What is the evidence that sound traviglv *o-cgk( y nq7c xf046aqjv2w5:fr,,pikels as a wave?

What is the evidence that sound is a form of energcl jj:od1vv jg3h,t) :exd7hwj3f ;.ny?

Children sometimes play with a homemadkhe wdno +o 1f;5l3ry/e “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave ond y+k/ohwr f53el;1travels from one cup to the other.

When a sound wave passes l2l c o,**x5 kydidy6nfrom air into water, do you expect the frequency or wavelengt*,li6k2l *xdn5dyo y ch to change?

What evidence can you give that the spee48ogy/5dq(a q(loiuna 1 ( nlyd of sound in air does not depend significantly on oq(a 4d lin((l5/qnay u1oyg8frequency?

The voice of a person who has inhaled helium sounds very f+rn ,km:)br;1wbg g( 4fqt lmhigh-pitched. Why?

How will the air temperature in a room affect the pxzw 1a4xir8e vb/j )a9itch of organ pipes?

Explain how a tube might be used as a fila. g 4n,o d9 h5guc(h4mxxcg oj*b25ndter to reduce the amplitude of sounds in various frequency ranges. (An exam(c254m duoh ax49 no b hdx.g5,gjc*ngple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together aoaii 9r jg(r((. ep*wis you move up the fingerboard toward the b ige((r* j.owiip9ar( ridge?

A noisy truck approaches you from behind a building. ,+o n5j,x//ofcr+zqwanmcj8r3dqww wf3l 9 8 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 3/o,qc5+zc fr,lfja/w+3w n8do 9 wwjxm8rn q on diffraction.]

Standing waves can be said to be due to “interference in spac2hldt* c4te ;,2iys9 *r thlcde,” whereas beats can be said to be due to “interferenct,l 2h2* dtcdlsei 9rhyc*; t4e in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wzw(rkj h, l*7aould the points D and C (where destructive and constructive interferenc hrk7z,a*lw(j e occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who kkit 89q)3c wll/wfx3work in areas with very highllt3i8f kx39w qc w/k) noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then 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 jwg-f ja1 v.8bvwpe+mq0+k . tcan be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farttg v1f.8 wev-mjwp+ka+j 0q.b her apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer movm, ky q5wa7p(o;xk1 qye in the same direction, with the same velocity? Expla mxwk; o,qa5(yqy1p7 kin.

If a wind is blowing, wifbc mzf1tb /8bc5w/: fqq p-w*ll this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocfq :5fq w8 b/fmc1pb/-tbw*zc ity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monx01ar en 4w6-9quvwpnkwgd25 itor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest freg- dx120wkaepqvnw94n56 urwquency for the sound of the whistle? Explain your reasoning.

  A hiker determines the len,f2h i3t *tkc w8i v;q1 vy)-gnop0hxtgth of a lake by 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 length of thpvf)v khtntqh3i,i *xcgo2 1t;0 wy8-e lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hearsyked495b a a1y95srt u the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assumebu1k5tar y9syda4 e9 5 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 wav+u ru mvlb5,6ielengths in 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 abov*4 wwz,uw (aqjnr*ll,e a school of tuna on a foggy day. Without warni qluwwz4r,**a n w(j,lng, 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 splash it ma-wctpdb co3ppgd(2r;bzq2 )6 fspt2 .kes when striking the pcs2qz- p dt2t dgf23rcbp)6;.pb (ow water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hugegz+q n ;)a8wte rk5)hkvjss +( stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air asezraqvs(;)8khn+wgt+ kj 5 ) nd the other in the concrete, and they are 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 distanc;0 jx0qz 2)hvm cyszh,e by the “5-second rule” for estimating the disms,0q2y0;zhc z j v)hxtance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the . u-uh jjgjzjt: t0eae428.6fgiw tk5 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 intensiu b(a -xg;nyo7ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sd 57l:r bb qize d6bu*6ofm7/sound level of 95 dB when fired simultaneously at a certain place, what will od qu6bf 7b:6rm*zi/ b7e5dl sbe the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancec:.u xcd3) u k9ougx:v from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensu:cdo9c)xuk v.:3u gxities, not dB’s.]    dB

