What is the evidence that sound travels as a wav- s8o-ddf(dsle?

What is the evidence that sound is a forlmw, h,1(uc j)/u3savefo )kqh+s8y xm of energy?

Children sometimes play with a homemade “t*4u aq gj7a;leelephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the ;la47qeaj *ugsound wave travels from one cup to the other.

When a sound wave passes from air into water, do 93pv2.df*cix ,eqo r iyou expect the frequency or waveleng2riic.,9f x oqp*3devth to change?

What evidence can you give that the speed ov ju*8369kh b hmy)8f xigzkg)f sound in air does not depend significantly on y)hj) hv9bf kgg8z 38*umk6 ixfrequency?

The voice of a person who has inhaled helium sound,xzlwe jgx) (1s very high-pitched. Why?

How will the air temperature in a room affect the pit)p 1h dupx3gmh*i 8-j7gu)rx l0kb-vl2 aiu(mch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sv3lqu sk.714py q;awsounds in various frequency ranges. (An example is a qysvu.7kq;3 1a wps4 lcar muffler.)

Why are the frets on a guo,i zi3 zgmfjht) .*w3a3g3dpzzq:l;itar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bl:z,zw.jihmtzq* 3)dz3o fg3i 3gap ;ridge?

A noisy truck approaches you frolqa tr tn/g,45rg s56um behind a building. Initially you hear it but cannots/ qn4u6,tgr5a tg lr5 see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due tbqz u*f39 4fan 2a8 ibf;gvdr8o “interference in space,” whereas beats can be said to b;vz984f8ua32f* b qi gbnd frae due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were jk*uc: yf9azl7 ;q /c83ks bdolowered, would the points D and C (where destructive and constructive interference occur) move farther ap9osycuzckj : badkq7/83 fl ;*art or closer together?

Traditional methods of protecting the hearing of py;kbzd0c9vk5 eople 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 blk 50v ;ybdkz9cock the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thoughp+mv7zzdfrwom 002eq0, j os1t of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–mq2f 0 vowz od+,se10mzjp0r7 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 +uy+f*s k/mhwif the source and observer move in the same direction, with the same veloci yw+s/*uhfk m+ty? Explain.

If a wind is blowing(lvwzxm+ lfyo34h0 z3 w;vc j2, will this alter the frequency of the sound heard by a person at rest with re3w l2 mh cvy3ozvw;0f+jx4zl(spect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chz8rfgr1(d: kv ild 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, wiz1gvr rf(d :8kll the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of /zqba w*7)k7kbkuv2 gn:jzb8 a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake.wj)8*/b7vba 7 zkuzng:q2k bk 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 waterline. He hears the .b atu epnx-ut2;r5 b8tsbs 02echo 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 withxtsb2bb; .trn2e5patus-0 8u depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air anp5ywm u/db2 :t 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 lk -7)xhv .stlncgbwh -w7l:*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 muw:bhcvsg w7nlt kl)h* -7-lx. ch 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. y vvb yp-kz-1hl4qb)(The splash it makes when striking the water below is heard 3.5 s later.vzpy4hyq b)v l1-k(b- How high is the cliff?    m

