What is the evidence that sound travels as*tdpl gvnma n+0rj 2 9ekbu53av;9c1u a wave?

What is the evidence th+,7o sv r,zlw+kjs iv1at sound is a form of energy?

Children sometimes play with a homemade “telephone” by attachinguxr qfa(l 2v3v *2f(vf a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup,f a2ru2f3vlv (x(f*v q 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 wataevn.)d/3j 0 hn1y nlzer, do you expect the frequency or wavelengthj.1) eza/ynv3 hln n0d to change?

What evidence can you give that the speed of sound in gy*;5t3m2 jlwk+ jte vair does not depend significantly on frequency3y m5klvtg;e jwj t2*+?

The voice of a person who has inhale *:v3hjyndltg gk-5e+2 p av7)l 72ktg sqv.lzd helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitqwosze : rlj0x7jutl,s,9: 5fhsy +2s ch of organ pipes?

Explain how a tube might be used as a filter to reduce thev8ez0*i q:ema amplitude of sounds in various frequency ranges. (An example is ei ma v:08qe*za car muffler.)

Why are the frets on a guitar (Fig. 12–30) spap q5vu.:*ezs0qaq8 4jidp a0bced closer together as you move up the fingerboard to z qvqaijd. 40s58pe qau*:0bpward the bridge?

A noisy truck approaches you from behind a :mt9 x-lc (daebuilding. Initially you hear it but cannot see it. When it emerges and youxt 9(ed-aclm : 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 +of4jod /c tz4;mrtwlu/ 89rq in space,” whereas beats can be said to be due to “int4+rr/q d 8c t m/9zwf4utlojo;erference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin6+;vhlkf- wq olef5 )vts D and C (where destructive and constructive interference occur) move farther apart or closv5el f -q6o)+hwv;kf ler together?

Traditional methods of protn toh(; ;z we*dmf)2etecting 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;;twte2 )h*fe(z d nom 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 ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig.m n lgp.xv31ag 53sr/m 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fgr1v pnasl.g 33 x/m5mig. 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 mwz e*q 1 ,ot2og7mj.luove in the same direction, with the same velocity? q 2o7gwz uj*e,l1to.mExplain.

If a wind is blowing, will this alter the frequency of t, yg 4ce//ppfphe sound heard by a person at rest with respect to the source? Is gp4ep/,p/y fc the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swin2/5tgm7cqii eq 2n5f3wkv4zsedt *j3 g. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, wn574g523qtwciiq 2msfv eztj3 e / d*kill the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of herm1b2j.xf zw+pss/b( vb) : svopo( )ca shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shout(fm:p .bj) s/v()2xszv+awpo c b1obs ing. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterliweb-*w jgt/kq . *loh*ne. 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 speed of sound in seawater is 1560 m/s j q*ek.tobw gl*wh*/- (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengb -ysep,8ch4h ths 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 foggy*5f+a* vbls f;u7xbf v day. Without warning, an engine backf +7*ffa x5su*v;bf lvbire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes le1hxgp4g-( .s4pl scwhen striking the water below is heard 3.5 s later. How high is the1. ss- phpc4lx eglg(4 cliff?    m

  A person, with his ear to the ground, sees a huge stone strm2 rd5ch+( ryqike the concrete pavement. A momentrr25dmqy +(c h later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile o.4;bi(t 4nox aywsv3w(no3w df distance by the “5-second rule” for estimating the distaso434xn.;o (wbnvywwt i3 (adnce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dBj ukmn,3;hv slc n;x:*?    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 iscfbk.j 6w032zy hiai6 $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelvg,cf8kxtzv2 t/: o*p9x qzc9 of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’sfcqv8/ :9t pz9z ,k2xt*gxcvo.]    dB

  A person standing a certain distance from an airplane with four equally noisy je/k k amzj7ngts9.m(u4 t engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this perso.nt( zk4uma/mgj7 s k9n experience if the captain shut 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, whereaealse h. 8joidd*0 lp7869jyts for a CD player it is 95 dB. What isalj8e 6y.jhli0o d7*9 s p8tde 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 sound from a person speaking in normal coy9;mrj q -i49lb z9wzknversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the moutq-i9 k ;y949r lzmwjbzh. $\approx$    $ \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 earjw ip lq ; mk) 5z,f6+i4og+gxh3jhco-drum 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, 6,czte tz2uema0qm b , ih1:n8while 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 ahqz 2,6 ,bmmni1ae0c8et t:uz 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 mh+cm)zge yhmwg7,+ 0p in front of a loudspeaker on the stamp)chh gm7e, wz++ y0gge.
(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 p(y. ,ax1)bp phz g35gegx+ z,5gxmm tsound level of 2.0 dB. What is the ratio of the amplitudes of z(m +xzx 1axg) g3y5mp,p.pbt5geg,h two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by ny1 zd+tt2-nkwhat factor will the intensity indn zky2t +1nt-crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displac.jo i 8svrvjuhi3/ 5k*ement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitie v/js i*3.5jv ihor8uks?   

