What is the evidence that 3ch d8wr1que1z9nj4 r: jh t)osound travels as a wave?

What is the evidence that sound is .(v szfea0 7c0ov elp8ckr m44a form of energy?

Children sometimes play with a homemade “telephone2/lw.:fx ,r4 7lfhv2m-gz pqg)nb whh” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be he gl2nf pb4/r 7v-gh2zqxmh,):w fhw.lard 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 the frnhjgoun0 u6(eq kb 90n3+a3xmequency or wavelength to ch6xu303na+mk(nqno0 heu gbj 9 ange?

What evidence can you give that the spe64ll p6ipdpvnmp6s:;0r 0 aje ed of sound in air does not depend significantly onln06ds4erv p ajp6 mlpi06:;p frequency?

The voice of a person who has 2s+yzh4m(tc ninhaled helium sounds very high-pitched. Why?

How will the air temperat5q7pu qdj wan k27;xe*ure in a room affect the pitch of organ pipes?

Explain how a tube might be used 2a2nj8pi upywu-6r -nas a filter to reduce the amplitude of sounds in various frequency ranges. (An example i6nu-2ynja28p r -w ipus a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together hmx 0*y f66rxaimd38n-hm fm 4as you move up the fingerbomf0ahy mhfd-n im634x8m xr 6*ard toward the bridge?

A noisy truck approachey .q:p-s3 laht8n 4.jue5j0uv9.wk2tyzy d a bs you from behind a building. Initially you hear it but c5y klv 0bjtdu4q- .8znua9y: epjawst23..hy annot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats 2,0crc)rm)**sybhh uc 2r cgocan be said to be due to “interference in ti chcsh*0g)r2rycm)u o,2 bc*rme.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, pjj ur*y6.,j lwould the points D and.j,y * jl6jpru C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecti4t 8 n(bgeg ngu-: ig+2-qvwmdng the hearing 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.itd:(ebggg q2gwn+-nu4 -v 8m Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of ascqoa :b7es4 zd:mi/l/ a superposition of two sound waves with se :m loc4ai:z/qs/b7d lightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the qov0z: xu(p )iy cbb2qyu: z15same direction, with the same velocityiu:zc(yqx:)voqzb1ypb u 250? Explain.

If a wind is blowing, will this alter the frequency of the sound heard b z x0(rz5 q19qy8sllm)kvhwe+y a person at rest with respect to the source? Is the wavelength or velocity chan w05lz rez+xl)y (8vqshkq9m1 ged?

Figure 12–32 shows various positions of a cd4qv ljfr0m3 ji nyo+c2h:s20hild 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 child hear the highest frequency for the m 24vr+ djy2fsh :0jql3n 0coisound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of h +gcrq(p*xp 7z8erg:j7 ld(eher 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 l 7gj: p( e+(p*zgd7ex qh8crrlake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlin+ + 7c,uutylye gasy,5oelsv(*hr03qe. He hears the echo of the sound cetr ouu,h3ey*,qvs7l50 gy la(s+ + yreflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavele cfm;+a .9tas qv5ftjy/ 1ikx-ngths 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 t it )giolz;1 5.tjpx5uuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away lg1tjii.px5t z u;5o )(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 ck : cxa34y /2xt qw6zyh1g;mcwhen striking the water below is heard 3.5 s later. How high is the clift6y41h3gmz /c;w: qcxkcy xa2f?    m

  A person, with his ear to the ground,xk 34gcxejp(96i :l6arawr1 x sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air ap 6i xrxk:ja(1l3 gexwc469arnd 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 error made over one mile of d:,e0 x5d6qfwd;j xad8fi* sryistance by the “5-second rule” for estimating the distance from a lightnifiw*x, dd6e0dsj8rfy a;q x: 5ng strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity oovps3vf95ci oxv1 )-f f a sound 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 whose iaz6ya 3pbhf 3;ntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pdh+qy i g-*nrbl4l+47m iu rs-roduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound leveb g4+ 4ulrln m qd*ys7hiir+--l if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wsrr2,*s lyqh4fv2 ur5 ith 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 shut down all but one engine? [Hint: Add intensities, nossly452 ,rh* rqurfv2 t dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, + sdjd07r0vka whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 5 d0raj+v0sk7 d8 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal coa j tt(0)syjf(nversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cet 0)asj f(yt(jntered 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 eardru65ijh 3w7pich5wwdm m, t) el(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 250 W, while the ms/e1.k,/r 1g6xrkaum jizbh 9yg9li1 ore modest amplifier B is rated at 40 W. (a) Estimate the e/.xihm9a1rzu9j, /y1 gb r1sg 6kikl sound level 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 placed 2.8 m in front of8-vnsg4a.ab (zsf y 4o a loudspeonassyga-v48 zf b.4 (aker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound z07bgo3 r djkdoufi9b/;,oy 6kz,0nc level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: rd0g,b kyzoj7 o f9 oc,0bz3 ki6dn;/uSee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wvo +5*uwop 1ikhat factor will the intensityoiu* kp1+ o5vw 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 twice td rl) 7/e lsbugmwn3;0he frequency of the other. What is the ratio of their idew)0;sb 7ul/3 lr gnmntensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds kmnm)mky0:wxmzs *y+ 5 ejk *b,sf3p dh(;y8oto a displacemeno *h0es;b3xmd,yz(fwy8 k: *skmm )5my+ kpj nt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as dnk (14itpv7,x zpaqv2,-ts +ihql n9loud as a 100-Hz tone that has a 50nk an,(pi4 q d,zqith7+ 1-p2svlv9tx-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies g7/b ko t77 tnzbo,+kythat an ear can detect when the sound level is 30 dB? 7o7tk+,ygt b k7o n/zb(See Fig. 12–6.)

