What is the evidence that sou9 .s nd.u zi7.weq2b6u7dytga*rcs m,nd travels as a wave?

What is the evidence that sound is a l.7 trxp3iw3m form of energy?

Children sometimes plaj,sh -crj pidqx.k f4* 2wv;s*y with a homemade “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 cd ihx.r f4pk*,-jw;*vjss2cqlearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fr(( dg7ithm kw8equency or wavegm i(k (7dhwt8length to change?

What evidence can you give that the speed of sound in air does+ulw2 ,6x u/pxugz m2g not depend significantly on f u6u2mxxp2,ulw z/g +grequency?

The voice of a person who has inhaled helium p7 6f*w1t l19viwlkd ; yqau)isounds very high-pitched. Why?

How will the air temperature in a room affect the pitcot wt3czf-;*r1k w4gzh of organ pipes?

Explain how a tube might be used as a filter to reduce the amplt- xicsgp 4x,1itude of sounds in variou xs4tgipx-1c ,s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12fz4irc: hw0ck. f a0i*–30) spaced closer together as you move up the fingerboard toward the bridge? ch.w a4kfir0*f0:i cz

A noisy truck approaches you f5o*goo6kh aa- nd2zw(rom 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*ak( naw5d o6oog2hz-–15 on diffraction.]

Standing waves can be said fcgij9 /b0wt9to be due to “interference in space,” whereas beats can be said to be due to “inj/icf0 b9 tgw9terference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were6ax8ahds) j8z lowered, would the points D and C (where destructive and constructive interference occur) move farther jx z 8h6a8s)daapart or closer together?

Traditional methods of protecti1eqr gg55z 7mmng the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. z5ggm1qre75 m 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 waveihkhi1hiv vqs-s(/ , 9 can be thought of as a superposition of two -v(1i9h/h q,ssvhiiksound 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 th9c :6zxtcy,ane same direction, with the same veloc ax6c9z:ny,ctity? Explain.

If a wind is blowing, will thizl7 sz58uq )y,nz4 fkus alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changed4l) 5 7zufn qz,zksy8u?

Figure 12–32 shows various positions of a child in motion on n rcd*q)yw1wqh.-i0ja swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of t0 -h.)qjqwinw1dr * cyhe whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her s- r+;4 kvxunrqf9pb prh(*.wdhout reflected by a cliff at the far end of the lake. She hears the echo 2.0x udqpv9* f-.4p hw+r;n k(rrb 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 6te.c)ssxq9j5tx yi 8 hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deeps qj it yx6sec8)9.5xt 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 q ;k2eis h7oz3,- hxkain 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 drifti5l drd05a) d, 9imt0ipqubp/hng just above a school of 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 559 ,0l /ipimb)ddhau0 rpqtd 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 splashi8c7b+i )r dcc it makes when striking the water below is he )c+ rdiic8cb7ard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the o/)*tovzkr*dqj*m .d 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)m/.o zkjvdort*q *d* 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by k nnx(z -gu y6t/cqo,7the “5-second rule” for estimating the distance from a licy(n/z 7t6k-ux onq,gghtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at ,,je cdp z1qxuz1nze1+),ody the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound wupn9f)b l/u9w3pk4v9 wpzg,g hose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sg fzrr zx;dmnf +08 e/8grbc-7imultaneously at a certain place, what will be the sound level if 0zcr8f gngz8x-;emrb +df7/ronly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dista/5auj 6hbf5g w1 xpae8nce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB1bugpx /e8a5 a5 jwhf6. 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 rati+4 ks ubp.jh0 o pi+0eye1c3fto of 58 dB, whereas for a CD player it is 95 dB. What is the ra1byei.t oke+h0 pjf 0suc4+3ptio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a p:dnd: p ju88 c hrbo1spvr *m2u9oz*g)erson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniu:gdbzh r: 8d)u12vop*cns8mp o*9jrformly 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 a j2/ksov0ub )v:z (mwyn 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 a (h6h t3+pyw2jy 1b mqgr3-kkot 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a louh bpq3 1-mjhw6(tkgkryo2 +y3dspeaker 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 metekxw95p(:h2zj a8ljc0g-dtr *py( s dar registered 130 dB when placed 2.8 m in front of a loudspeakerwdj5 p ya8r 9 ax:s2j(hg-pz*tk0 c(ld 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 d/sq; /aw zgbs4b0z7w rB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11zr7 /4s sbqwwg;ba0z /–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fr idmsw1s)u-r3 1qho )actor will the intensity increase? Increas q-woi)1hss 13mu)drr e by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudm.6r/ ut mwhb7u6 gv5 njrc5x,es, but one has twice the frequency of the other. What is the ratio of 5x7mjnr5cm vhuw6g 6/u, trb.their intensities?   

