What is the evidence that ss c:6na.g8yj vound travels as a wave?

What is the evidence that sound iscqy:y0;a* topah jd*) a form of energy?

Children sometimes play with a homemade “telephone” by attaching a stringaxd/c-76 tz,7ir a/(dzkx mta to the bottoms of two(7cam7a/z -,x / dt ktrz6dxia 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 how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect thes8l .kjj o(fii+,d a5x frequency or wavelena5 j8(ol.jkf sxd,ii+gth to change?

What evidence can you give that the speed of sound in air does not depend signifh m qi.5wx6+ cf1ekmxful:-e3 icantly on frequencyk5m:e 1mu.6le xicw xq-+ff3h?

The voice of a person whl+f2p 8unz -ato has inhaled helium sounds very high-pitched. Why?

How will the air temperature zd6)- i(fwf brin a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduc 6,aoo7 obynlj/r ;0jwe the amplitude of sounds in various frequency ranges. (An example;6 bno ljroawj y0o,7/ is a car muffler.)

Why are the frets on a guitar1c 7o5l/2aqib pqp-( vz/od(pp) dga x (Fig. 12–30) spaced closer together as you move up the fingerboard(g l/2idvqap-pa)pc7/o(xp 1o bq z5d toward the bridge?

A noisy truck approaches you-(,k +0mqkekuv-q(vf meqi k8 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(kqk,iuevv0(fm qme-+ k k8-q on diffraction.]

Standing waves can be said to be due to “intpo+z 3a(yy /zxerference in space,” whereas beats can (3 yx pyz+/aozbe said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wojlkm 96 lr4/) etj wp-+ tfkbnv,e0a-muld the points D and C (where destructive and constructive interferen w09krktjj-)l4 af t/-m6e,p e mlbv+nce occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wor;c :wq 2/, ,v) rpc)rdww9vq.zlry stqk in areas with very high noise levels have consisted mainly of efforts to block .r2 9w:l)vr/ ,wwdz, ptcqq)yqr cv;sor 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 wah19jc y mrsw( -m*9xfjcj/d-lve can be thought of as a superposition of two sound waves with sli/j xj *mmyw l9r1cj9hc- (-sfdghtly 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 m vmfi 6*n2qrmxn(64a 0xbwe.eove in the same direction, with the same velocity? bx46i6 ernxn 0(mqw.a fev 2m*Explain.

If a wind is blowing, will this alter the f)6en.u w hqde5mw0 c8rrequency of the sound heard by a person at rest with respect to the sourceq5mc0.e8w )hnr 6uwde? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monito/oe kn.k.n9wliqjs-;oj+f k ,r is blfk.o-ns iwjq;.nje 9/,l o+kkowing 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 the whistle? Explain your reasoning.

  A hiker determines the length of a lake byylzyr7/6h6u p w . txngbr-g5, listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lpb wn.y gu6 6z-l rxrhty,75/gength of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the si9aqt:lst7n*9( do ht ede of his ship just below the waterline. 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 h(le:7s9aq*t9 otn dt 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 inz5+97rdgnh 4 :x 9mu-xu zzqgb 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 abovelh, xl+k/5 hqq a school of tuna on a foggy day. Without warningh/qqxkllh5+, , an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The sp6.y n7ac pijo,kz1k2clash it makes when striking the water below is heard 3.5 s later. How hi7jy,6ic pz.21nkakc ogh is the cliff?    m

  A person, with his ear to the ground, sees a huge stonewky,c 4 l:r m9dant0drk. j2f,8g9 qyq 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 al 0cqrm9q g,kd9y,kj.t42 ry:w8 anfdre 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 the “5-seco*e yt57kxn9atnd rule” for estima5 9ak nxtt*7yeting the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a ou-z 3 b0ol78ivhs/,6ko d aulsound at 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 whose intwp6 5z hh4fsydu so),mgi;3e8gc7 5niensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whe famnl) ,qe4p-n fired simultaneously at a certain plac)eqa4,mpn-l fe, 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 four equally noisy j/v:j/t p5*kho+nva rcet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience/cjvo t+r5:np/ a*kh v 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 mui l+,ubfbr2zpa s0-*a1a2 v e.id r1of 58 dB, whereas for a CD player it is 95 dB. What is the ratio ofa 0eb+arb-d sil,1*a2zruuf p12. imv intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spev-4b trww z);i y ajd,jhqsq,xqb-*)2 aking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on thr)q-xv b)itw;s-qw hb d,a*j2zy jq4 ,e 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 ear+jy ac:96r 1gyeir fl/drum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while 5 cunrmw5g xs*zb8wn 9 :w8nh)the more modest amplifier B is rated at 40 W. (a) Est)85msw cn zwrnnu9 5h8:xb g*wimate 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 1rl68 azj)v/a rs2mqk :30 dB when placed 2.8 m in front of a loudr6srkzv )l 8m/j2a: aqspeaker 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 dqu0w-d*jexctv6 rcu0k7.+s9 5 g yt iuB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hin6vu9u ct0- *utdesj7 r+5.0y gqkiwxct: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wh :sz) mmy.dx:oat factor will the intensity imod:s:mz x.)yncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemend+on0o q k8q.rt amplitudes, but one has twice the frequency of the other. What is the ratio of their int.r+dooknqq8 0 ensities?   