  What would be the sound level (in dB) of a sound wave in air that co)w2 :mhsc+hc jrresponds to a displacement amplitude whsh)+ccm :j2of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wpfvyzewxyaaq:avmb:o g9 z * /,t792,hat sound level to seem as loud as a 100-Hz tone that has a 50-dB so97yaq,a/z*ma 9go v2 wx fb:zv, ye:ptund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whe 5)hco-nsj: )bwl nm,1r etv2dn the sound level is 30 dB? (See Fiwn5hc es)-vdr, mj1 bt2)l:nog. 12–6.)

  Your auditory system caeqls7y m :d 4a4bht1n(n accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity atm1qdtn( h a:bls7ye44
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fu m+v o6yxtyo kfz(*j+0ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the striny0fvko ( *jxm+6t +zoyg be placed?    N

  An organ pipe is 112 cm longja h l /j/b72k7vw7kcd. What are the fundamental and first three audible overtones icj jbd72 7/k 7l/hvwakf the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of a(l9c+sm6 yu ncn empty soda bottle that is 18 cm deep, if you assumed it was a closed tuycmsc9 (uln+ 6be?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pbsv- 5f3ezfsjmg-s -6 ipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be theve5fj- g-s3s bfzm6s - range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What willl*r3ld a7e fm9;wb;dp be its fundamental frequency if it is fingered at a length of only 3le ;bfmrwlp9d7a *d;60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lw2rn7 y5fg hde/gu;q+;6rg elong and is tuned to play E above middle Cfew;5g67+nld2eury;g/ hrg q (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emitsq6hhxah js6d5s1 v)*h middle C (262 Hz) when th hh )hqd15xav 66*hssje 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 at 20 n )p5v34bld1c grcmo-$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shou7f az* s6:uzdwld the hole be that must be *afz7 ds6uwz: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 resona5:zakv8cyt1e j n*1mvte at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (18jyc:znv kv team 5*1a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at tw-rw;.wu(opu l;j* u-yzi bu -hd(ju a5o successive harmonics of frequencies 275 Hz and 330 uu;j-; l(j*h z .uop uru-wai-d(y5bwHz. 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 (+ ) 0ldb qjxqnffau*pos).u7$^{\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 af83ic4vlsw0*sc4 u.;pac2xls b c7 blre present within the audible range for a 2.14-m-long organ pipe ; cs.0l3l xsba4ci42pwl8 vc7cufbs *at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. I68az wcpn4f43 yody*lvo e;8plc 4v- vt is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing wavesd4 ;e czvoo 684vynacl4*fpl8w-yv p3 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 , 5v03 ytk nep(jf );ij4zpchgadjust two strings, one of which is sounding 440 Hz. How far off ighj5 ,;jpie n(t )fkc3p yz0v4n frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hupcho7v3 v +p6v /jb7ntmmu 5.z) 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 m8/ ,j;y,z b,tvblmppkHz, 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 frequencym,pt,mv ;z b ly/b8,pj 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string producesdm+z-f3/z ei 0jsf f;k 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when soun/+ef z0-kiff3 jsd;z mded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned toj)(3 o rl-+gctxa1wkm 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 play-ka(wxg l1mt)ojr +3 ced together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heaf rmcw5ryxhzb(q)q)aw)8: 8zrd if two identical flutes each try to play middle C (262 Hz), but onm) 8 ywzzhrqb) :acrq5wx)8( fe is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fo1 o2.0o/03bqkui t pwyxbq9 z dst0t4orks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard0 t bp b/ux0ty2q031s9q4o .ikdwootz. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one ss ;zy2fyyn ylfhtr(j*1 x( /l;peaker and 3.50 m from the ;nx/yfjy yl2;*fl y1r(z (hs tother.
(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 a piano t8a 38bn*qau0 rfu zr)suner hears three beats every 2.0 s when they are played together. (a) If orra8uz83*a)n q u0sfb ne 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 t z:bnutvncnp+a, gkj+1ha;owt nz, 4-,q p352.64 m and 2.76 m in air. How many beats per s gn j+ nwnbnakp34 t;-v tp5,zt+1,c:hao,zquecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certa+yt 0dkh /:h x xgmxc2vb,y-9pin fire engine’s siren is 1550 Hz when at rest. What frequency do you detect it vpyxh+0x9xg2d-/ b: ,y hmkcf 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 wh7rmq( ; ff,byd2w q0azose siren emits at 1550 Hz moveyar;7z(0 q w ,2ffdbqms 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 so nd8 -1aarb2q mku+5 )q-bjjyyurce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactlyyb 8qnj- jy5-2m1) d qk+aurba 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. Whe*ov qu3ia8 fls0 (8;q g.z7xd1hhswri n 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 frequency the hornd8(q v 8qiu .x sfw*7 31sorgz;hi0alhs emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 505gl uz9danm:) .0 kHz and receives them returned from an object moving directly away f mga:dz5l 9n)urom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spe46lb -cdo7zq hed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with fre7-6bqcd zh 4olquency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originalv rlnqvvwxe8)n04 ) 8k Doppler experiments, 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 frequency was heard if the train car qv 0l)n4nvw)8r8ve kxapproached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flolxs eazs7td(eymnr:9fdk(x3gsv*9i .:n 9-t w speeds. Suppose the device emits sound at 3.5 MHz, and the speed of souna*x dinl:f t sv3 (dx(yset9kz-grn7.:9ms9 ed in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrado s6fyt) -oo/5+l ksmsonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity y+ 3t 9s(akknris 12 myn3 s9t (rk+ak/s from the north, what frequency 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 onquhzii14,nc9g qce (. a8:ltr 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 1qvkuqca+r pw2s8 wg5 q3a, m6the speed of sound is 310 m/s (a) What is the angle the shock wave makes with th2wg+c rau 6spk,1v mqq8a5wq3e 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 rq4ciqjua )esfzn;(p,3c:;tzr6 wp7 planet where the speed of sound is only about pzsriq pzwn;(6 ut :c,7ca;3)ej fqr 435 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 oceand-te j 2czsun45 .lcw/1 f1atf. Determine the shock wave angle it projn-d25fa11te4t l.s cwczuf /duces
(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 .ik1t47pfkj c$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan.gwh/ +lf(lvllju5 d9s,;ht fe exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hg us/l+jltwhf l;9v,d (fh.l5ear 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 xpp:rmp 17,g ssonar device that sends 20,000-Hz sound pulses downward from the bottom of the brxs :p7ppg,m 1oat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how mayv1, lw(fe5a 9 kpamf+ny octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. paz9r9o3 r1i5* tsyeu It consists of many plastic pipes 9u5*3oaerp 9zys t r1iof 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 person makes a sound close to tlw;1sr/t q rs3he threshold of human hearing (0 dB). What will be t;s/s r wtr1ql3he sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound acy :.2m aq,z8gybp2ahre heard simultan2y b. ,zpa8am2gq:cyheously?    dB