  A cassette player is 1d1 dcndz7,wf(sd p w3said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the w1dszp fn,dcw d317( dbackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound froqx utpm/w k,0 05d(aon6cpd(hm a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centepw0auod/(n5 ,0h6 (xc pdmtkqred 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 e2r + rt.ii1*uydnq zw7ardrum 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 r+nx xte/l*b-oezwn ;p 00qs(bated at 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 loudspeaker c*ben bqe0t x w;p0ozsx/(l+n-onnected 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 13vhcjmr30 9+t/ w6brsgd db7 2g yt0s4a0 dB when placed 2.8 m in front of a loudspeaker on trs 0 63 +hwgct9/agtbvjsrd myd4b720he 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 typicall/,/lj jkhibh1 qzk; 8gy detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: k8;bk/gj1,j hq zil/hSee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor ehewgy3(x690mxgl1kse - m ,m will the intensity increase 10l6m,- ge9sm3wegyhx( k xme? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement rr/3j:av ei3gamplitudes, but one has twice the frequency of the other. What is the ratio of their inter g/r3 :ai3jvensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds toc0d4q1m;k jam jg0wk; a displacement amplitude of vibrating air molecules of 0.13 mm 0mcgwm0a ;d1j;k 4q kjat 300 Hz?    dB

  A 6000-Hz tone must have what sound47pqaamy6( :a l* ytjc level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) j(al :q7 ytyap*am6c4   dB

What are the lowest and highest frequencies that an ear can detect when the-z4l zbg n5)p8g1+vcxs* rz md sound level is 3+nlxgs81m4 5pdgc brz z-z)v*0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What isvid /rx,m)3 xo2 :hlst the ratio of highest to ls vi ,x3mx/hl)2:tdo rowest 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 fundm ftue2 +vu usyp5y*:3amental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a masse s * v:fumuy2p35+ytu 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 he e3lyn16 z10bs(gm ethree audible overtones if thh0b sy 1 neem1el(6z3ge pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the t09/ch bhlzhb:op of an empty soda bottle that is 18 cm deep, if you assumed it was 9/c0hlbb:h hza 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 spanningiu+c.uw+zu8n ctnm4sscsng8* 7 yn23 the range of human hearing (20 Hz to 20 kHz), what would3cwnzuin*n .t8su4y 28c+ gc u+s7 nms 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 540 Hz as its third harmonic. What w4 g,myfln 2j+wln*.uwillly 4,n.+wj*ufnm2wgl be 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 abo7ci74 uz .zhgf/tywm9ve middle C (330 Hz)m./ g9f tw7cu4z7izyh .
(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 opeqteaxok18+s v 3z3v1 5jmolr6n organ pipe that emits middle C (262 Hz) when3t+3sz1 oko8vx1qje6ma5rl v the 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 at 27; c bkb gr1gq9i+mqvs92k- /csqn (bn0 $^{\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 tt jteqzt2)5s7q: hq 5should the hole be that must be uncovered to p jt5q7th 5 )qest2z:qtlay 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 H0 e ypdlm3-fyw45ifz,z, but not at any other frequencies in 0f4ei- w yl f3pyz5dm,between. (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 inbni3- :.jco2qxpa7at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330ioq7a j3 nxp.:-nib2 c 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 ucktf rsc4l,(e16 c*x i6zll,$^{\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 arey vi2voi8)uh94 f*aae present within the audible range for a 2.14-m-long organ pipe a ai2f*v 4iuo e8yav9h)t 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 outsi7w3cmm yc2 p7w 2j6cxa.hpzv/ de and is closed at the other end by the eardrum. Estimate the frequencies (in the audible raxwj2pc73mhw 7v 2ccmz6ypa/ .nge) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust tm5-*jz .pn7 +rfd2iy(x1 jj/ptiq0ijtn t p9ywo strings, one of which is sounding 440 Hz. How far off in frq+2j*xfp9ip ntiij0jj / dyn( 15yttmzr.p -7equency is the other string? ±    Hz