  What would be the sound level (in dB) of a sound wave in air(py6h mpql3s;v,4tks that corresponds to a displacement amplitude of vibrating air molelvqtyssh(m pp 346 ;,kcules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have ;f5x xda yb)th t;)qhb;re4+uwhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Se ea) )xb4yfb;urxq h tdt+5h;;e Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear c qlqs *tn8cos;4-:za ig3g+fqan detect when the sound level is 30 dB? (See Fig.+ 3fl snt:aq4gzsoqi c-qg*8; 12–6.)

  Your auditory system can accommod)mx2ig6f yp )gtu ,md/qwd8xu c+0*dgn5h j9uate a huge range of sound levels. What is the ratio of highest gwu5gp/d) utmx6idxqn h fy+8cu*m dg9,)j02 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 fundamental frequency of 440 Hz. The length of th 21ebdwcc etjm4xomznm xo873 h0 f:*3e vibrating portion is 32 cm, and it ha8 7fch *eo dexm 2:cjz1o 33t0wx4bmnms a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thesv8* 2suf a*h.uhp+xg fundamental and first three audible overtones iuhsf+*pa 2*hxsuvg. 8f 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 fuf 3el ry w7igd j,7me72;m)oarom blowing across the top of an empty soda bottle that is 18 cm de3rjom77e id2f)age 7lm;y ,u wep, 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-5x 3bj,d7f ly gazglhc .bh)9/tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what wcl5397bh,./dfy)bxgh az j gl ould be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5qmhao+w2na0 xe -dg97z .wdq (40 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a lene2d-w anhqw+zad 7 (9gom.xq0gth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle Cf e*6woeke(/ qc;(w 3-bo ijtm (330 Hzec ; qfo6w keem3-b*tw(i o(/j).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whenxkb 8aa.r) u)j the temperature raak8)bu. j) xis 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 201d7;(lvg gl. rgvvk5n $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole ndczf vaw(ksk2 l*+9(be that must be *ck vz9sdn(a2l+( wk funcovered 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 resonat 9sh /scnlyvg7*6s m6 roj0qk4/rr) ize at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betwisvl7 jg4co9sr yr6 /rk0z mhn)6 q*/seen. (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 resonat: 4yv0 .cyx3zk kizr4ees at two successive harmonics of frequen: r zvxyiyk4czke.403cies 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 kdp;5peh sc:/ p;zsgvji.2r: $^{\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 arepwvk7g 9,u b5g present within the audible range for a 2.14-m-long organ pipe atk5bpg ,w g9v7u 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the ttwk 0zzh c zf/o0l,8w.ya,n,y -0fyqoutside 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 zzy. ywnf/ht8-,clz0,ky w, ofa00tq relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two73axpjmv q un07ft*3x strings, one of which is sounding 440 Hz. How far off in frequency is the other strinuxpv7n*t q0fa7 xj33m g? ±    Hz

  What is the beat frequency if middle C lx5zrxkr:a c7 ;ihxce/ g2e25(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 whistlg2mgr .y 5qbl/e operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when play2 b/g5.lymgr qed 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 sounded with 3k)z 2f.a3ad/zsbwd2f)jldw a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the strif3z 2ddf/abls.k2d)a wjz3) w ng? Explain your reasoning.    Hz

  Two violin strings are tuned to the sai5 p9ayby 3j-,u n.gusq r9ln+me frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two sanp +9.b5 nyy3rq-usl, j9giutrings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pllyz9 2f+ h(cs,+waid eay middle C (262 Hz), but one is at 5.0°h,(yl9 ew sfd2i+ca+z 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 ul f) sqvr)17(o03v i hhu;hpiof 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possiblv ;s3hi l7o1uirp0)(fquv h )he when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A pj 75rvf6a.uauerson stands 3.00 m from one speaker and 3.7.5vja ua6 fru50 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 st9vlu(x vs2mi4mlu m9*uy7lnk2iaa1 t y14. aupposed to be vibrating at 132 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, wyil4xv9a t ui s1.9kl2u2 mm 4nvt7*(1aymulahat 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 w-/s4 .voj c3b-)fgt.2khq vjcusy5 kzavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? 2vb czo/jqg-fu.k. jc-4s y sh)k5tv3 (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencyn a(7zcfhx +)g of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with h)7gnfzx a +(ca speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequex99h;dp /p/eee ycyr( ncy do you detect if a fire engine whose siren edp/p c 9hx9y;/(rye eemits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in oet35.f6p(vmezaa / o frequency if a 2000-Hz source is moving toward you at 1 36v.ofpe/ eaot 5ma(z5 m/s 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 hvhu69 zp,u*31wd vgz same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s thvz dh zg3h91v* wu6p,ue 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 at 50.0 h/5goqay/i+w kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fr 5w/ hoai+y/gqequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at r c xtzo032stvy0pm:3a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kxotm3vp02zry st0: c3Hz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plp)zax-hp r3 (zayed on a moving flat train car a-ahprx pzz (3)t 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/s ?   Hz