  A person, with his ear toua*( kagd 5-jg the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apartaadj -ug5( gk*. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error may ;g p*igwhj/76ecd;m*baw *wde over one mile of distance by the “5-second rule” for estimating the distance from a lightning st*6;aje7 ghi/m wgw*cyp*d;b wrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of aana3;icipcg l95+l4o sound 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 intensitew3dcqsnpih 9s 2 m/,zsn+ke 5wh1s66x, y9gty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leveu +l:gs1 xm(f i akhyja-e*(+cl of 95 dB when fired simultaneously at a certain place, wh-k ljgfh ( +s:ya*ax(me1c+u iat 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 f3dmn1 z8k3bdc:a4odej p8,s jb i0;mj1k ciu+our equally noisy jet engines is experiencing a sound+adsmu4c, c:i3p 1j ojbmij1e8 3 ;bzk0 ddn8k 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 have a signal-to-noise ratio aut1 g;n8 d,v )nhx vk3zbr8tv;.;s mvof 58 dB, whereas for a CD player it is 95 dB. What iunn.8k bg ;xv r ;tt3,;sz1vdmh 8)vavs the ratio 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 person speaking in normal convers-yp s qrb bn 5y.v3-4s*u1jal8yfug3pation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphupljsf53y-v1 bn yy-gp 8r*.buaqs34ere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eztva 4yxwwj4k68ty. / ardrum 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 250qugi-vda3o au22+ dw -x f6pd+ W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in3-gd 6x wdfvoiaad2- uq2p+u+ 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 cp;4 ncfqq71sfront of a loudspeacq nc1qsfp; 74ker 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 dj ecdwso7k) 05etect a difference in sound level of 2.0 dB. What is the 5 wsek)7jcd0 oratio 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 ity, diil- .mlok7) *iolo;1 jds tripled, (a) by what factor will the intensity increase? Increaslio,) 7m.o -tl*diyjk i;ol1d e by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bustyw) o28+p /8e xpmw;zu-kx it one has twice the frequency wtm-;u e xsp pio8)xy2w8/+kzof the other. What is the ratio of their intensities?   

  What would be the sound lwe9qy7xsosm w1e;ox 3 cke3/:evel (in dB) of a sound wave in air that corresponds to a displacement amplitude xe9cyew;owe m/ 3:qsx1k3so7of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that 81lmrxlvu4(a)w98 n a9wd tk s52*eackf5 teowr8ekd k59 59a(8 ata2)c 14mfeto*vnlx uw slhas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whenkvfz sqve:6(* the sound level is 30 dB? (S*v6 fez v:qs(kee Fig. 12–6.)

