What is the evidence that socd/ik 9z 4qx8pund travels as a wave?

What is the evidence that sound is a form of energy?ds yvsmbz*p. q1f. d ru5ld7/5

Children sometimes play with a homemade “telephone” by attaching a string to t0lf n0e(lp 4vt 3m6kxfhe bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard al(em0 4xvpk 0f n3lft6t the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passea -::xe5+l cef 6bxfchs from air into water, do you expect the frequency or wavelength to l abcxe+f-x6 e hf:5:cchange?

What evidence can you give that the speed of sound eh5- cw hosta.(e0;qmin air does not depend significantly on freh0o(5w .; mchas-tq eequency?

The voice of a person who has inhaled helium sounds very high-pitchnzme(re*. 1 vxed. Why?

How will the air temperature in a room afl pg21g.z2q, g i5 ,u8ygrezhkfect the pitch of organ pipes?

Explain how a tube might be used *2i9e3dl or2hr 0 gzmmue/dy)q b,(hxas a filter to reduce the amplitude of sounds in variouh rl*muodz i he3d)(y qxg 0m2e,rb92/s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer to0s,;,g fv.3nbfr rbvkgether as you move up the,brf ;s gnvrbvf3k,0. fingerboard toward the bridge?

A noisy truck approaches you from behind0(p, uyekg ; /l t6g8w svj(c2yrvk*dr 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 on diffravu6kgy;s y*2(trlk ejrv0(8/p,wc d gction.]

Standing waves can be said to be due to “interference in space,” wv-ve;0/dj g9j) ekzoxa7:ime hereas beats can be said to be due to “interference ik j zmev7i0x;a:j-9deeg)vo/ n time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointq 7 hq:)l s8of9vw1yc uw29apvs D and C (where destructive and constructive interference occuc)7 qu wh v:wsqp82 9yvol91afr) move farther apart or closer together?

Traditional methods of protecting the hearing of pe;+ ugirotl(,tss c0 - ;kkg/cwc, vko/ople 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 o k ctlco/kicu(;,+ 0ws ;rkv/g-,t gsare 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 r //tptk2 ns5dhbib( lfz) ot:bz1f0. can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which2:./bp ht fz(b10brfl5d zn)ksto/it of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thedt1; 0ce6 q-irpl, pvh same direction, with the same velocit ;idlv0 qh 6,-rp1epcty? Explain.

If a wind is blowing, will this alter t/r voxorn h y,/4f:6mche frequency of the sound heard by a person at rest with respect too/o/nv :4mr y chr6,fx the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monicblms2 a- ieg)c yt*,k9a;0m jtor is blowing a whistle in front of the child on the ground. At which posicac y9;kg ,0jm-tml)a 2b*e istion, 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 by listening fo ( 11xy5icu 1 o(hsgs,jnj6syar 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 lenys5g,1ans c1j(hi y6( 1sjo xugth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of c5 z6jsu0f ry6)nbdb7his 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 speed of sound in seawater is 1560 m/s (Table 12–1) 56cfubyj0r6)db n sz7and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtczrqw8vn s dj2g:0xw4 v*u5 o0 om-ya(hs 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 above ; 3wqthyh-j 0s8ypl p87rm,wy,c,d dqsi*4ar a school of tuna on a foggy day. Without warning, an engine backfire occurs on dh,cp0y*jw7wslq ;aq 8p-s th dyr3i4y ,m,r8another 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 makes when striking thn8 zzz8z*kf,)g o :i;b.ygxvhe water below is heard 3.5 s later. How high is the cli gigbnzk :*zz;o.x,y)z 8 h8vfff?    m

  A person, with his ear to the za 8ri+6;qbs tground, sees a huge stone strike the concrete pavement. A moment later two8iabs6;+qtz r sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over okse-eu1 g-+wd.d*f q mae+,mlne mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a-uasm*e , d+.keq 1gm+w-lf ed) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the painve)wn.fj m /uz ytfbzp6f6528 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 inepn* ,s6 cb4xhy4y6b mtensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneoustfpz620 ucmrw7 te.- )cb;jpgly at a certaig7t. t2bpfwc) z0-erj6ucpm;n place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane - t47e zhu abrxfpo4.6with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this p4hobu r xtep7-z f46.aerson 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 rmhnjlol4 72s :atio of 58 dB, whereas for a CD player it i 2l :lsohmn47js 95 dB. What is 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 e cap1s -gpnk7rf,u-- conversation. Use Table 12–2. Assume the sound spreads roughly uniformly -s, eng pk-1-cupraf 7over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose arpqb i: e41oer)ofy86 hea 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 nw)ngw07 vw ht0u7zt4250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sou u70tvnwwtwgnh 0z)47 nd 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 registerk+qf+q6uso-- cm:c9 w9b4(wjd mzkyred 130 dB when placed 2.8 m in front of a loudspeakeruw9y6c+cfd-+-kw(q9zmsoq jkmb :r4 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 le0-jdu 0pl9gt z91wgh1(j x wgd-w2cky vel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? x hw2 jjz (ytwk- u0gcdgg1-109dwpl9[Hint: See Section 11–9.]$\approx$   

