj c9k*hv(08 n i0,noqox.dgrvv*8 at rest and the other is moving toward thj0vd(vx0n.o*9*i ot uknv8c r8o gqh ,e first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz an+(.4 ao4 t(vk.tmz q 4qpnfkced receives them returned from an object moving directly away from 4qt.4 at(4v(qc .kzne+ fpkom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at oosq8ml--8o 9h:ttpl f rv* (qa speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 -o9ftq r8s v:*o-m (o lplq8htkHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a ox;/y eh)q2gk+b tl7)j t*ig*ta ym ic5 *u1hqmoving 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 * xltigb)e qom*kt1h)7cga / y *u;5ij tq+hy2speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flom8doa 3bw2 o: qsy6t;u8nx79x ptxe +pw speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from them3xx o2 byot6u p9qswp8n 8d;txa+ 7:e sound source?   Hz

  The Doppler effect using ultrasonic waves of fresq3l ,p b-do*0 sgi6fmks9v;u quency $2.25 \times10^{ 6}$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 :) *g9*vp o -vsvkhj7xlhfwu9ay p9+isound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what p9:v)sa9gx7uhlpvvo-k*y + 9wjf i*hfrequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its g.pv,(olvav1ft++ x gqwu(,v speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a)vyvjwa14ug 2gd:o m/( What is the angle the shock wave makes with the direction of the airplane’s motion? (g:vwvm1/dg u2oj 4ay   $^{\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 .n ptzsg34 p(uwx av 2uy0(8loof a planet where the speed of sound is only about 35xupgz( p swn0 .at43 vu2lyo(8 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the sjp.)l+ vd7/6erpvep w hock wave angle v/7ewppl6ej +rv )d.pit produces
(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 6 l9g, vxz30hu n2 thik:lmta,$/theta$ 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 abovvj,:9jc(l 41prtli x we the ground flying faster than the speed of sound. By the time you hear the soni9lx(v:ji,wt j1p cr4l c boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pxzt 5n/ 8asn8(s md/ bd;xdwm7ulses 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 xtd/mbw;7n(s8s nam/5dz 8xdpulses (in fresh water)?    s

  Approximately how many octaves are there in the human auvd* 8w.bj.5ilzfy l-xdible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has .tnt-m f .l.9yoepx1s a display called a sewer pipe symphony. It consists of many plasti t9flx.pm .ty-.s one1c pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a perbta3s0vl. vb xg-p39xep y7) nson makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mos)pt 3 3pb 0v9 ae7xbgnslvxy-.quitoes?    dB

  What is the resultant sound xp;o 2h7*vkkx level when an 82-dB sound and an 87-dB sound are heard p*x7o2kh xk v;simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What i72dquv ur3e;v3 a tl58jo(pnp s the acoustic power output (W) of the speaker, assuming it radiates equally in all dir3(l vpva7 8p;erduonu 35t q2jections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output d1 . a-ooctbvq5rops by 10 dB at 15 kHz. What is the power output in waco.1o-qt 5avb tts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective-lq7/g0)pndj z nd,nb devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be t)ql0bg7/dn -np ,j zdnhe power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems) w kpy2)rsu.e zx8/e:uwjq8 w, 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 violiom .vvj (nrv38i- nh;bn is tuned to a 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 violin is 32 cm long between fixed points with a fundaifm 4/2:y7k i,qa;ss la eysl8mental frequency of ayiliaq ;sml8:,2 y7k/sfe4s440 Hz and a 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 above a vertical open tube 2+lwrdj0 lyhh3lhh 2sog /jh2 *u7ya;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 ther7;h2yy+sj guol*j32lhh0 2dl /hhaw 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 mas84w : m ioywaiu-8w9j /zj9hwtbsk)p;s 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 its fundamental mode) wwa8z hb/ uwj;ii:9ws4- opjtk9 w8 my)ith the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full o-b.b0r3 dt-lm.v u ionizb (5loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz rs2l a0s 1z31 djhk+z0+m9+cddwu m kkzange 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 farth+dmjw 3 kkzd9ud0zhzk2sm 0s 1+l c1a+er from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistlsw/x3zsmvq0 xqz0m - 9es. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is/ wzqz390sx-0mv s mqx the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After i0kcn0bt i-2n:*ydi.klx x all9ok(v5t passes you, its frequency is measured as 486 Hz. How fast was the train movink a*dx i:ll2.kvl0(5-ot xckbni y0 9ng (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars justxrh- 0 c c3g.:iwptx*k by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car i.h x*rcg:p- txc3k0 wdrops 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 together, produce a beat frequency of 11pejuwaecuj .:1k90- ge6w xd7 Hz. The shorter6cpk0ewag dw 1x9.eju -ej u:7 one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mubn/.o yko)gb ,h.1cg u65gqaoves 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 observ6byk ,g.5huogb .) 1/qucganoer 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.lmugs)uueh 7vds 88:. 6tbzg+32 m/s what beat frequency would you u gtgsud87s+6 hm.:zbe8lvu)expect 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 moth igj n66e+ntt( ks 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 tn6+e6( n tgjkafter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it xj(,p q,qfj zrio vha,98 :sj7approaches 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 returns before the next chirp is emitted? p v9q,,j( :,jqh fjxoiza8 rs7   m

The “alpenhorn” (Fig. 12–38) was once used to send signals froc )3/. uvas 7)vstvggly -f-dxm 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 w. sx-y ls/)g-7)fg 3t udvvavcay 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 overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by--n*rt 3cvwfu tu(7a p the presence 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 wid *pa tuvr7 --cn(wft3ue, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv-zyec4;idg z 74h6 gjoolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sin74 ; hoezz4gyjgdi6c- g,” 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 th e .6g5.hgsdejl8xdq:x8 ks3a20imjk e human ear at a frequency of about s.xa: dk.x5jskm6e qgi 03 degl288hj1000 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 observero03sdm; x mv goy80tg+ on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitudvoy +g0g0smom t3dx8;e?    $ \times10^{4 }$ m

  The wake of a speedboat is 1540r58jn+gvrw ldsu3 k +nmw.u $^{\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