What is the evidence that sound travels as a wave? o:hs0b a/;bh) /etuzp.jm*ys

What is the evidence that sound igpc7p grxzv,1b8 ( ix)s a form of energy?

Children sometimes play with a homemade “telephohpwmu, j )48fuawey8c)c5 r/j ne” by attaching a string to the bottoms of two paper cups. When the string is stretched and a childmfchj/ r)8,8a ww j5y pu4eu)c speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into w (kiiz5 ji3:2ril/ukja7- atx ater, do you expect the frequency or wavelength tia 2iu:kl7 /- r t5jka(izx3jio change?

What evidence can you give that the speed of6zzh :crez)t)70grg* mc1u kf sound in air does not depend significkgczu hrf1g76z )m:0etrc )*zantly on frequency?

The voice of a person who has inhaled helium sounds ver5ug2 dowwg7su l,a.4s y high-pitched. Why?

How will the air temperature in ak72y(j :dlm ev room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sou1obq* zu/oz2 pnds in various frequency ranges. (An example is a car mufqb zoozp1 2*u/fler.)

Why are the frets on a guitar (Fig. skkjse x- pq.:)y+*dr 12–30) spaced closer together as you move up the fingerboard toward the bx re*sy:.j-+ d)pkqksridge?

A noisy truck approaches you from behind a building. Initl8 jqxrd-no+n7 7yh -4agb0dm bnkh13 ially you hear it but cannot see it. When h4- n 078omlk dqn+-b 13ydn7rhgxj abit emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” mw) 8eyj1vx)j.lowz 1 whereas beats can be said to be due to “interference jxlow.zvy)1wej m1 )8 in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the puguq t8-oltsn ;i2ic2b)1in. oints D and C (where destruc1un q82ic)s.l t2bgiit ;u-notive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peopleh mwwj) af6 pwqwb+:8i1 jaf93 who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feb1wa6iw)j fhfwm9w3j p8a q+: eds 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 thmu uy+o+euu5)q; nlz0 ,ukq)bought of as a superposition 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 farnmolky0+zb)5que u u),uqu+;ther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directv8fp h 35so i5lx.fha+b):vipion, with the same velocity? Ephsb i+ vaxf.vpi: 53flh8 )5oxplain.

If a wind is blowing, will this alter the6,i gw (q8xcgi frequency of the sound heard by a person at rest with respect w 8,(ix 6gcigqto the source? Is the wavelength or velocity changed?

Figure 12–32 shows varltp.-rlk2r i ;zm0k eg+ :g-hnious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, wilrl pm.-:2 nhkg;zk -gli+re t0l 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 her sho (gckv-khc 9* grp3.nuut reflected by a cliff at the far end of the lakec g3g*(n.9c- rkvpukh. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterli 4l g uitb-,2+d*sj c:cjl9fcene. 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 (Table 12–1) and does not vary significantly with depte-futljcg*b2,c d 9ji: 4c+lsh.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in w ,7e8ctarr( c4orawpz c9)q .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 dabjdomrg6v :5i :hle;2y. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses bevij5: e mb62dgh:;r lofore the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. T yzx n xcz/m- 10,ztaor4r4on.he splash it makes when striking the water below is heard 3.5 s later. How high is the cyn-0 mx nx4/rtoo4,r1zaz.z cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pavekff +0 (d )-wmt;pujhement. 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 awa phd +w0ek) ;(ftm-fujy did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-sebz/2j2q 1iin scond rule” for estimating the distance from a lightning strike if the tempeb/ 2j2sqzii 1nrature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain oq lvpi 5p6h5ko 0v03rlevel 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 whoseqfykm7*4t+m g sj+f6z intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producen)2 m2lcw;ntfj 4j5vpl 0t4ybt7ft n9 a sound level of 95 dB when fired simultaneously at nl tt2tnyl nf 5 f74m ct29bj4jwpv0);a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fo/c+k+)y gvh x3q gy5xyur equally noisy jet engines is experigkxxvyy/ +qhg+yc3)5encing 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.]    dB