  The sound level 12.0 m cqyox(1xq 5h8q(zc t: from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equallczqx((tx qoy8 h:c51 qy in all directions?    W

  A stereo amplifier is rated at 150 W outputgf4kninqk. ,0 jb/tg23co l s596nxq9 oi) nxi at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts 2i 93b,kg64/9qt q)xjnn0n g kfl5ncoxoii s.at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earjyh) algshbckzp:q;e a 7dka01,5 *p4s. 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 the power intercepted by an unprotected ear at a distance ofeha 4* ybjc7p h;z,a)l1:s q5ga0kdkp 30 m from a jet airplane engine?    W

  In audio and communications ,xqb3/2c drspx5h x-asystems, 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 rqy*o)plnv/ 8 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 -bu0;r zte+d ypoints with a fundamental freq -;zue0t+dr byuency of 440 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 i,0k +zb+v re )qzbe6b-u9irennto vibration 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 lev)eb 6 n,0zueb -+qez9vibrk+rel 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 near a tube tuji d.1 ck4aw7yio7 )lhat 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) with th acijok7 1u)4i7 .ldywe third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as)ip-;y dwl3 rd9sda jpa3bm7 + 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 sources.0-89vheuc nr v The sound is loudest at points equidistant from the two sources. To detervcn8eu9r- h0v mine 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 trv nv70to2ki se5i8gd *ain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. W7tv8ok eivid5s *n 02ghat is the speed of the moving train?   m/s

  The frequency of a steam train whistlu )hl -,q(mjyle 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)y u,q-lm( lhjonstant velocity)?    m/s

  At a race track, you 9yzo nr+k31fd1i d r+0xmuzz-ppi u33 can estimate 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 halknfr 31+uz op3dx+3i1 urzyz9ipmd0-ved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounda em) a;kcc*v5ing together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m longc; 5cva*)ake m. How long is the other?    m

Two loudspeakers are at opposite ends of a i7k ca6zwk,t-railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, wh i-,tak7 c6wzkat is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the 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 iskwf ozn(i(1y6 normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves weyfw (kinz( 6o1re 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 is flying toward nlrbfuky d 5w,,tu-55the 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 ba , nwt fyd5,br-uu55klt after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sogd3 ovkmho0r0a) ,8qb7/ wnjdund pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far a)obodqw7 0,ajkmg0v8 d/hr n3 way can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine v ,yi r8n)nobfhbi-3(:65pk6 pb pvvlzillage to another. Since lower frequency sounds are less suscept vp ippk n:r6zvy8 ioblh-5,()bnf3b 6ible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromis(w kb+ r)7scox glvem(r1r71c ed by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure n lo+(1r cr7r17eg mxsc)k wvb(odes. 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, slhm1q+na 0 sz5iender 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 “sing,” or emit a clear, loud, ringing 1zh+inmq05 sa 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 jt968 ep p*gax )ctr+lfrequency of about 1000 Hz is8j+r *lptc9ge6 x a)tp $I_0$ = $1 \times10^{12 } W / m^2$ 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 hears c:zm k8zyu 89jthe sonic boom 1.5 min after the plane passes c8z m9y z:jk8udirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i-v bj2e(l. yiq pg;qx9q(br5is 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