  Your auditory system can accommodate1nt stg g93l;b a huge range of sound levels. What is the ratio of highest to lowest intensib gltg3n ;ts19ty 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 okh1ght.lgj( (j hrejc l339l.f the vibrating portion is 32 cm, and it has a mass of 0.35h.3l91l j3 (hrge(.gjkcjl t h g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are tnqi0hw1(; pi6d tr sm,ge7dd4he fundamental and first three audible ovnert(1i,6ghd d dw0i;7 qp4ms ertones 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 frequency0pzr.b yf )3*e+zmrb5rimn+sv n z0:y would you expect from blowing across the top of an empty soda bottle thatz+ n rvrmfe)50 bz mb:y0ps.+i*z3 nry 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 t07 7/zn 1 4lwepysiwshhe range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? 7wsi/s 4welh 7pz01ny$L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frj2(ng (5f tplhequency of 540 Hz as its third harmonic. What will be its fundamental freq5j2 ( tlpfn(ghuency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lon bd:ctgtyl7iet4e21no ( m5. vg and is tuned to play E above middle C ( tb :lg7 4e 12nyevdoittmc5.(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of andti fnkau-ayx 883 yl144h8 sj open organ pipe that emits middle C (262 Hz) when thatda -y 81fyj l8kx 84i34nhsue temperature 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 3zy .p1oyt;jaat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be thawdh u* +d8oib uv-;er*t musure* dbd vu 8wh;-*i+ot 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 Hz, and 616 Hz, but not a/f)vih u) xfw.t any other frequencies in bihu)fv.x)/ f wetween. (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 resonates at two suc2 (s4ks1s2)kuiuez 6 ye.mxhacessive harmonics of frequencies 275 Hz and 3sm16szy 2. hks)4kaxe (u u2ie30 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 cecdan9 a6o(-j* v;(zb m)1attk0npp$^{\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 orga)hu5wyz )p5fvn pipe f)w5pyh5u v)zat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxima)yqko44 p2ixdbm;f 1vtely 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 w kfd4m1 ;)vi2pxb4 oyqaves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat o;ko sa ,c19m9badam9every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. Ho;dmo 9aka,o9a1s9b mcw far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262c+oo/f8wq6n c-y 6fqf Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at po 5,iu1)y th9ve656wpwu lnv 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 frequee6wui y)uwn6hop, 915v5v p tlncy of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuninpdl 40pn s8yo;qq/v 6hg fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationaphp ;8l/sqq 046ov ndyl frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in on . cbebju/lm2m k:it6ry.r9g8e string is 8:t mib mr9gjyrk.2e 6lbcu./then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middlet.h2do(js zg(qyma*e1 w;mtr7k ul2 ( C (262 Hz), but one is at 5.0°C and the other at 25.mk2.oj zt71l y( mesr a;h2( qu(*dtwg0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, an7as yjl3s+ ;h1pwcg:g5vu *9xvdx5 ysd C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What byjg79 v5g: w+1x asp5hdyvsucx 3;ls* eat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 b: *.a(rhooh8 baue(xm from one speaker and 3.50 m from the oth hb rh:aux*oobe.8a((er.
(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 vibratingjop m)e.zu q9;omds/+7 6qrgu at 132 Hz, but a piano tuner hears th6po gq.ouz+7rj )smq;umed /9 ree beats every 2.0 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 and 2.76 m in air. How yhj-16j6 pkhu;l fvu1h4aj) xmany beats per second will f6ajl6ukyh p11xjhvu j)h- ;4 be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirevq8h ,)hkxf, c6)yt j2;fjccon is 1550 Hz when at rest. What frequency do you detect if you move ,jhtho)f fc) 6yvjc,kqcx 2;8with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stiht*65ert7zm1c o5zoy 92bjxq ll. What frequency do you detect if a fire engine whose siren emits at 1550 H j5c oxtzzb9m 5o6eq*t721 yrhz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency (syn 66vfz,y xm lb,wp-55oko if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are tz y ,p ,l(6nmsxb5kw6-o5fyovhey 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 ondopemlr8qz,/m;:*(z2bbzi qm mvd*1 e is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beam *ze:;o v2bqml *q18idrd (zmzb/p m,t frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrason ka+, u0 (sq-as3oqizgic sound waves at 50.0 kHz and receives them returned from an s,3 aq-o(kigq azs0+uobject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a fm1fspxz:f/) c(uf g2speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave wi1xf p2f zcg/mfs:fu()th frequency 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(p)ce n;nqzsl gw.o.) 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 l)nswzc.( e)o q. ;gnpbeat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wave(5y/c+ b*vhl.knel7 1zov *sujxmo9k s to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in j*v 9vn m.h7uz5kclb * +1oseoy(x /kllarge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of (k7wq dzar17vzcr,7 yfrequency $2.25 \times10^{ 6}$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 frequew,*h o+o9hgenncy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will obs geo,*9hwno+ hervers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spe 6vqsi6m:*8ahf8.vq g9 m1cv3armbeb ed 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 Ma m8ad6e2s:mghrk1/xaa ih(,vch 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s m m6 (mragiaxsh/ad8 vk1e,2 h:otion?    $^{\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 of a planet where the speed lnmp9mpwec8( 9m m t1(of sound is only abo( w ncmmple18m9 9ptm(ut 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. (bo64zf6 sab9h+ lip bDetermine the shock wave angle it oz69ifb+ ba6s 4pl hb(produces
(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 5fxg ea-) dr8s$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a(i,ue+yypr;q .xft4u plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontali4;eqyp fu.tuxr,y +( 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 son(tpze1;2 wo yiwq, zi(zy (g3iar device that sends 20,000-Hz sound pulses downward from the bottom o iziiyw e,(3ygp(o z2 (t;1qwzf 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)?    s

  Approximately how many octaves are there in the human ab/(:5s1 6 hr*5ln. u ebrac6rn,gwycy3a wtgqudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. 2mj3kd 1/kbwqIt consists of many plastic pipes of various lengths, which aw 13mkq /bjd2kre 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 close to the threshold o2qdh9:tkpsl 1y9la5r0j*ue 7lgram v1 w/8e xf human hearing (0 dB). What will bel7d jsm:xr 9ekaaeryh vw ql91tp /l05u*g821 the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dn2qb9)asm6)jsckg(m 1r y7 r pB sound and an 87-dB sound are heard simultaneou csp sn9 1ym2arb6)7g rk)m(qjsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105c ey h.7invpf97-rir8 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all diivc7-9i . enfrh r7p8yrections?    W

