What is the evidence that sound trs g+d 6g ub +.d32+ail88wwb/r+tl,vfpk imraavels as a wave?

What is the evidence thao5 kdx(0 mcgwim.p2s4t sound is a form of energy?

Children sometimes play with a homemade “telephone” by att,f 44qtdok 2m9m ;ukpgaching a string to the bottoms of two paper cups. Whdm9t kf4um4;2go,q p ken 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 waterx8lx 2e76gotka y/i:s , do you expect the frequency or wavelength t7 iy6a8s: oxkteg l2x/o change?

What evidence can you give that the speed of sound in air does notwz w9yhysn+88fz cs+q-4 5 h+nk /xpqi depend significantly on fre+ i8c kz/qy +wf+zx -8nwhs5pnq94yshquency?

The voice of a person who has inhaled helium ip/:jxr.je 8k81by5 khzz;;ed1ju9o1p s xjdsounds very high-pitched. Why?

How will the air temperature in a root1k) q+vksnlk u,9k2 /8 zugstm affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of li.6 8m q4nn .wox4htjsounds in various frei8x 4.m.6tnhq ow4jln quency ranges. (An example is a car muffler.)

Why are the frets on e,m0o4 t i)t vhvpj1e8a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard t,)1 t048vp ijem hteovoward the bridge?

A noisy truck approaches you from behind a building. Initial7. e3seqh6s 1-qv zianwyly;9ly you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — y9y iqs;z-nye1 wv.3a7l hsq 6eou hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be duv0iq ezlw 87xl7l+ze+e to “interference in space,” whereas beats can be said to be due to “interference 0zei++qzlw xe8vl7 l7 in time.” Explain.

In Fig. 12–16, if the frequency of the speakergxr*+ yhgisvtx5)7gkh7k3fu: we0sl, cb 2p:s were lowered, would the points D and C (where destructive and constructive interfe+ *5e,u 20:7gl:k)hiy 7ch kstsxg frpwbvxg3rence occur) move farther apart or closer together?

Traditional methods of prot53, l: veh* oq1cmxqqkecting 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 d hkq5 cqmx3v ,qe1lo*:o 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 Fis)tkeij z/.(e+jm n5pg. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12n)ej ptk mz/i jse(5.+–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 in0mjyszfp 3 zl10vj50j the same direction, wi0v5j1zzj 0fy lpj30 smth the same velocity? Explain.

If a wind is blowing, will this alter the freque;t3/: lo hnp3o/ qzqgoncy of the sound heard by a person at rest with respect to p3tqgo/3n lh oo;:zq/ the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chils-7y 6)e-mkrfvlokz 1*gp *)4 cc aahnd in motion on a swing. A monitor is blowing a whistle in front of the child on t-76y*lh) envpk* -kf1ro)zsg4caam c he ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines thxw5f3y14wh6 wt + iy *uvwwm3we length of a lake by listening for the echo of her shout reflected by a clw461t*huwwyx+wi5 m3 wyv f3wiff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shdqq2nq ix8i 1(9,3l dnxirxf2 ip just below the waterline. He hears the echo of the sound refin x2df 9dxxq8(21n3iq,l iq rlected 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 wavelengths pi c1c ;n nu5e/+mxgt(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 tun3*xo p(whk6hdp 9nb.na on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time e.knd*(phh6 9 poxwnb3lapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cukyb(as ; wl2lm 0w *,bg-k*ifliff. The splash it makes when striking the wateswl f(k2;wgayl -,*bub*ki 0m r below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete prh(qfl;w 8n 1pfoh57 uwg:x,aavement. A moment later two sounds are heard from the impact: one travels in the air and the other in l8f :(forhpwgu5;qw1 7xnha,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 +slq es pn1k88of distance by the “5-second rule” for estimating the distan8ns +1 lqk8spece from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sh-w( tr898c0)ublbz-q2oqxza fc sl( ound 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 intensity m ck e6kr28;y+u(vnro is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousl:*o onf1vz. 7 eiy-oajf 5pa.ry at a certain place, whatf poyo7r.o. aie-*nf15 ja:zv will 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 with f )e(v-zplg u,per/0egour 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, not dB(e0e-/ggrpl p )ue, vz’s.]    dB

  A cassette player is said to have a signal-to-noise ratio o9p u-qd9ucd) vf 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the udp- uq9d )vc9background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal ,)*o-0f kkltdf2laf -t9ji9kem *3sp+rqtwkconversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered*wl-k+-9ffp3 k m 9lr0 i)d s,kf2q*tteo ktja on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose areaq o4vza/ )1ayf 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 aktdt ye(; b5;omplifier B is rated at 40 W. (a) Estimate the so;e bkot;y 5d(tund 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 1xp ,k91kb)fq .ra aox/pgi gctb-57 2w30 dB when placed 2.8 m in front of a loudspeaker on thexo , gg9) bp wi7f pkqa1/.r-c2ax5btk stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of9bgn(,af- r kal/oo6p 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Secb rnga,9kpo( /6-alf otion 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, ( 79sknioy +)xip+0crta) by what factor will the intensity incr7t 9 ci+)ykxis o0pnr+ease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, buu yxp729qcbgpp-r::43ofz kdl3r ns /t one has twice the frequency of the other. What ir 4qpcg73so- l9:fp/y rpdxbu kn2z3:s the ratio of their intensities?   

