What is the evidence that sound travels as a wavgy ye:ed q39dxn s6u4:e?

What is the evidence that sound is a form 1qg29g zxec +zej xdp13,ba /bof energy?

Children sometimes play with a homemad:i it6 9pytl/ue “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly 9/t l:p6uiityhow the sound wave travels from one cup to the other.

When a sound wave passes from air into water,: kyf*w( s*fj+ju 7oifc ozr:, do you expect the frequency or wavelength to cu+ci*of(j: r* fw:f 7ozsy ,jkhange?

What evidence can you give that the speed of sound i;fl+xe frf. g6n air does not depend significantly on fef.g lxr+6f;frequency?

The voice of a person who has inhaled helium sounds very high-pim240 wdaxu m2lnk5f* lc8g 9xitched. Why?

How will the air temperature in a room affect the pitch of organ p of5-o mm3ys:zipes?

Explain how a tube might be used as a filter i k:ce (c*,,lmnnv w m:yp,p-eto reduce the amplitude of sounds in various frequency ranges. (An example is a car muffleiv,p,y:nm -:*(ewp ck l ,cnmer.)

Why are the frets on a guitar (Fig. 12–30) span p0lu,s9 o7beced closer together as you move up the fin9,e u p0b7slongerboard toward the bridge?

A noisy truck approaches youy)wn;/xy d c/n from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffray)c;/wdn x n/yction.]

Standing waves can be said to be due to “interfe2 vqfh6ro)oux cp)14gpce6; brence in space,” whereas beats can be said to be due to “interference in time.”uq ;) pve1frc62xb4 g6c)ooph Explain.

In Fig. 12–16, if the freqw 2nf m/0q(jzbuency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togeth0q/b zfnjw 2m(er?

Traditional methods of protectinbt2ju (;-yu qng the hearing of people who work in areas with very high noise levels have consis2-qj(tny; buu ted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be tho pdgcz9c94si bp,g7x;q g+*prught of as a superpop9brg p4z+ scc d9;g qgi,px*7sition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in tl nl29u 5zj.ubyf3ok 4nfdi5lw uz )-.he same direction, with the sam5dluob9 -lyw.ujfu53nnil2 )kf4.zz e velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a perojj+0j1 wc3*j wy.plnbjd9t8ua 0w- bson at rest with respect to the source? Is the wavelength or velocity changej+cn01wja -yb*d 9l8tbw.ujp jwoj3 0 d?

Figure 12–32 shows various pozn3-uqyc2/ji x ei7 l:sitions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which pi3u2/ xicyn:7eqjl-zosition, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length o79f c;pqq ,l8 8om syyzqjqa:7f a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the eo 9q ycspy;mj7zq7,fa8lq:8 qcho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echpxt.p -4; c+h3cdu kzp0jjkl /o of the sound reflected from the ocean floor directly below 2.d3u +jclp hpkp;kc - 4/x.tjz05 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 (msz 1djq*b,j 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 /o/uvd rhqt r3kkr;-, tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard dk3;rthu r /v/qkor ,-(a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whehg, gcbda/*nd5 tf1p8n striking the water below itgc1d*p dh8f n /abg5,s heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to thxy+9g7 zux ri 3z4g,oiwf1m3re ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the yz x u9g,irw+g3xzfir1o473mimpact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by t5tnh3qq.-(fu 2n qf n*frl m8 /k;zrfp* ,cnmqhe “5-second rule” for estimating the distance frq8mt*fn fk n/3(- q;lh .r2rc,q* zmnn ufpfq5om 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 thpfewo5roqm/ ; (2+g m(v9kalde 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 intens; r1kuu ;8hpufity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce s0 rwv 4r37gzva sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add int3rwg svvz07 r4ensities, not dB’s.]    dB

  A person standing a certain distance from r -e cnq,pk;- w/.fghtxrrw:y9,5 ug gan airplane with four equally noisy jet engines is experiencing a sound level bordhxy, gprw;,5- :f9gn-c/ue rrqt.kgwering 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.]    dB