  Your auditory system ctrpcy pf3 ,6zl hn.hqfyz55;9an accommodate a huge range of sound levels. What is the ratiz5p t6yl9n5f;f r.h,qzh p yc3o of highest to 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 fundamental frequency of 440 Hz. -hk(yupeor - 3yi1.d 5p(ri glThe length of the vibrating portion is 32 cm, and it has a mass of 0.g dho5 1ilryk.u (--eyrpp3(i35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibljz+b4 *kpxzqjfu5/+f e overtfx j/*bzpq j5 +z+4ufkones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequenc*wnas;l*zk1vxu - c9 ry would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, ivrsc 1u -*w*ax9 kzl;nf you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes sp6( 8g3i2jji 2ukzzf9xp3ju esanning the range of human hearing (20 Hz to 20 kHz), what would be z(3pz36 28xks jiue 2 fjguj9ithe range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenc32iakti9 ru (py 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 origi(2kat9ruip3 inal length?   Hz

  An unfingered guitaryx- *t*oskla- string is 0.73 m long and is tuned to play E above middle C (330 Hzy-*o*la -sk tx).
(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 midd,m 5ihg: 5auegv u08zrle C (262 Hz) when the temperature0uz8agr5 vuim : eg,h5 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 y0bl:qufr+c9 o:*q heat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthp*q* i/ ffpx*smiece of the flute in Example 12–10 should the hole be that *q/fspf *mix*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 a4(m 3n hm gz8ul+llh)can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Sho3g4z)l8 lhnlam+(m huw 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. 81hhaa ox2( qlf :6zd*uq(brxIt resonates at two successive harmonics of frequ:1ud a62*qxh8h(lq zr ox(a bfencies 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 bcy ja 66+t- j3cuks1tox,zy;$^{\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 withtq6b( *vvj7bain the audible range for a 2.14-m-long organ pipe j bv* qv(t6a7bat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximjzghf +m,e.r s5xf(j 1ately 2.5 cm long. It is open to the outside and isz.emff srg5,1 hjj+(x 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 trying+ i* 3q-rah bswp,,x9bk8kock w-vp,f to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stringo+k,w ib *8xf kh v,rbcas-wpk9,p-3q? ±    Hz

  What is the beat frequency if middle C v3v/vc0 fso x,cfskp.g,,n+u(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. sbeeeqru jew d4s9d:/(p;kf;//+itw5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when theuiw/w/edf4kdespb;:+9(t;rse / e j q y are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz t2ybavlm57u +l uning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Whatylm 2 5a+b7uvl is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freqtu(wd3xt c9w0 uency, 294 Hz. The tension in one string is then decreased by 2.0%. What will utx 9tw0(3wc dbe the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if t2a.h pr c 8,hrbod;e-ewo identical flutes each try to play middle C (262 Hz), but ocae-.;hd ho82 berpr,ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency eex5+nfvy,qm - ju9v; of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C j9+ q-x;vmefv5 enyu, 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 from one speaker j:a8x1g3d qj owcp6b. and 3.50 m from the qo g31:bj x8pd.ca6 wjother.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but.,jp )lh 9 m gh66eliaste9i,w a piano tuner hears three beats everi6 jw a9l,.h),lmpg s6ei e9hty 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. Hy in,:d1x9* rzdky6xqow many beats per second will be heard? (Assume T = q19y kd*yrxi6x,n dz:20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wheje+6qvppvb wy z+ )0)hn at rest. What frequency do youywjpbv )q 6+e hvzp)+0 detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose si oju.l, ;qp-njren emits at 1550 Hz moves at a speed of 32 m/s;jp. -nu,jq ol
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a b2pe2o96ou2g nkk1 cq2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are eg n 1obq9cp ku26k2o2the 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. Whe6dfgd(gn1si-:o*g milnug m6 1 8nos2n one is at rest and:1* ui6l o g2sf6dm isggn on8mn-d(g1 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 = 20 $^{\circ} $C    Hz