  What is the beat frequency if m kq(fo bo8 u/ig6a+/lfiddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5rg+;l22cv z uuvu ;89ihi fyx5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate fg 2+vxzr8u9cui h;lyi 2v;u 5the operating frequency of brand X.    kHz

  A guitar string prodk9b w+pz6d)jskdk09.e iqu /z uces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Whab j6kk) /9pqdszkuz+ed0w9i.t is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one s)d+2zbhnevftcp,o ; tqr 3c)5tring is then decreased by 2.0 c2n)teo+f zb3crd, ht 5qp)v;%. 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 middle C (1rjf54ix /91a jgiatib98l qg262 Hz), but one is at 5.0°C and the other/81r54q9jjgigt9 1iaa xbfli at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, anu(7kt3 ngdl j.nzbvs-.g*v o1y gt 6h;d 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 beat frequencies are possible when A ansnhk *1( oz7jydut.3n tgl;6 .-bgvvgd C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are edla:6mm /)rum l)g0v1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other.)le amg0/ :dmv)mul 6r
(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 piano tut +2jbq)j7g xc5xwzs ody 3pf z:z58-mner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must b 5-xo )gp72bzj tj5:z s3qwydzcfm8+ xe 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 many beats peygp,8zf/ukcv*zii(7 r sef87ziz c /yv*,p(gki ucond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire r -vx)dzaw+yy p.*o*tengine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with r po+- *awyt.ydv*z)xa speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you deteak0 3sb pme-k9ep/vqg 23)matct if a fire engine whose siren emits atem39 g q0p) kp3 vs-etakb/a2m 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequ--rog1g+mnr 6 q yo3ipency 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? Arp1m y ro+-r q6iggon3-e 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 sam96*qxt,cyy( t4 acoyl07k iie e single frequency horn. When one is at rest and the other is moving toward the first at 15 m/,ykyiyt0lqo6x( 9e cc47*iat s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves /702 t6m+giwhvu sbanat 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound f0h / nwbi stu7gamv6+2requency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it ,-d5ufyg zir3qqg2y8b//(u t dmxij)flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frfx5 ()bud uiqq-d 3yyjz2g8tm ig,//requency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wa .m pcro4ee0kxv6 1q3cs played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat fk3r41q.xc 6emv0ecp orequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speqq12t2 dl jcxci /5g3geds. Suppose the device emits s qlqtjg5 c2c3x /gi12dound 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 ul pvm 0amd )5q7ntlp87mtrasonic 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 so49. pi7jfah9 o((9g2apl dtwx .o haewund of frequency 570 Hz. When the wind velocity is 12 m/s from the norw 9 x4ho(wd p 2l jg.9ahaf(7i.9aetpoth, 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 if its speed f 3 yvzfmm0xtp9f58,glseu8-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 qt9rxx659s udh5y; t iMach 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 motrttxq5;599yi sxhud 6 ion?    $^{\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 of so.njee *,l opm7und is only abou j*7oe,menl.p t 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 str uv 6c9 rxa6ekwygsga+gmfjp8w 7+zv( 9*c14bikes the ocean. Determine the shock wave angle it rf4 kxu+vwz gsma7ja1gb6w6c9 9cg*e8 v+py (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 n2zu/o- uq*o m9eyj5b $/theta$ 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 the grouq0hl o/n .-(pynpn,kmnd flying faster than the speed of sound. By the time you hear the sonpq(ymlkp n .,/n-0oh nic 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 downwac*masegk7aj tp2f 1* 8rd from thm e17*g tsjpck*f8a2ae bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaveb(l11 ir34 a ikrmlx7cd6on4b s are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a4lw6* e9onokl display called a sewer pipe symphony. It consists of many plastic pipes of variousw l4ok o96enl* lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to theh+b 4qsr3tn7 ik(x1fs threshold of human hearing (0 dB). What will be the sound level 1k hf+xbrs73snqt(4 i of 1000 such mosquitoes?    dB