  A cassette player is said to have a signal-to-noise ratio ofviy4nu ww zyjsmp4p; r;5+2m. 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backg+zi;;s4wvr2.yy wm4 m5pnjupround noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe8 z3ob 1ad /d1 3r9gixyi7nscbr output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly u1ni dobs r9a3yc713dgbxzi /8niformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum57z5)gx2 mfueb z i4nm whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while m o2j4p* n og*.zuv,vtthe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at av2,o o4 mvtu*npzj.*g point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of a a-5wntm;hk w:loudspeaker on the stag;h:-ak5w wm tne.
(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 differencepot5 *u*ey(ye in sound level of 2.0 dB. What is the ratio of ty*oe* pt5y eu(he amplitudes of 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 what factor f ru gjhvbf7 p*t7n ,im e:1mvjm01(q.will the intensity increase? Inmi,mn(bve ftr1 pf.0 qj *7h17mujv:gcrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have em *visej2/,6 z m(ta whzkjcakw1 4+o(:i)a cxqual displacement amplitudes, but one has twice the frequencm: h(1i c/j6cza) ( *2mzw+tx e4wos kaikv,ajy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a soccm9h e2yc fm0bc(t77hpqa qq:mm7x ; . ai.,ound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm c fqm7o p.qe .:t;c7m achb9i a,c7yxmq0h (m2at 300 Hz?    dB

  A 6000-Hz tone must have what sounttvuh sz5x zbi9*:: v 6v1c)tld level to seem as loud as a 100-Hz tone that has a 50-dB souni59xhstb:1t: uv * )tzlvvz 6cd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wp,o-l b /.adb,+ gg* yukiyg6when the sound level is 30 dB? (See Fig. 1 db- p+ o,*/uggkb.yg,ilyw a62–6.)

  Your auditory system can accommodate a huge range of sound levels. What 895vvjk 4hriwwo;at- is the ratio 9tivj5avwh4r;8 -k owof highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamentaxmznzz7d;u: zp xnp6- ;kwg3 7l frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mas d 67;px;gm zn z-7xnpkwzuz3:s of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What*j vv8v mbbi1( are the fundamental and first three audible ov*ib vm(b8 1vjvertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the tob-hu ,wgfin) zz(gw( 6p of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tub) n gz(u6bfw, hi(-gwze?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe orgotc7of d2x/0+gs b.n ian with open-tube pipes spanning the range of human d/ 7.gfno+0cbso tix2 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 w (*b gahe.8tbof 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingereda(*w gbheb8 .t at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7lc ka7p; 0j :mo18 t)/whtkddhb*n:ms3 m long and is tuned to play E above middle C (330 Htm0 pk1n 7od/t:k;*ah wsm hj)lc b:8dz).
(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 ap9k3-es z*jy44 kf 4mgllcs;1rd*djdjj(k w5 n open organ pipe that emits middle C (262 Hz) when the temperature izd-cs4w5 *lr3g jdkjkj4 e; y mp4*lks(j1 9dfs 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 attj.ynp8 2rz; x 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 Example 12–10 a(n ml76 ;. pfqsy i4uo4*ovvdshould the hole be that must be uncovereipvalny uq *7f4o(ms;dvo. 64d 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 resu stjsmb07dl4 p5a5/xonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an openm p0 5ds atxuj5l74bs/ 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 atcpi2 f n9mv9,zo6u+ zi both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz.ci9 p,z2z6 io+9uvmnf 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 bn 9x,m tk).co$^{\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-m-l+zn4k, sha 0tbong organ pipe at 20s,40t+n hz kab $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately ti+ .*(gsxcos97n t*j. pakkk 2.5 cm long. It is open to the outside and is closed at the other e7* *o+ sj.anxcispgk9tkt (k.nd by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2pz2+/ go:ifze.0 s when trying to adjust two strings, one of which is sounding 440 Hz.zg:f+ep/2iz o How far off in frequency is the other string? ±    Hz