  If the amplitude of a 2fv7l2/f)t t 6efslwv sound wave is tripled, (a) by what factor will the intensity increase? Increlf/7fvwsttv f6l 2)2ease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fre.qvt/7xb4nd np ,jzm,quency of the other. What is the ra,xnvz,. b/dnjm pt4 q7tio of their intensities?   

  What would be the sound leve0e d /fjhiv4qnp.;y9dc d,, aol (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 ef pd9dnd qo;v,0ia,c/4.hyj Hz?    dB

  A 6000-Hz tone must have what sound level to 4zrv(r*s z,dzpminku p4). g7seem as loud as a 100-Hz tone that has a 50-dB 7m zrgizz rp44(d.),sup k* nvsound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can deuizhb5nh(sys5l)sh* cgd 348 a a/xhr)/v1artect when the sound level is)c5ys1as3(xn4 a* a h rhdz/)uv8s /h rbhgi5l 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is fg) prhc7+4 wn/r+kiuthe ratio of highest to locp )+r i+g/n7u4rkwfh west intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a vio(pnsq;48aw720 ztc;fu nqf+p i 8yeeblin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mustifys nab(8870qpwp;+2 t; qnu4fezc e the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental andib 2u0o(p1xt ;yr-agy first three audible overtones if thrayb- 2(1 0uigpyto; xe 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 2n8 xtv9ojny,kw p9d7 the top of an empty soda bottle that is 18 cm deep, if you assumed it was a nw,p vx9tk28jn7yod 9closed 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 ote4)q uk(t54jp7wg oppen-tube pipes spanning the range of human hearing (20 Hz to 20 kHwogj t 4eup (7pt)q4k5z), what would 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 freq:wz zra f6s5,nklxi1ln z96q+ t:rl2suency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is f,5sts+lanxrz 2 r9l:6:q6nlki zwf 1zingered at a length of only 60% of its original length?   Hz

  An unfingered guitar st rti3ay:3qo f+5b pz-btx k+4tring is 0.73 m long and is tuned to play E above middle C (330txt5zq trkiyopb3b:a3 +4f +- 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 an open organ pipe that emits middle C (262 Hz) whd-kzdv h vyr/:2) xahm; 1a.yten the te-hak2t x d.;vrmhdy/a ):z 1vymperature 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 a/jm+ov*2 qa mj1a*yc 4ii c)hw36feuit 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thr/azep;ho88 ; qb 8(tsj4rzcte flute in Example 12–10 should the hole be that must be uncovpsjt8t 4b/zeaho8c;;q( rr8 zered 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 vdq; q:dl4hg1 at any oqq4v g1h:;ddl ther frequencies in 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 longj zf,*dqv 9+wy ez3ka- is open at both ends. It resonates at two successive harmonics of fred*a- ,eyjw z3k9qzv+ fquencies 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 *;x lpyo en(nkt6um./ j*cn/j$^{\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 fo/g e 5bfc6 n7kzl)ct)br a 2.14-m-long organ pipe at 27fc)kbbt)6nc z 5eg/l0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatwz0+qzvj qf/e 3ym,7 u(h4blkely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the3vq/,(+bu emh7lwz4k0q jyfz 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 two strings, udir vq 9t b/:fv;i7*0wdh6egone of which is sounding 440 Hz. How far off in frequency is the othweq* i;0gh6:itfdv/vb r d 9u7er string? ±    Hz

