What is the evidence that sound travels az7m 9rz j5itg:s a wave?

What is the evidence that sound is a form of en 2idfsoux e64*2mt n.nergy?

Children sometimes play with a homemade “telephone” by attxo : ;yacbt9d0aching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one c 9:b0yodax; ctup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or44 aw0 jos+loi 0ba(vh wavelenw4bavols ji 4oh( 0+a0gth to change?

What evidence can you givevrtr1 *hib. ) vp0py(f vd,vj/ that the speed of sound in air does not depend significav,vipfd/)rv*rp 1tv0 . (yhbjntly on frequency?

The voice of a person who has inhaled hej)v0/(( cc--tlzbybz8 q eb ielium sounds very high-pitched. Why?

How will the air temperature in a room a tw+ -rt/zby3) xsg:ggffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of souu/t p)il*j symb*i9g9;i/gl) f5v p ipnds in various frequency ranges. (An example is a car m)5*;9 yt*pj)iisfb /gilgump/ i pl9vuffler.)

Why are the frets on a guitar (Fig. 12–3 r,ap(hloa0y ee84a*im ) bn1b0) spaced closer together as you move up the fingerboapeaae4n oyr0 8a*l1m b i(b)h,rd toward the bridge?

A noisy truck approaches you from behind a bui 0idzt5zsu81m rc* yr+lding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explm0rz s cuz1it85+*y rdain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to.7sy e7s( htz st0ai1kzk947cdgvv -w be due to “interference in space,” whereas beats can be s vv19 w cdst4hkz0(tgyi77s.ae7s z -kaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowerghjez f; kh;pt f8snh*:k x;v)n7*ib. ed, would the points D and C (where destructive and constructive interfeb)h7;.:fhgts* e8p x; n*kjzvn;kifhrence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who w6n/ wip2ifmb,ln e) 8rork in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphompn bir)lwen2f i86,/ nes 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. 12–3h1gbb.:9c l +ttn9a rlbf 6/ns1. Each wave can be thought of as a superposition of two sound waves with slightly different fraf/tl6nct bbnlr9. h1 : 9b+sgequencies, 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 ifozy2q zf4c/1;l (ud7o7u4 1 xpvbryxf the source and observer move in the same direction, with the same velo17f/4yz f dpxv oocrul2ux1;zy74b (qcity? Explain.

If a wind is blowing, will this a hd, :obkfj+q,1rbp t (7dd;xwlter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or d7q :fkbb x ;w(td+1rpjod,,h velocity changed?

Figure 12–32 shows various positions of a child in nof3u7cd70) ho(a tx(a ysxs9motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which positio93 o0x(t ssayou) 7anxf7 hdc(n, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines t6wg0o + k8r1ehnhbxbiyr:gxq z ge:x3;29kf ,he length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the leng+z bgkenx :ewbrfx:g168gx k0h;oh32 9qiyr ,th of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sii+( i ny 3nhassnnq+vm0ufjasd 2/,8xpp8, ,q de of his ship just below the waterline. He hears the echo of the sound reflecf 0 8nn+ , s/pda3xvhsp8mq, ,iuny(qa 2+jinsted 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 in air at 2,co 6ulk+.atj0 $^{\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 foggyq0a au/o81c uzu j7da/4g/ lxf day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapsc40a/u/z fgu7x8o jda 1q/luaes 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 ;i tork0 xypvu 638vm1splash it makes when striking the water below is heardi xp0v;r 1moy3vtuk68 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grounq p- rvf3r7m209 ib3g r+sqkc g4lrz4bd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from -+gfic04l3rrv 2pgbs3rqmz9 bqr74k 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 errofrm0 zfny)cgbc i02b ki(p39.r made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strikcg9z(n pkf3cii)r2b y0bf0. me if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain l t;whfjt3u 41+.iytaqsu5u g;evel 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 inte07ite 9lt6g/5vqm 6 epz racl:nsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired siz gkyj/cez.b)0qf2ysl+8tj 6 multaneously at a certain place, what will be the sound level if only one is explz2ekzs qy8yj/0+ l.6tg)fcj b oded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fokvdph3c,ff i*+0gpq 4r,00.tz ecbf aur 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’s.] ,bctkpd vrf 0zif*aq.ep0c30gf +,h4    dB