  What would be the sound level (in dB) of a s+i+x wjt)a-ebound wave in air that corresponds to a displacement aj a)+-btei xw+mplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone t/5h7pn ( dm ackas :xi e1l*ag72tdu3dhat ham1xle:dpaun2h(g s7i*a 3/k7d atc 5ds a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the 2dji;e:et*e actk4r)sound ledkr)ec *t2;at 4:ejievel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommonn4hzd0ofd 3 /date a huge range of sound levels. What is the ratio of highest to 4 f/ noz03dndhlowest 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 y gchr.+wk24 yhc8mv v*4w)p8 g 4joocgqh:b5a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Underjo +w4 2485r:p.yg)qhbgkmc4c8v*gh c ohy vw what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental asx/woqe ;j w(*nd first three audible overtones if j*wxe /qo(;wsthe 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 mkx8yc ,qx5as kv ycnq j0iy)7d99s(;1hye 2wwould you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if youv7)hx1k,59mc8y swjs0 2 yqyied; ncxy9 a(q k 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 spanning the range o pzu;0bk8pw; )muigq- r9rrvn8 w4 4nwf human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requig;pqwi 4v u-)0npr8z8rw ku4 m9nrbw;red? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thi+ lhl o8yn.tc,6jblf.rd harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origina6ly+hf,lt c..8 noljbl length?   Hz

  An unfingered guitar tuz0hi: nd 1h.5y jaruz -.bo8 z(ek,nl uo,)sstring is 0.73 m long and is tuned to play E above middle C (330 H,8r- nsh5o(z oe.. kz0,nub h:yzli td1ua )ujz).
(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 pipfi1a2ffs,50 z0 f 2ozzi4xjbhe that emits middle C (262 Hz) when thisz2zo xb5fha0f 4f izf120 j,e temperature 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 ah;mn5,:jd0.b aibmb rt 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 E c0k*k1go*tspn/ :a rnxample 12–10 should the hole be that must be n gna/ko**kt:10s rcp 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 can resonate at 264 Hz, 440 huqv*h+ r4kls( nc5,eHz, and 616 Hz, but not at any other frequ,5ulqkhe *ns(hc+ vr4encies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.+9ebbq6bkah-md)b,0f s . wvao r)r+v80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What k bqde6o sarr.v,-9fvw0)h ) bbabm++ 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 3sgy d)p ;-ix/xjgua:$^{\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 w .)fhjo8,x1u 9tv,ws6afyns audible range for a 2.14-m-long organ pipe a9js8 ,a)sw fwtfu.x6,1vonhy t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open t;dwxax1a: 0bqp :ggm i/h0vn,o the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing0 ,pgvai;0 1b:xwhax:d m/ qng 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 to adjust two /+1rdk hjoj); /ea1*l baiascstrings, one of )+h /cs1j/;b *o ae1i dlkraajwhich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 H/ rbl/x sof,w y:/sa;vz) 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, whil*hsrb +p ,)anbe another (brand X) operates at an unknown frequency. I,arpsb* +bnh) f 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 frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wjo,*/1scg9gavj46 h ijv3l bd ith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your re lgvobg634i / 9hj d1cav*sjj,asoning.    Hz

  Two violin strings are tuned tzd/j 5nr ))c)ssks)wh o the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.] 5z)s /s)dc kh)n sjrw)   Hz