  What is the beat frequency if m haplubo5)iiw(-y ;q *iddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whiletys oswk7 o s;vcttm-)d*a5) 9 another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans whe ty sd5kc*oa-w vtts9;)7s)omn 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 soundedygf- *6j vsgm5kc 2qzm,y,d3v with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is f35*yzmv6 kmyd,,cqggv s 2j -the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. T kidtgmv5u;387gxg.u he tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are 5i.gkt8du; 3uxvg7g m played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tryby9ftw pgr8 w; 9bba6) to play middle C (262 Hz), but one is at 5.9bgw twfb 9ra6;p8)yb0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of a+6l( xkq3kd l;*w+ajcosog 9441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded togeckq9kao3*a wogx; 6l(++dj slther?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stangq( i5yi p:m;mds 3.00 m from one speaker and 35 imp: q;mygi(.50 m from the other.
(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 132a1na ttyhwmii7 0/++l Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of tt ywl+i1 0 i7tm+h/naahe 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. How many beats pezy, s; jzx2d2cr second will be heard? z zc;j,2ysd2x(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren iw+ 5wabopyc 50s 1550 Hz when at rest. What frequency do you detect if you move waob0wp5 + ywc5ith a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What.lz krau9j8gunw3 g6 / frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3ru3gu6 lj 9a8.ngz k/w2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freque6y0l **;xyz wv9dm;pbl kvhl; ncy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it a6 w;y y;lxkpvl0zdhm b 9v*;l*t 15 m/s Are 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 equipped with the same single frrbi/g fu2c3 u75 /vtlg txg mt.cv27(mequency horn. When one is at rest and thebut vm2rfi3cm(77xtu/5gvl tc 2.gg/ other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves a7urxr zes4 )8r hmd;p3t 50.0 kHz and receives them returned from an objectu)rer7 r s3zdxm84ph; 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, the bat emits an ultxrbub;m7p szwej 7)7( rasonic sound wave with frequency 30.0 kHz. What frequency does t wjzx )mur7e;pbs(b77 he bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playedgnhzdr 8kgd.e)fv:v k i49:z- on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played th :gvd z-:r9dv.inkekh8z4) fg e 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/s ?   Hz

  A Doppler flow meter uses ultrv2(ys bd5l0o yasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.52od(y0 bvy 5sl MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultra(z;5vm h znba+sonic 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 wi3t/,j8 a8p kcqrihunwd87/clnd velocity is 12 m/s from the north, what frequency will observers he7kin au dh3tcqpcj8w r,/8 8l/ar 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 20l/-ch.lpe+ ub $^{\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 6q w9g/ qghs+v310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motio9 q6 gswgh/v+qn?    $^{\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 tp( yro)c//)y zl vuc8cpe b5qja2dk 93hin atmosphere of a planet where the speed of sound is only abo vly/dy 95)cuo)z c2pepj(q/8ka b3crut 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 strike9eu .kch(maj w rk(/f0s the ocean. Determine the shock wave angle it pru kfwmeh0 9aj(/kr.( coduces
(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 gnc- hjnxx1h 63vv*r :$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pla/ ap,a6e y1kbn3njqxq; (qk+lne exactly 1.5 km above the ground flying faster than the sp/3 qap(+ jq1 eqx;,nbk a6lkyneed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pul( 7f9+ r5wr lgat oii17luux8wp6brp*ses downward from the bottom of the boat, iof (7upual brw l r+9ir w68*1xg5pt7and 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 many octaves are there in the human au;km39)aw;7l yqsctw+w j v-n cdible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manyt(- mo +y8ljkr plas-ty+ ( jlo8krmtic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a fsx0vd 8*4 -b mxw)qqsperson makes a sound close to the threshold of human hex -bdqm8*0s4)xs wfqvaring (0 dB). What 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 are hea5.htuf zch3mwrj bh;0a,5 p .pr c5t3pa b.pwm ,.zuhjr5;f0hhd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. 8o a t)6 c4j2pcixnt;qWhat is the acoustic power output (W) of the speaker, assuming it radiata)2i cpqt8nj c txo6;4es equally in all directions?    W