  A cassette player is said to have a signal-r1nhr-;pd* z:rztbz (to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the b* npt1rz- z(:rrb z;dhackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakingdq9 vuwmq-:02tklt3tm,mk4 c(,wsx e in normal conversation. Use Table 12–2. Assume the sound spreads roughly49m3s duvt t2 :tw0x ,klqcewm(,qmk - uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave s dy2c* 2 /fdn;ej1ixaqtrikes an eardrum 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 rate 1iku. 9p.emvzd at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you woulzmie9.k 1v.pud 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 methd/we 4pt;vu :j46 bea,tr2vzer registered 130 dB when placed 2.8 m in front of a loudspeaker on up 4t2ehv:a6te;zr4j wv /bd,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 level of 2.0 dB. Whau7m8 htcnv xk25xii( .t is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11 tk.h2vn8mcu x 7(i5ix–9.]$\approx$   

  If the amplitude of a sound wave is triercwbhjwq.me jbm5m3q5 t-4 g cw0685pled, (a) by what factor will the intensi qqgw wcb m53j54-jec6b05m 8re.t mhwty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement a*6+mk+hfhqrf;ez4q n/ xb 8 upib2hl23hm 8ygmplitudes, but one has twice the frequency of the other. What is the ratio of tbq8x++2;i g3pqf8m2 /hmz6nf ekulb hrhh *y4heir intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspy,/y9ttvh0 eng8rn2 ionds to a displacement amplitude of vibrating air moleculesr8n hegti2y0v/n ,ty9 of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soug yi3nj7) jtaxa 1w+/sgcs;7bnd level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (3a sx/jija1g7bn) +7gtcyw ;sSee Fig. 12–6.)    dB

What are the lowest and hduxq,9anp70 nighest frequencies that an ear can detect when the sound level is 30 dpn uq0dn ax,79B? (See Fig. 12–6.)

  Your auditory system can accommodate a h m )ky6l4.zadmd /ps+cuge range of sound levels. What is the ratio of highest to lowest intensity apl / dmcyakms.z6)+4 dt
(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. Them8dsl b-i2 0uj1bo0 u*iof3m n length of the vibrating portion is 32 cm, and it has a-d s ol*bi3m12obj iu0 n8f0um mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundj75 b0p okj5nqzbo5 4hamental and first three audible overtones if thbh55 45j qznjopkb07o e 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 th98kcpyi4-1 3v awpb she top of an empty soda bottle th-9 3v ap8iskywc pb14hat is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ wiirzq vmt82t9x (a b/w/t(s*ubth open-tube pipes spanning the range of human tq8t/*ma9ir w( sutzxbb2v/( hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5x72mf 1gzc fa740 Hz as its third harmonic. What will be its fundamentz gamxf2c 7f71al frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string iq) ar(75f pp sc0ux9v:dkzp7gs 0.73 m long and is tuned to play E above middle C 0uz pvs)c7:kr p(d9afgq x7p5 (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 emits middle C (262;qnk h+3/grftsvn 4( l Hz) when the temperk;( v3 ngt+nlsr /4qhfature 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 g juc3b3r58gb20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be tha n witn7.fbg,*25 iccc xk5h-ct must be uncovered to play D abotn cgc7h. ic*ciw, f5b5xn-2 kve 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 reso 5t-*.ppfje fxu ,rq7mnate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betw-j,tq rme .p*p75fx ufeen. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It 0b fa*6m1gactresonates at two successive harmonicb61fact mga* 0s of frequencies 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 jk yeeb2uz3j (,tl* +t$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-wq 8 ito51 rk4wyt4x*u4szht,m-long organ pipe a5qr,y8t txz hiw4ok 4*w1 s4utt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long0u+u.ll8 6ee.slx-le o/hve c. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequenexc le 0/+u.v8.s-lo lue6 helcies (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 /2)yxmuee;.n v,g ofa ) ryhd,beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How fa yv, ).;m/gex2na) y,rouhf edr off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C jaw 0:9bawzdodd cybe3 fy0z4 3*1f )e(262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (br qt; kutfzy2th4mue ;./3c+b dand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separaq k d4;tb ez3+mu.u ty2hf;ct/tely, 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 4ocfg f-a)x/0c beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrafa0cocf) /xg-tional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Tp ;r/+:684hyhcqqzuzp cb hmv1 mr,2ehe tension in one str h2;muhqe4p6qzzb,vc1ry8c/ m+rp : hing 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.]    Hz