  A bat at rest sends out ui +r2hye4 v4fvltrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it a24+e fvyrih4vt 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fb3gxmd1 x19 m+s zjn5llies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wavxxzmdm95l 3 b1+ ng1jse?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentlr a4l1 om9j2ws, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frjo9 wlm214rl aequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasounzg /t5a;miufe4n0 )h( yr l5qsd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cr s gnlh)/mq5 u;fya i540e(ztm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency o:yhb0( 2vdhravdv*rb) c )mfkv p/; 2,rs*xn $2.25 \times10^{ 6}$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 v8 (52k(a:wnu yktsuzk elocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, 2: skku wtnkyz8(a(5 u
(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 ;kdg v+): +auoq+ujqs 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) Wd:c65x;l jc(e ywa)vh i-up;zhat is the angle5 z )y;he-c:d pi;j vx6w(aulc 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 enters the thin atmosphere of a planet where the speeqight* tp-sp3 my 4gmy9r)(d*d of sound is only about 35 m/s hg-*qdg p *y3r) t94ystp im(m
(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 shock wave anf ,wtdp7iwttw9 h 6yda +)h/s-t.okm2gle itaw )tk7,hmfy / swwdtth29dtp+o6.-i 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 -29iy ku7mzjr $/theta$ 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 abn7xqx q 64j8jkove the ground flying faster than the6jkq84xn7 jqx speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000yo:b18 (p) ik muo8avt-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, 88 umyvba1 i otp:)o(kwhat is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range? w ze1gih4u n,k1o,l d-$\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists op:w uir 2qvlc:8+jt( zf many plastic pipes of various lengths, which are open on both ez q pr(v:2:c8wu+itjlnds.
(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 threshold of hlvy4 u;nt s3bu(w93eduman hearing dv bte 33uy4un9l(;sw(0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when anxe za:1bb:iwzj,92 ao 82-dB sound and an 87-dB sound are heard simultan9aj2ew: oazb : 1ixzb,eously?    dB

  The sound level 12.0p t:wl w./a;koy -zxu8 m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radi:lyapt 8. wk; zou/-wxates equally in all directions?    W

  A stereo amplifier is rated at 150 W o wch nm4wa)-3nutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What ia3- h4w)nwmn cs the power output in watts at 15 kHz?    dB

  Workers around jet ae 0ql0;dcu5dy ircraft typically wear protective 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 ey 5d0uqed lc0;ar 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 syowe,s ldka 0uj8 kg0jn7/ y2l1stems, 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 frequencgi+ g)r2 tmvv3f6 ls;gy 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 betweqc;uzc)x d*ig x m(itubsb; +g7 *,.dgen fixed points with a fundamental frequency of 440 Hz and a mass.*isxcgxbig zb+,;g 7)dmct duuq* ;( 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 tuf s *--qdcf:sxy 8aoj.be 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 hea :x-. -fodf8jqss *aycrd 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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is nea.h kfz9*(qlch/0ts zvei(v 4jr a tube that is open at one end and also ./evkzfsh9v *l0iz th(j (c4q75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonank*bobarx ,** te 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 500–1000-Hz range coming from two sourcestg4o6iv.as v+zf(kf bqbp-1 0. 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 soundbg 4 .tfkv b6q+-ao0sz1fv(pi 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 stationary. The conductor oolp fcgek1-6x-d p3+dn the stati -l+1e3-pc k pox6fddgonary 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(uvg1 s r: ,1dezfi/c1prnyj+ train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was thedjer:g is/zr+n v1y(1c ,1fpu train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by yoy( q)n k 5whrhp1-(su) 1fnwlistening to the difference in pitch of the engine n s1qh)ryw-knu5p o1ynhw)f((oise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes6nkwqcz ,p:n9g 9zxg: , sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the o9x npgqk: gz wn,c6:z9ther?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statitlk4 c/10 z6iw cal/agonary 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 whenkl0a6ct g1 w4/ /izlac (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 0u c(lox wdz4r90k 5o(xw c96gz.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waveskwc9r0l cu69z5 (4gd oo(xwzx 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 is flying toward tjy,*cwl et3 cqkd,udc 88(zr, he 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 thale8w cqkjc(dyr c 3,t*udz8,,t wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Th0d8 e xp:jh zwn1-r4lne pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How fpnn dl -hx1zrw4j8:0 ear 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 dxdyw* 6d l3.9mf4v 2ifimk:rone 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 m4w3mkvi x .f dd*fl2r6i9d:ymost 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 0jgk-71c:b1eg71 nk ud bp-/jivdkoacan be compromised by the presence of standing waves, which can cause acoustic “dead spotsgjdb1:ge1k 7u-i nokp- b jc0v/7d1k a” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv dk(fd1qv 0 ;uobhd:-bolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hano (d1bfdkdhbq:;u 0- vd. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human 32 byrgocahkv0j b: ;wpe9*6 bear at a frequency of about 1000oca vy bbr6w*bej9gp 2:0;3hk 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 o/6rw 3u-((wj yz.lzd.t sczpi c6+uyu :c x/qobserver on the ground hears the sonic boom 1.5 mwwzz. +3qyr dxu :6. i/o-uy/zjsccl c t(pu(6in after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i g9-1yqjmayvb/u(4 mzs 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