  What would be the sound rd2y 9fu2uwk:bo/5u u level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecu du:25bkofwuu uy9r2/les of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leve*: tporma e1 0aej/e2el to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. ae1 ea0* eprmeot 2j/:12–6.)    dB

What are the lowest and highest frequencies that an ear can2fdl)9gydpyu :(w :,s8 suu gln/ysy: detect when the sound level is 30 dB? (See Fig. 12–6(::w) ,ysu d gygpusd8lylysu:f29n/.)

  Your auditory system can accommodate a huge range of sound levels. What is the rb1vyy*xjj y 9 *i39qqvatio of highest to lowest xiqyj 9* v 3*yb1y9jvqintensity 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 fundx2l v./pl ur hwfn30kd) 1e/dhamental frequency of 440 Hz. The length of the vibratin.n2lp flk/uv 3d10hd exr /wh)g portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audisf4 w-*n(n ewkble ove-fn 4ww*ke( nsrtones 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 acrr7s+bu7wku g 6oss the top of an empty soda bottle th7+gs wr7u6kub at 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 with open-tube pipes spanning the r-0cno 1waewb/+ a:97vot dqi)s-dz jt ange of human hearing (20 Hz to 20 kHz), what e ct-vd zb+nad 9q):ow1jt- 7i0ws/oawould 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 frequenq6k o2 ipl n2g+modyn9 o+9oz5cy of 540 Hz as its third harmonic. What will bm+9niolo +zq k9o22 gd5 6oypne 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 tuned to play E above middqelb n)yxcpw9ekek4 vz)3 6+0k* fi6ple C (330 Hz). 0wb+3*k) y pvxecielq4k6 k)6z9 fepn
(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 m3zl0bi4btmks tx 8+j3k,6fpyh08gfoiddle C (262 Hz) when the te+0bto8tf ,08jf6 mz l x kk3b4gs3hypimperature 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 2 q)yqery38qq3x v(-/ q7 5 dozc6i/kkwtutd2z0 $^{\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 ho; e4 sqk (wupyb-b,0zrle be that must be uncovered to play D above middle(pyqe-bw ,kz rbs40u ; 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 Hz, -d)/z fjkx-pnd d. bgp;f;hf9and 616 Hz, but not at any other frequencies in between. (a) Show xzp p9)d.;/fjf hdd ;-bgn fk-why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at p8s7l w8y;r vh*/lslv two successive harmoni/l rsw8v;hp v*8s yl7lcs 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 w:y:i +s ticb/fz)0k 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 withinwmug g w,g.c1tbdqmv +z403j ;:f tn/i the audible range for a 2.14-m-long organ pi4 tj vgqf0u3mnzcwwb+ m/ .gg1d,:ti;pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It9v+ez-o3 jj7yz r) jrn 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 rye9j+3rnvj j)z-z o7 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 bea99qw)yidt q7 ki 9wl1keq4a ;lt every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How f dwqq4k7kle )ai91ly 9wqit9;ar off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and 2d9k)p /szpir $C^＃$ (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 anom: ly* nayk n.,v,pb9sther (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency vb *yaskyn.9 plm:,n, of brand X.    kHz