  How many beats will be heard if two ident:o 0trcaoq t6h c;/j,fical flutes each try to play middle C (262 Hz), but one :o0trfa;th,/c oqc j 6is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning for)ze- jpdfs)p,xb u qj2xa 3e7;ks, 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 heard. When B and C are sounded together, the beat frequency is 4 Hz. Whaxz2fb) ,)jj sep7x-d p;3ae uqt 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 arevpr.t6nhkb 2bm+/e.e 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the o e .rk6 b2t/.vnmpehb+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 supposed to be vibratxeaf*f 7xuw*:q/pp a 1o7mo(cing at 132 Hz, but a piano tuner hears three beats every 2.0 s when thef**pw7 7cpae/f(m uo: oa1xxq y 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 indj wqyr0f9tqck0+ ( ,j air. How many beats per sek j( 0df9rc,wjty+q q0cond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequv +spkcb*1c ,si;c+ yfency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you det 1sccv ykfi+b c;sp,*+ect 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 ifb)exk .p oee/8 2yl0jm a fire engine whose siren emits a 0)o .belyp2/exk j8emt 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz+ q8yrem p-b9q source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly-qqy+r8 b9mpe 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 singy7vswa jv1tq5vo p 4()le frequency horn. When one is at rest and the other is moving toward the first at 1vovw a(pvj74qts 5y )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 ultrasonic25fbc tgn)b2cv + b )hgnhv*m6 sound waves at 50.0 kHz and receives them returned from an object moving directly away fcbf n*)htb)6vg 2 +n2 cmb5hvgrom 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 Axhm,or9 unc0/jn qsg35p*82l pmgr+ts it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What 2+8q xlrrpgn 3n 9hpc,mt m*s/ jgou05frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played ot1b/ 8lf .da 6+y4yw-i 9jxfi w5rqtbon 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 10 m dxqwtaj1f+.f wby-b46r 5/l ioi8y9t/s ?   Hz

  A Doppler flow meter uses ul3zd 3v9:ke wwqwb0 u3etrasound 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 flowzw933k :b3duvewe0 qwing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequedotsu7*jcb9*vd7+ i na84/ jkmj 2byincy $2.25 \times10^{ 6}$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 emswww1v9zi+8ewx(sl shq;v :1its sound of frequency 570 Hz. When the wind velocity is 12 m/s from the+ hw(;v8q1w s :v1exls 9zwsiw 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 on land if its speed at u;a w50k ),vy+tmmvwn)pzfz 520 $^{\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 zp p3w 5nun. (reut6aofd871 l p4t/itspeed of sound is 310 m/s (a) What is the angle the shock wave makesdw/upt 4e13pt(rno5f a p7 8n.zilut6 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 it7y7b7 njxre0 65n6a d sike2phc7k,the thin atmosphere of a planet where the speed of sound is onl,byen6 is7r0aed7 itjcp6n2 57khk7xy 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. Determin bkq:37klu+fi e the shock wave angle it prod 3bfikl7+q ku:uces
(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 ij 7s8-icw iy0$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the groucs4tkaq0g w 7 gn87a.bnd flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–37.k7bg4anc 8gs wt qa04. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound p1sas) ( n6ietsulses downward from the bottom of the boat, and then detects echoes. If the maxises) (1atn s6imum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human(6vt xmbme ijj00s 5,e audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of75zy0yx(a,d3wf diw d many plastic pipes of various lengths, which are open on 7( dixwd0z3ywad5f y, 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 3,ivs q2 3wjdkmakes a sound close to the threshold of human hearing (0 dB). What will be the sound le vjsi,w k23qd3vel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 8,tsv*3bj7ikkuuei :b ) op2 w67-dB sound are heard simultaneouso2 ikspe:uubw 67kb 3)* t,ivjly?    dB