  A stereo amplifier is rated at 150 W output ajkcy00mh5r zl(of e5)xjd+t+ o *o( sbt 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHmod(oz5+rjc +0bx* se)0 l f(ho5kjyt z?    dB

  Workers around jet aircraft typiaw*nnco3 ze5q: 29n*a ujni y. ogs)1hcally wear protective devices over 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 intercepted by an unprotected ear at a distance of 30 5o2ni. *gnazohca) su* 1q nywnj93 e:m from a jet airplane engine?    W

  In audio and communications systepkda +1vwy4cs6w7 ull* q3 2nzms, 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 a ocy- 53k8evfis 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 pointk+5 iv3uo6ldw /*)7ofjj vhqus with a fundamental frequency of 440 Hz and a mass p7)/u l6d3+vwoqkjvi5 f *uojher 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 /j5bl*re, 590bwtbon4 jau bc vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it d jonb/j bb,ub54lw *r9act05eoes so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that isbie3,uj,0d lz b zc2h4 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 fundamenzdh ezbl302cj,b4 u,ital mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full l sg2 bk,2;yi sfn)t5laoop ($\frac{1}{2}\lambda$) 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-n jhec4 1c*c*igrmv64Hz 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 isj4g6ch * nircvme*14 c minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationgies0z ,im9v9 1;5ujh+74smd kuu qckary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movinggduej9+u s 7z159vskcm 0quih;i4m,k train?   m/s

  The frequency of a steam train whistle as it approaches you / rxtsch((d1- sokydr+ (i.bm3t ejj-is 538 Hz. After it passes you, id/(.b -1sysro(x ri jt keht+d(j- c3mts 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 bx v+syl-g7s5hy g1nf +y listening to the difference in pitx-+yvfggy1s+n5 s 7lhch 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. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. b:dw.bvynk74 g( i 2:pqxdv+zThe shorter one is 2.40 m long. How long is the ot:bvz.vy dn2kbx 7q: id+gw p4(her?    m

Two loudspeakers are at opposite endx fs7fm+ rk;lo2,oup1s of a railroad car 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, and (c) he hears the speakers after they f ;+f17xpkru,ool 2sm have passed him, at C?

  If the velocity of blood flow in d, tluxoz)+,opbz1 2fbp3 *ye 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 the waves trav+uxpzoyp3t ) d eo1b,zb2f,*lel 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 flying towaryt3b 0 nox7 ax0cku;so 4aj*h.d 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 that wave reflects off the moth?o3c4; hatk ny*0 .u0sojba7xx    kHz

  A bat emits a series of high frequenjyr jg5kirg)/ 9(e 5wkcy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and i5kkgr rwygjj/)9 e5( 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 tf*,lv aoiw+l7 o 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 musila, +*7fw volical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening jp*:q)x:*gdkx/g,:q i s-w 3eey nzec can be compromised by the presence of standing waves, which can cause acousti: jzew ggx *y* :/qc3-nke,iq e)pd:xsc “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 this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a 9y*qov(ykn bt hjz:.jc3x*k/ 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, jc*kovb(yyz/ * xqkht3:j.9 nthe rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearx;tkf6y3skv 4 zh- *vag,, yhfing for the human ear at a frequency of about 1000 Hz is zt,ayfh4kv 6,sgk- yv*f;3xh $I_0$ = $1 \times10^{12 } W / m^2$ 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 Machkl*hhw 4+cu5 it.a: f8sy l q.52pxblw 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passesathl5* k y: +.pb8w5 u h4i2lwlfxq.sc directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 v/ +j fvqvp5(5vsow: xjd5uv7 $^{\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