  A cassette player is said to su hw0 -0w7vzil; ma-p*h,fbshave a signal-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 background noise 0p,w7a*mwsh ulihvs; - fbz0- for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversc d;t*z9dbc 9cation. Use Table 12–2. Assume the sound spreads roug9 dcb *zdtc9;chly 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 strikes ay x4 pt ertg7p duu ion.,/h.:ju:v(c)n 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 rated at 250 W, while the more modest a77etq s2 uz adsx3dp*+tqbf :7mplifier B is rated at 40 W:fzpbtsq7t *a 23ud7e7 xdsq+. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front 9j6z .zbbxnw 0of a loudspeaker. wnbb0zj6xz 9 on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What isc2w9 b ;ygpd/7wbbb f. the rati bydgwb9.; p72bw/ bfco of the 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 ftrgwc1;,g r;a /jxltu vp7:b 5actor will the intensity increase? Increase by a fact 5tbu;rp:x/,ca ;r wjvg gl71tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freque v: 8uf4cgt/ v8+k yzjvd+yvj;ncy of the other. What is the ratio of thei+yd8 8/vvkuf;z:tjjvc +gv4 yr intensities?   

  What would be the sound level (in dB) ofinqbmqqk3ps +/(23 rf a sound wave in air that corresponds to a displacement amplitude of vibrating air molecule3 f(rpni/ 3 qkbs+q2mqs of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level ta d-c .1(w hiin .qsdjl8eo2y2dwu2lg 2zj m0:o seem as loud as a 100-Hz tone that has a 50-dB sound level? (S8n uhocdy2g.(wdd ilsze .j0- mql:21 wi2ja2ee Fig. 12–6.)    dB

What are the lowest and highest frequencies ,qeqn i94d-kyghfggj *2hk:4that an ear can detect when the sound 4 :qie9h*f-,ghq g24dygjnkk level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a k(6hzq q lllkyd)b /b2*v9v8 bhuge range of sound levels. What is the ratio of highest to lowest intensity at /qylld*vkhz9 kb 2v(8b6b l)q
(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 frequen; epef81 g-a yp(uscu2cy 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 strc8 uyu;pfegpe-( 1sa2ing be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thv.ti(do u y+9hree audible overit( u9v+d.h oytones 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 acros1+syq iye1 knm5ls477h ld c;ss the top of an empty soda bottle that is 18 cm deep, if you 7ysh1iqnlmles +7 ;csy5d 1k4 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 lf* .4 ccchfh dd:wo3 dczz.6/a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of4.holwhz dz*/ . 3ccf6:dd ccf 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 tho p 1;/nao)x*w9.gug iat0xha ird harmonic. What will be .hg;)*axt g9aaun/ p0ix 1woo its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunewm47kdo-on:+kngz h 8d to play E above middle C (34kdno+:wzk- on8 7hmg30 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 lengwvps4 ke5.:e2sih -v gth of an open organ pipe that emits middle C (262 Hz) when the temp:4-sehig2w v.pvsek 5 erature 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 f dnd9jl;tx42$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpioal5/nmg 1u2dfk*8qtts8r 17 opj,l mece of the flute in Example 12–10 should the hole be that mk15ja u l1moq do8fr/7 sl 2*g8tn,mptust be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 z6mn5 -pa q)lnv*/ewkHz, and 616 Hz, but not at any other frequencies in between. -e5 pzlwqk a6*m/)nvn (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 reso2( w by:sf.h0iobn 43ahsd4 dtnates at two successive harmonics of frequencie :(bdyb s4asn3.i h 4hft0o2dws 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 fgh01 +x4/qlh + 2npd a.3fj bn5xqxzi$^{\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-long or.ggx *gbgco) mu zh k4b02h2l5gan pc *2bg2k hx m)zglg0boug5h .4ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal giwy4v)* .wk jis approximately 2.5 cm long. It 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 waves in the ear canal. What is the relationship of your ) k4y.ij*gwvw 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 b.*z2 ct bbdbg6 6mwzo)eat every 2.0 s when trying to adjust two strings, one of bd2bg.mz6tz * wocb )6which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequencyhkzlf r h :f9kp1-+6mkpb0 p-t if middle 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 whistlqbw(zj oy1:3+)tpuyhha.(m ee operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of freq.zo:tjb a (p)e (h+1uy3wmyqhuency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces btmxx ; wbkftq u41ytd-0(d+zw:7b.q4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What iw :dz(u mwkbt b q.t;xfx-1b4y7d0t+qs the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sam0183pn,nj ebf*wcpk ze frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recalp j1k,p0f3wcn *bz e8nl Eq. 11–13.]    Hz