  The sound level 12.0 m fromozw wh +ntc3,8 a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output + hz now83,tcw(W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Tg0 7 fxwdgy8t 5-nk15 fla*syrhe power output drops by 10 dB at 15 kHz. What is the power output in watts an1lwg dtx8 kf5y5sg-*0ray f7t 15 kHz?    dB

  Workers around jet aircraft typically wear prot-tr7op w+rzh;gwmfs4 f 98qp2ective devices over their ears. Assume that thp m7h sg t+qzw-r9wf482f po;re 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 of 30 m from a jet airplane engine?    W

  In audio and communications66h lrpnyap+l +bmz ud/9:uk7 systems, 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 frequency 1k)jl 86 )s.ou c1mfaiue:ra(f $\frac{1}{2}$ 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 wtp/u s5z.0l cpith a fundamental freq0/pz.lt uscp5 uency 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 into vibration above a vertical open tube filled wihbi+dzzxgob d-*p 5/)th water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What io5h*gz)bdb -zp xd+i/s the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one ends1c j+q6c7 hcv and also 75 cm long.s7 1+vcjh cqc6 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 reso)da(w; gk x5o+is,stla,r 9u5foxr7 gnate 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 fr/f jvqt*4 mescf 756fqom two sources. The sound is loudest at points equidistant from the tw /v5fqfjm* f6tseq 74co sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train i.j6e(ntr/ gdks stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train tg.6(r jkne /dapproaches. What is the speed of the moving train?   m/s

  The frequency of a steam ed v** z4wizi:train whistle as it approaches you is 538 Hz. After it passes you, its frequency is meazvz*4w* id:e isured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lisjweeruoo ojz2 ;0+; rd/gjrp6e6c7l2tening 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 (frequen6rj+edr;; r poecgoeow22/jz 6u0l7jcy halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes jfv,xcxs seo8v.-(+lw3ko, o, sounding together, produce a beat frequency of 11 Hz. The ,lveovwo so,(x f+- 3j8xk s.cshorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it midm)v3l7 /j; bz-t,wwdz 2 htioves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical som;t z ,ij7v/ t )hbzddww3-l2iund frequencies of 212 Hz, what 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 is normally abou z p5c6- vnouv6k s9rfq5l,bn7t 0.32 m/s what beat frequency would you expect if 5.50-MHz rozs-56c vbvl9f5 p, 7nnu6qkultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 ur yd2 ;-.0ht sjl1trsm/s while the moth is flying toward the bat at speed 5 1 0st;srhl jt-yr2.du m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sou rm,fzcufj+ilz3)+x2 nd pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted)f2c mu+jx3zf+zil r ,?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals j-.oy o eivtrh(e o9:8from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is cal-.iroeo ot h9 (:8eyvjled the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised /,9uxbi ;lbfn2ov 8:n t0;lo mfy2bezby the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Clb x;e,i;t/zuo: n2vy fb0o2mnb8f9 lonsider 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 gqt):xnh 6q c3rods,” involves a long, slender aluminum rod helxg h:c3 )qntq6d 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 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 rij76f dobak1(r2 0.al:acwzhuman ear at a frequency of about 100d1(0c :7wkra a 6izbojr2 fla.0 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 a/gs, ah* hbu*the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the p** h ua/gabhs,lane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ik:arx:)tg g5 00l gzyds 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