  A Doppler flow meter uses ultrasound wavo yxnx:68olid)qk +gk8ei4 ; e q.;udtes to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the4i+:dy 6.u;gxqdnqok e;eti8x) l k8o 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 ultrasonic waves a6u5 p3ug9 axb l0)kgzof 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 57itqe9r2/0 hyfhg ) 3ybpi(zj70 Hz. When the wind velocity is 12 m/s from the north,i(yp i2yg70e/)zhqhbrjf 3 9t 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 w1-(keognd+3tx, 8 bw-qkyaaif 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/.d qj:hd x mdf(pe4ja5.b4 fxdf.6w )us (a) What is the angle the shock wave makes with )fdxadfe:.j hx45qbju (46fdd.m.pw 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 atu,erjrn 6,a )fhxwm+5mosphere of a planet where the speed of sound is only about 35 me j5nhar x,+) wfumr,6/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/lyqfoh* hxz i +j33ojgm3p631s strikes the ocean. Determine the shock wave angle it produ3*3o g z3+ ji6qy om31jpflhxhces
(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 uzs*so14) 9g(kx2cqgwhn,j b$/theta$ 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 ks.i ort kl w-90)t*gsepz, ;dwm 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. rl9t-zwwse 0dgp)i;,s. o* kt0 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 pulw8) 1hy: nqhtwses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 1tw h8y)hw q:nm, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audahtjw; +et2x4ible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pi8r,nj(nafp + 8bsqc;xpe symphony. It consists of many plastic pipes of various lengths, which ac,fjnbar; +8 px 8(nsqre open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound qwn -u.kassp19y +tzu-cq) p,close to the threshold of human hearing (0 dB). What tp)ucn-z s+qau ,k-wqp 9 1.yswill 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 3.qp yp zp6vj,hqpi 7-are heard simultap qh vpj7pzy,.6-3i pqneously?    dB

  The sound level 12.0at 3+71cszv un m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power outpu+tna7c31v u zst (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power 1d24 8a:ntsyd- goep+vr)jitj o7q2soutput drops by 10 dB at 15 kHz. What is the power output in watts at ip8yjq7d1gn- +2 vta2so)o d r:s4jte15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ove)v5cy bq *)pme4y x3kmr 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 5p)kb xq vymc)3ye*m4 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 srd5e/hyvt g ;3ystems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a6tkb/ha 0a7 bm 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 fun,4ovj2 :ox:rsfvv*ncdamental frequency of 4j s: rfv4nvv2oc,x*:o 40 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 vibr w6rby t2pzh*c)w7 uc6ation above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the achwuw 66ptr 7c)*z2 byir 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 (wkjmux,e 8. )ib o,co 7oh;sig 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 thw7 k,)j,uesmiooxco8 .(i b;o produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ful-8c 6zdk/)lg yo jw wqq2bx*+tl 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 innt hl: t5mh /loyv(:2tzs3oy 3 the 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 the sound level is minimal at a point 0ztt 3m 3o/l(y:shhyo2tl5:nv .34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condu38 zk og0bx0bsctor on the stationary train hears a 3.0-Hz beat frequency when the other train apb z3 s0obkg0x8proaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it ap2cf,/o,nkjwo gsyhr +s x0y b;h8 )s2w1b:sucproaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assu hh1 n;rws8,2 yk2sy,x :s0fogo+jwcb)bscu/me constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to a siz;vbr ,x6 x05.imfthe difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway;,vi0 x.xzrbf6sm ai5. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequev8cyl m6 sm9ru- fpx391b52k *hqhaghncy of 11 Hz. The shorter one is 2.40 m long. How lo*29 xhm 59 -b 6ahvrkpus8c f3q1glyhmng is the other?    m

Two loudspeakers are at opposite ends of a railroad cau-5xlf 8 ei,olfm6qv9zt( r;jr as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, 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, i lj ;,5mexvf-qo9t( z68ur lfand (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what b/g)pav3ue x 4exkgk32eat frequency would you expect if 5.50-MHz ultrasoundp e24g /vkax)guk33xe 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 moecsdi+n4 1ct a 6c:21pn,zo ezth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after tha6eccns1 :iz2n4,aop1ez dc +tt wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound-ppyx2 9lqsd b :rq-n) pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that t-qrp n 2xqs:y- )lpdb9he echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signali/i y)l9t h6vbs 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 mustbh96yv/li )i t 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 cg9saq4q- 8tp y*f9w6 6se uetwan 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 frequencies for the standing waves in thi*y-ws 6wu ea4qft6t 9segq98p s room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvek gh064( n5 rjwrqgs:vc8r;cx s 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 rod can be made to “sing,”:n ghr(xgq 86;kv45cjs0 cwrr or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the h- qyof.mur6q )hi,ct5uman ear at a frequency of about 100muo-.y5f c,h 6qt)iqr0 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 Maetcv g6j)oo; 7ch 2.0. An observer on the ground hears the sonic boom 1.5 min af ogoe67 ;c)tjvter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa7tt0 b0r:b iqzt is 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