  How many beats will be heard if two identic:2tt1a6xj b nsal flutes each try to play middle C (262 Hz), but njt:1sxatb2 6one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; 2xx t ur(v.8ayew x;n+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 tn xxta+w2r8 xve.y;u( ogether?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker aw7x71/vz 0owpb to:muf/t hk2nd 3.50 m from the otwk 7z/7/w0fbohpu ottx2vm 1:her.
(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 suppac2j/a;mgk9)/m) x e/tu tv tg- zp.ssosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2se9/ua ; gastk) .ttc-mv2 x/m )p/gjz.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m anuyftb -vru*7 7t jx9zvk1) jz(d 2.76 m in air. How many beats per sxjvurt1 b y -)utzj*z7f9kv(7econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencra*wv.a)x7thksrg f44 jn8juc 8(k q9y of a certain fire engine’s siren is 1550 Hz when at res*na4.k()svfk 8uhj x rc w7r48g9tajqt. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What il69(1z+i2ad s x hrwsfrequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a sp l21ih i(s6wxzr9a+sd eed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz soucz1vt9shr-0u;(xqimvd72 h rrce is moving toward you at 15 m/s versus yo0 - ;79u qv x(r1mdhsith2vzrcu moving toward it at 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 frequency horn. Whe)z s1v i(ea s+ a*ojhvkp46c2yn 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 horns emit?v*ec(h1)+ v6izks sj ao4 ypa2 Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz azg-zcs7z ;lbc5jw/,cep8k ,q n- 2mt .zz;ouvnd receives them returned from an object movingw,qmtuc. 5p8j,z ez7vbsgck;zon; l -z-z c2/ directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall atwdm h7v1dm:i ) a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear iddm71w) ihv m:n the reflected wave?    $ \times10^{4}$ Hz

  In one of the originauq6 7g 5mk,zqsw.gup9l 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 wagk 7 u6wq.9mqu5,spg zs heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mea)ro z1a1m;g0sxihqc 9 sure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly awayr;hsxq0i m 191)coagz from the sound source?   Hz

  The Doppler effect using ultrasonic wa)* (c79j+u eniyy(ngphw ( xswves 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 velocinl7(nj;jq3f gv :ih5ity is 12 m/s from the no;f 7nqh in3j5ivg:jl( rth, 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 m+i v- gxubeh fdw)xr(k1+z3-if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What is 7- x2) vsm i4p 1smbd3fp9mnhgulmv8 28rl*sr the angle the shock wave makes with the direction of the a)8rvp-s82 rgmi s4l3 mdlv 19uhn*m p7mf2bsxirplane’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 atmosphmc s25 poqwtd6jnpzm)-6l 3 q3ere of a planet where the speed of sound is only abo3sp3ldmtpm6qw cq) o6n5j 2 -zut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shoce* 7 wlq (d6bqla.anxj. i/f5x;ohm6ek wave angle it plj/e* q . ebx 6wdoihaq5n;lxa.f 67m(roduces
(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 vm g,fu6 x+ox) xij5w4$/theta$ 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 je* :xnigqh92km above the ground 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. Seej :i*29eghnqx 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 25rgev: wpj(azg2h0anm2,t* h 0,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)h 5:v*gjw 0trep,2 2zmga hna(?    s

  Approximately how many octaves are there in the huj)dv2ho id6)k6,bsguu /mxhx-/qa( v man audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has aph7 ;g 85w-: ;q/l5 vf ll45ezzi zm9vyksmgsz display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which aremqzfw g i 55myvl e9v/ z8l-zkphz;s7sg54:l; 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 sbe6j2iodil;- :;ugwfrom a person makes a sound close to the threshold of human hearing (0 dB). What 6;j2 s g-biwod:l;iue will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant soun77kela ,(m1ky vui8wnd level when an 82-dB sound and an 87-dB sound are heard simultanle 7m,vyk( 7ka1u8iwneously?    dB