  How many beats will be heard if two identical flutes eachdz.b rxlfw9 gk5 f+1)e try to play middle C (262 Hz), but one is at 5.0°C and the otherr x)wf5fglde k 9.1bz+ at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; when;n lpbi9 c,c.hqvz y(; A and B are sounded together, a beat frequency of 3 Hz is heard. When Bl;c;yv,( zc9q b. nihp 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 from one sbkxsl/*n miw)oypfqu (0(7l d-q 0 .lqpeaker and 3.50 m from the o(s/ (p0dxil b7l.l)0 *kw unqom-qqfy ther.
(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 supl*ld8cru ca3ifp. yo fj4070kposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they ar0*dlioak 3847cp 0jlyfc .fure 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 0xh+(bstyju25 )cjtg . How many beats per second will be heard? (Assy5c)+ b2 xhttj (sguj0ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren i0whd4wk4 h hx,s 1550 Hz when at rest. What frequency do you detect if you move with a speed of , wh40 h4dkhxw30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engi(ogbk/*re iuaa)b9 rk1h)d 4nne whose sirenu9/4g1ade)kh *ari)rbo b kn( emits 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 frequ ;))bu*;kfghg sof,jwency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Arehw)k;ggffoj;)u s* ,b the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are e64zhmjyl .fd4 quipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequen y.dmzf6 44lhjcy the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soundjr,7v lbkc ;9h waves at 50.0 kHz and receives them returned from an,krb9;hlv 7jc object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, thi: ;c. 8vikqvye bat emits an ultrasonic sound wave with frequency 30.0:.iiyqv 8;ckv kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wahg , r)j;,mh0e sxyb.2p; onhgs played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of ho me ;.,sh),;pj x0ngr2bgyh 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. S1wfs (peio5o2l 6buu 7uppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is takenooe1spi5w2 7(lbu6 fu to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of f hq*qe5 8tud;orequency $2.25 \times10^{ 6}$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 sztvp y57vb5ydspzq 4 s:*b7 j.ound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will 7p v 7bbv5jz4.qz t:5 dp*yssyobservers 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 objec21xqi/zs n0k xt 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 sound is 310 m/s (a) Whag/:e c*b w+ txb)hrv)at is the angle the shock wave makes with the direction)vbw grh:e) b+a/*cxt 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 speed of sound, -y.q ;.rt0)xolkz zpzezi f; xux1,l is o upr-ex)zk y0z;o;xl liq x.t ,z1f.,znly about 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. Determine the shock wave a.2khhfo+ jd(3j)z 3vixcb* ec ngle it h.od jvf 3b(k2x)eh+iccz3 j*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 3tqg ,e :rm2;t-sfoo t$/theta$ 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 t2lr) isig(3 zzn1 qua0he ground flying faster than the speed urs(201azzg ilqi3 )nof 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 20,000-Hz soulm h uo;5u 8rx;kdm79cnd pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to kxr;7omc5l 9ud 8 ;muhwork is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are ther,sh gd(eij.+ ymj end6(x(69f: kfji de in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displav*ppc76arrhb5v ,r x) y called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both endsr p,xvc) *pvbahr 6r57.
(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 thresc d2r xk(s2m9zhold of human hearing (0 dB). 9s 2dm(r2cx zkWhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound a9k.t3n rm v584by+ yj plic7vgre heard simultane9tb.mj7k gipnlr+c 5v 4v8 3yyously?    dB

  The sound level 12.0 m from a loudspeaker, placed iul7tf 7+sy +m6 4 0twy1bjkeu+falc(n n the open, is 105 dB. What i0tln4+ ftkcb1(7s 67 a ylu+mweu f+jys the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1002 e ntq7h.u)pnqn3 v3 u,ql6ac0 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in t.cealqpqvhu67)n u 23nn ,3qwatts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices v:wy y*y .3p+uyr j9cwover 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 earyy. +p9yw:vj rcu3w*y 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, trfl 9l.1mf ne84lc9mq he 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 d 81kro1- 4cs/qrtw tvtuned 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 fundamentalga0n25g0 x 3 pyd8z3qy;f psdg frequency of 440 Hz and a ;n dxy 3qf0 3y pgdgasz80p52gmass 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 vj-:a(mzbb etg9tsf t6 8b ,ya+ibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m an+ 8bte-s:(ajt9g atbzmb6y,f d again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is qkq4sldcob 6.x *ofkn5+9e 2 wg1du (lopen at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamenood qw.b (n2lek 4fu5x1+qs l6 kgdc*9tal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obk wkz9jb p3bm7/h yulus*0.) gserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the8l)- k* afzd xfz(/cfh 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sourcf*8h-fx(dz z) fk /claes. 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 source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor oef:;wbecis) h 1 2so1jn. lk-en the stationary train hears a 3.0-Hz beat frequency when the 1e)sh 2e1w :;sckenoil bjf-.other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whi(cxw j.wstmua7p6zyx;oh,m f )d *(:pstle 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 c*x ; (fy j mo,7)6spmhu.a:cxzwpdw(tonstant velocity)?    m/s

  At a race track, you can estimgzpu4 flcz6hxd/w / h,mhg0a51 m ;lg/ate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on tpcu5ll d;1/46zwhg /xfa,zm m ghg/h0he straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of lnniy (11zn ;p jv*4il iewt2;11 Hz. The shorter one is 2.40 m long*vw4 ;tpyn1leli ji12 (;ninz. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past lk;useq: r; ci3;h nj2vv6h4pa 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 3plc 4hvh;s 2knvi;:qru6;jeobserver 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 aommt+n+wp4c2 y5d5w21kmgbjeif. easf6 /i x5rta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel witf 5be 2cm+2/fadnits+pwm e yw5. 41imx5gk6jh a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whilekuu+*d n,b1ofx3f 9*qz ntdm; the moth 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 rd fod3 *b9tn1znmuk+xuf;q*, eflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a,)ewz0mphl o 6 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 retw)ephl z6,o0m urns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from r bci 01juhw(+one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used (i01wu hbjcr+ to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listen8n6h(tpju ( suevf/t/ing can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locatt/(fpsu ntu6/ h8ve(jions 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,” involves a long, slender alurf)vgph6ncgz3kp3u o:d ) qx.--cd q -minum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little pracdgc-)nu3q r.ogc vk 6pph:x zd-q3)f- tice, 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 ear at a frequency 2s8lmnv 7vu3 vof about8msv2 vln3u7 v 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 the ground heai:e6d,ni ylr ,rs the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitr6i, indey l:,ude?    $ \times10^{4 }$ m

  The wake of a speedboat i ee44c+tk;zqm lg;wftq8sf0yb /t((l s 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