  A stereo amplifier isb5qbp 9x s;b 9+nxa6lo rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 ;5bpls9qx9b b n+o xa6kHz?    dB

  Workers around jet aircraft typically wear protective devices over thesbvkgte7-j+uns2+ x. i)p1rdir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, kbr1t s7-sine +u) xdv.j2g+pis 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 communications systems, the gain,j1s6517l t7wu rtzqcobk 3k,o $\beta$ 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 t3 qhnqvnvw( je9r+.p/o 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 cfa)qax vxot3,h+ ( q8vm long between fixed points with a fundamental frequencya 8f,qq +3 xvx(votah) 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 vibe3lg)vs,nmx+4 syv y) ration above a vertical open tube filled with water (Fig. 12–35). Tv4x+y)vl)smnyse,3g he 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 is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g iuo*;f b*oen5y2 6qrdh s near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce reohyf o5qu e26nrb d**;sonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed i(yyqp/cz+6;v k xsxt1t ulo j6h ;(e8to 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 the bq+vh62 ho+55mcrcwumt x4 ;m 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that co+vrt+6xhh45 u2cm;qwb5 mmthe 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 we++d 6p;mb 0s cmc7mcshistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the s6s7;mcccm de+pmb0+ other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it wfpk* e .r:bw6 r:9ty0ak9skn approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant vnrr kky*a69ktbsw9 e.:p0:wfelocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening1w +uw btyw:se8ag*j ; 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 octavej;wwb tag+uey*18 :s w (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a bi )s7e c ) hhmbp0f3fm(cu;y.aeat frequency of 11 Hz. The shorter o;ye )cbmfca(sfmp 3iu07. hh)ne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car t(04rr3jl 1qq2 m0cmolrymf 4as it moves past a stationary observer at 10 myo4mcrqmqt m4 frr 1(l20j l03/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.5np o93f 1w zt-;zerbvp oh ph+y3/p+n32 m/s what beat frequency would you expect if 5.50-MHz ult-ov+zz+ ph9bw po;/ ynr3p f1he3np5 trasound 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 t5 xynv 2:r61izsxlr +b.ek r e6v70qtat speed 6.5 m/s while the moth is flying toward the bat at speed xv.en i67+y lt5b:v6e10sq2tzrrx rk5 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 sound pulses asgg o*g7luxy (c4/on t6 it approaches a moth. The pulses are approximately 70.0 ms apl6ucx*o7ng o(g y4 /tgart, 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?    m

The “alpenhorn” (Fig. 12–38) +infnb;3a4 hz7m,ke zwas once used to send signals from 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 called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which m4f7 n ;hnzez,i a3+kbovertone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presevbzn3 0z;r;bp0 m-k;; cpj xidnce of standing waves, which can cause acoustic “dead spots” at the locations of the pre- bz;p;00 i3vzpnm;xrc bdjk;ssure 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, callwurr4o 9cets;favq u+s) )7 tfa)ui5)ed “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the r)u5a it c);sue)t)ro 7f9rfuv4ws q+aod 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 thredz8 q dked;dnl-2 )ngcqo5k6/shold of hearing for the human ear at a frequency of about 100gkql)e d- ; qc2 dd5koz/n68nd0 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 hears the sonic boz6urgcg4)z p)3hitccwo e:);y 1izg 9om 1.5 min after th4ogy 3r)izep)cgt1zui ); :c g 9zh6wce plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isv) n-k+ 8u btq*0vssht,0ll1 daid9 me 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