  The sound level 12.0 m from a loudspeaker, +y) tw 9san-llm:zsrx2,k1typlaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equa+-xmtykayl1trw9lz s 2,sn ): lly in all directions?    W

  A stereo amplifier is rated at 150 W o8:hwt ol+i0 pautput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What +0 w ai8pho:ltis the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earsj l:u 9j ad6/hslksi8,. Assume that the sound level of a jet airplane engine, at a distance of 30dkl ,:8ssl/u9ahijj6 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 communications systems, the gaczxw +2i3e7b7vi*n mbqtk-a 2in, $\beta$ 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 tlmth4b-dz3blv*is) *nvp+ wvz 1u4g / 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 cm long between fineswz.:w0bod;tem +3 0bwzt4xed points with a fundamental frequency of 440 Hz and a mass pwtzd3o;.4 :wen+ be0 wb0mz ster 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 vibmg.r9 8j/b b n /2.ea.a ;s6poxkf*2kxila pvqration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is afk s8i/ .2g6p abbr le.;a2x x/*j mqovkp9.n0.125 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 that ihj qo k5yq**m5a/b6e f*m9mf as open at one end and als 5fm/qe*j5oa9fmy*qah* mb 6ko 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsersm0v ny;z8, hr eq1r4 kola/;e6ress:ved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range comi;.3lj(fnv n0y dnt zg(ng 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 the sound level is minimal at a point 0.34 m farther from one source than the other. ldfntnjzv n(.; y0g(3 What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the scramjtw 0 5y:6tationary train hears a 3.0-Hz beat frequency when the other train approachesy5t 6ma:wj 0cr. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches 02rncyq21n.re2)uh4cjvre 3qzf g 4s you is 538 Hz. After it pas04r2gn) 1n43 fyvr2uqcer es.c jqzh 2ses you, its frequency is measured 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 listening t ;5nqmg cenrb) 7 02)kqinwxi.o the difference in pitch of the engine noise between approaching and receding cars. min gk);x2 n 70brnqc).wi5eqSuppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, prodeh q7i.+oxbv)hjl66b uce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the o6 x7bljvo6ie b h.+q)hther?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pa*ipmj-tklk 8zy d(l80st a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the 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 passedl-p 0kyd zj8ktl8*m i( him, at C?

  If the velocity of blood flow in the aorta is nors5 kypnesd-y9, 3qd9 z,lz9tgmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the wavee ns99t35lzdpy9kqyd-z,s g, s 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 whiloct4cb9a3/3i ;qqut )s o.y++amscwmwsk6r 2e the moth is flying toward the bat at speed 5 m/s The bat emits a sound wa)9ri y; a4/qsswomq3b 6ac 2t++coc.tsmuk 3wve 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 freques-2 fjtwkjv*zp3 7tkc3d /5yu56kc)ciev h )qncy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms c)) z3t5k/cqyuvt2dpcf* kvk j- 675wheji3s 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?    m

The “alpenhorn” (Fig. 12–38) -/rfs3wu 8sry was 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 alp3s/u8 f-yrrswenhorn 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 compromised by the presence of sta )e3gnv-o-oxr qgg)3 fnding waves, which can cause acoustic “dead spots” at thenv) -o3 e 3-gox)gqrgf locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a l:3y oj gmyocl+6pprz2j7e9.q ong, 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 rod can be made to “sing,” or emit a clp9erc yl o z.p+23j7o jyq:6gmear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ea*0mg 9l4ib9. tyekt/trvhmt 0 r at a frequency of aboutk v/tm0i e* ltb90t49 yhtm.gr 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on thh98f 6up z6) :aswukvce ground hears the sonic boom 1.5 min after the plane passes directly overh fwpczuua6:hs98v6) kead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isqy7:+bc3i vjo 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