  What is the resultant sound level when an *bgj8zg vw- u) um0g)r82-dB sound and an 87-dB sound are hear- bmg )gg) z8uw*jurv0d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 df,ty jyy.ej03B. What is the acoustic power output (W) of the speaker, assuming it radiates equally in alety 3fy.0yjj, l directions?    W

  A stereo amplifier is rated at 150 W outpnp;* p7 * p*o80dqbqhqhm6qk jut at 1000 Hz. The power output drops by 10 njp8h7*o06phqkmq* q q;*pb ddB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typi(t,d:)3 vwm yfcf6s, fc0on djcally 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 m from a jet airplane en mw,d( t cyc36osff)f0nvj,:dgine?    W

  In audio and communications syst9ra3u einr h51ems, 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 a frequency 1d fu4x1mx8ayrr ib3j;*k pa4nb;*b,k$\frac{1}{2}$ 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 w)2g7b) jhlg*k e8evwe ith a fundamental frequency of 440 Hz and a mass p7eg g) vl*)bje2h8wk eer 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 vibration above a vertical open tube filled with wa:. svfhls86 u;9ldt fgter (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 0.39 ;dfl 6 svtg8ls.f:h9u5 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass4ps4f : r m.m0h4bme7iiax z,n 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 nxre.pim7 f,a4iz4s:mm04b h is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obb/pxt5g+i- mqbpw e3czeo 8,. served to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure t *pwiihc1+j +bie c/0oone in the 500–1000-Hz range coming from two sources. The sound is loude0/h*epjoi 1i+ cwb+c ist at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whist; vpu b kf*; loo.yniq.w. klh4-h;9lrles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moh ob.yfk;;4or-h.nw *9p; villl .u qkving train?   m/s

  The frequency of a steam tr: lk7 c* ihoan3cb: h)r2:(ehetjnuhmw4js-+ain whistle as it approaches you is 538 Hz. After it passes you, its frequency is mkubm2* (4 j +:ahhl:eerwnci h-h)on3 :ts7cjeasured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the di7rux*3xa ;zg9u* mwfq8g4x pq fference in pitch of the engine noise between apx9fugpx7 r 83q4w;ua*g qz*mxproaching 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 b (nla7tm3r h0veat frequency of 11 Hz. The shorter omar0 hn3tv(7l ne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pan.18 v-un 6x.gbi irzsst a stationary observer at 10 m/s x.-b.16inn rugsi zv8 as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s whath cm9x c4*0rir beat frequency would you expect if 5 hx4r9c0mri*c .50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at spz*pq,d0 hw6t kxd)d ,reed 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 p6zt*d,,kxr0 wh)qdd. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaced o3b2a9sywg90.z3be baw :jhes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the mot 0b3b9g:ew b9ay jwaed3sz.2o h 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 abfke(tc. 1z+ send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an op+z1c(baftek .en tube.

  Room acoustics for stereo lihz c p3 -s7.lvyrx,9glstening 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 3,c9 pyh .lzg l7rs-xvm 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 a9,a mymxxmk-7 long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is k a9mmx ,y-x7mstroked 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 of:yeg9+ ;h-n qqrbaq6+ve imw,z+ buw9 hearing for the human ear at a frequency of abo+; ziq:rnq+,u +9eb-ew ghawm6 v9b yqut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. Ab-1 j0pcck6q dn observer on the ground hears the sonic boom 1qk6p-c jd cb01.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa7z-ui5qsmj 1.l3 6 zv kplx.fht 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