  A guitar string produces 4 beats/.oygdfu8/,im grk)3 b/sthnasiq392 +k. dhas when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationalm gk fa3+byhr2/is.ns uo9.8dahi3 /)tq ,dkg frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The 1huwcotjhe8 d5 x) 0/ny1*pcptension in one string is then decreased by 2.0%. What will be the beat frequency heard when the tw)opd5 1cy0h uwtx1e8* pn/ hcjo strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will bea +u+gr()al i-ftch 5bu:-nqd heard if two identical flutes each try to play middle C (262 Hz)+ahq:lnu5r-(-i g+u dftb)ca, but one 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 H:yw :3draepv w0le *2mz; 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 l aw 02yw*eerv:: md3pA and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person s n 0ts7h-jn-mpe5uruf6xu1,mi sj8 m5 tands 3.00 m from one speaker and 3.50 m from the other. m10j 6xuujiu-ntens 5m mf ,7h-s85rp
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a p-1 1qf;tat xh8k p7ffxiano tuner hears three beats every 2.0 s when 8aqpftx;hkf tx-17f 1 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 and 2.7ruti2 sk p4x. 2bh66bq6 m in air. How many beats per second w6q6 hb.s2u tprk4b x2iill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at c9xa :n9pt( d; uqlh-srest. What frequency do you detect if you m p;9( tcxnql9:a-udhs ove 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 detexoeeec:zhc1rtu+5k b 8+ y3;+y3 fhwuct if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 5 u++be+euzh;o3f w8 1ct3x:kyrhcey m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source i2k/jvxv2( b+q *vssgf-2fory s moving toward you at 15 m/s*s2 r2kvgxfjfvo +/bvsy-q2( versus you 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. When one isp, :gd esiq-g) z1ao/l6ld n9e 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. Whogs,q9-e) pne/: adg16 lizldat is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kkqgcrp ygn(idu632dkjk b0 k:72fs .3Hz and receives them returned from an object moving directly away from it at 25 m/s Wr.3fkjbdqs6 k p cy3 k g2idu(02:k7nghat is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As d5n.q )bf48qje 5xcpk it flies, the bat emits an ultrasonic sound wave with dx4c.q be )p85k5j nfqfrequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving f9zzqteo*tmhx5/rq3c5b/ gm updp*4 4 lat 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/5 4 dq *hm3grz4*p bo m/qp/5ez9ttuxcs ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood- *70 k,xacpi16 ; nwrmkdzbg9jflow speeds. Suppose the device emit jnxd*z9a,br cmgwp07;ki k16 s 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 away from the sound source?   Hz

  The Doppler effect using ultrashr/jsj,8- bcf onic 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.wotff1zs5s1 1 2r ,vvb When the wind velocity is 12 m/s from the north, what frequtvo1v21zwrfs , 1s5bf ency 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 wo;mj/k7688weeqd (qc yz pr,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 tt) nr6p.1zlqft2wc 4rhe speed of sound is 310 m/s (a) What is the angle the shock wave makes with t42lq p c6fn1tw)z rr.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 the thin atmosphere o x vujh0 qayfx4)mw-+*f a planet where the speed of sound is only about 35 m/s*aquh)v xxf0w m-+j 4y
(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 v3ouw-urhb f4 c n bk3:/ z-bcpr0r-p6klq/q( m/s strikes the ocean. Determine the shock wave angle it 43p0 q-o/ ku zn-k -:chrur( /6lcb3vpfbrqwbproduces
(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 35ex(s k f-abj$/theta$ 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 hgs.n *aew/;k the ground flying faster th.gn a ;hew*/ksan 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. 12–34. 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 pulses downw,yw wt6 mdxxq2 -*wpz(ard from the bottom of the boat, and then detects echd,wp q-*w z(m 62txwxyoes. 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 aud2i 0o4jql 6 ip;njsh.6rbq,vj7 pf8wk ++oiax ible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manya2w8.h3du a h n vd5:;(agjant plastic pipes of various lengths, which ar:;h2j ta(3an vhn5u8.wada dge open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sg ww t8tnp;ig8 o,qd21ound close to the threshold of human hearing (0 dB). What will be the sound level of 8odw2 wgt g8 pt,;iq1n1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound ar sx o* mj0tw-(9w 8o2v 9s:uy7eisbpgze hearde js ugps99*zovbw2w i(7:o y- 0xt8sm simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in t:yn3r m8 km),mb m+hf ephim,i2b w7z.he open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radin3y: mihm,27rpb hmb+mezi,k .f)8 mwates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drony mujx/o d: ,ua2:;t7cr+mo ops by 10 dB at 15 kHz. What is the power output+jo n;ud/:ormx27mt u :y,o ac in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ol0 2lillo)yi otdy(*(x)j9qvver their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepl qxtvd)( )(yy0o lilio*j29lted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicaj3 usdhco83wy,ax+ 9ky5d qo8tions 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 violi5vm agf:1in;i n is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fu7umn 51mpl4t8 qeva r*ndamental frequency of 440 Hz and a mass pelt *v4am1e 8uq5m7rp nr 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 vibrlevl: uh*+e 6o9y.bec ation above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning f.*u el:e 9b6oh+l evycork?   Hz

  A 75-cm-long guitar string vpozs+j 9dd6s46xp0 6lsb vr3of mass 2.10 g is 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 resonance (in its fundamental mode) with the tp6jrv0d+so6zs v l db694xp3shird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f6*n /ly rz6mz-:rpw;f bzg/i/jg, 1krc3fo pwull loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from :v - ub)u1l ;gls(vnn.u)3p yvf1 rfdxtwo 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 thxl . vudlv g)u f;1n(b- p:1sfnury)3van the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Onzbmoaawezqe/4yh7 8x2 kx3 k)efcp 8 7i3z: 6ge train is stationary. The conductor on the stationary train heaxep)e433h8 ikb :6 e7y 8zx7afq/2gc aow mzzkrs a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachesz e xkmfi8y-lrhi+3xw21 3(tg you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the traik w lxrft2 i13y3zm -hxg+8i(en moving (assume constant velocity)?    m/s

  At a race track, you cb rzr2s75j3rtan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain rbzrrt 75j3s2 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, produce a bd3)hdj7cko ly -rt)p 7eat frequency of 11 Hz. The shorter one is 2.40 m long. Hothoc-p3djk )d77 )ry lw long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves /95f3 8m1b/x uyp:dawcz pbyupast 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 (c5/xu3ym9 8 b/z1ucpp y:dfawb) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow inuoxqeh2sda) ytyajqo,c ;0 u5 8c6)p( the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that tcjs;2qoyu8x )oaeh c5 d(ayp0q ),u6 the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flyinik7vq 6tv,rh *g toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is,q7*vt6hk vr i 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 as it approaches a m/xy 8p*6o6 rmvpcx/fy4r4buc. imf . xoth. The pulses are approximately 70.0 m b 4.v cuxmp*rmcr4f /.6 x/yopx6yi8fs 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) was once used to send signals from one Alpine vill;v+/ gk j4tl)qymld6qage 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 calkt q lyg4+)m;vj/ q6ldled 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 rjo.fwb-5u6+ggg 5u slistening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the 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 frequenc rufgs5uob56-gwg.+j ies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, callehavv5 q68(tyzc v42ml d “singing rods,” involves a long, slender aluminum rod held in the hand neql (v4v52 ahmty6cv 8zar 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 oxzav: e6onv ,0f hearing for the human ear at a frequency of about 1000 Hz ia xvz0o e6vn,:s $I_0$ = $1 \times10^{12 } W / m^2$ 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 o j)8jdgc26d 9tbv( ta-njarb, n the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? jt,r -jbatj6a(2 gvd8cd)9 bn   $ \times10^{4 }$ m

  The wake of a speedboat is 8 gw4qla 7k/rh15 $^{\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