  What is the beat frequency if middle C (2622rkxctad,mt 53rsf ;s4w1q 9 j 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, whil.ljm87knr dh ud-1*uje another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of fre*-nljuhur m 1k7 8.djdquency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 8o)dc ivqfyo7: x,hpnsriwx3+ 0,lh: 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Wha0l:oxv7)h+drx, oic8 iph3fyq,nw : st is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency,lcgkc;:9lai 7 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: 9c c7laig;kl: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play midda2 ker cqkpnb:(h1.j:zp6f-vle C (262 Hz), but one is at 5.0°C and the other at z.ej: qvckfa6-rkn p(p21bh: 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; xj p);ggh ka 8o8ct(a0z:hc4hwhen A and B are sounded together, a beat frequency of 3 Hz is heard. Whenxpa:0g 8 t8o(c;c4ghkhzha)j B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded 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 qi12jgbl *ff+ person stands 3.00 m from one speaker and 31 2ifgl+bq fj*.50 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 supposed to be vibrating at 132 Hz, but a piaz mnv8(i.y 3qnno tuner hears three v8zn3mi n. qy(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 a s znea5)+oq;xx8:hdaei 6.zzir. How many beats per second will be heard? (Assume T = 20 e+s6ix 5qe )zoxdh; znz8. :aa$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1 r)zcx5x 3t b4lu/xvo6550 Hz when at rest. What frequenc3uo5/64 vxzb)l c xxtry do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do6e: +ph1 qy3ygq6p, epvkgye+ you detect if a fire engine whose siren emits at 1550 Hz moves a yhpqe61pg:yke6q+g p3,e v+y t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mov,g jnb1lg/o:hing toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are g oh lng,:1b/jthey close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one toy qqbe *l9g.- *tf0vis at rest and the other is moving toward the first at 15 m/s the driver at rest hears to9b0v*tqqy -*e. gfl 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 o cg.kw+y9j( lgt vi*5fut ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the recevf 9gj+k gli(y*.5ctwived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bag gt;padb 5 8oij.gd(2t emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the refl8 ( .a2iog5dtgpd; gjbected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movcl)icjo,8 ope;e j a/;ing flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a sp8;cco /lpjj e ;eioa),eed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasounrmd6d w. a lel ,0/mh.*imva,wd waves 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 large leg arteril,lr*wmiv6ahd m0,wa .me / d.es at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wav u) v8faovn1,wes of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound o i3ka3mc25 ;s end )fkc0:i8u*ceonewf frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequo0ws ak;)3e*2 nm5c:8kicnfe ed uc i3ency 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 movinc4pf wyv4k selkw( )tnr9)g.46uf8zf g on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What i58xgk l 7tlrax4agz75 s the anxk5 a57847rx ga tlglzgle the shock wave makes with 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 acur4 sfzt; sw+tf( zf,3h38hdtmosphere of a planet where the speed of sound is only abo h;fd rs zh(u4,3w 8tt3+fcfszut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the*g kjpt53jtu-wfz 8f5 shock wave angle ip*ut 5jt3jwfgk8- f5 zt 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 tgh.*b wbpr2c-2; c0yur g 6tx$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and ulvg0mxm c bc-/h zqd ++a8+t/see a 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 horizontal disth +dc/x+m u+/bmg8tcq-l 0a vzance 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 so,s.1rcf o6 zk)o9fr iends 20,000-Hz sound pulses downward from the bottom of the bofo9r6)o. oizkf cs,1 rat, 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 manx ul,1m:vllo+ y octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It conaexwkub /* tm3 tsu/27mr zg6/sists of many plastic pipesg 7me36uxam z*/ kbtw/tu/rs2 of various 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 the threshold of huf8wpw0cqm: oi 8n n3/zman hearing (0 dB). What will be the sound level of 1000 such m8 z/ 8qno0fww3 ic:npmosquitoes?    dB

  What is the resultant sound levelce ;:ydi: fur8 when an 82-dB sound and an 87-dB sound are heard simultan:8:u frd;e icyeously?    dB

  The sound level 12.0 m from a loudspeaker, placed in tgpjz1y5qbq -(a z d6:xdfr*g5he open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directi15z6-ybg * (rx z:daqdgfq5pjons?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The po+zkz*:gg;px(p xcd zq w/h3q 8wer output drops by 10 dB at 15 kHz. What q*:3xxzh 8gc+/;zgz(dpkp qwis the power output in watts at 15 kHz?    dB

  Workers around jet aircrazqgfdf*xx/+adp n-wu14x.z *ft typically 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 unpxgfxa. *fu /nw-4 zd *1zq+xpdrotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, thcaybhl*n 1+ s3e 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 iss 5rgz4 sai5,pp; cwa2/fvz7x 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 betweengr dk6hr58zk2rh2h 0 *sv j/ym fixed points with a fundamental frequency of 440 Hz and a mass per unit 2 *m2zshrhyd j/0gkk658vrrhlength 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 5cktzltzx ly(+6w:x8 a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard (ckwxt8zt5y +xl z:6lto 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 *c8u;6 1nf loza0 nzwfo9 lx;pa tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tub;a60nlu9 wol*fzc8fz; po xn1e?    $ \times10^{ 2}$ N

A highway overpass was ov:94uxksvxz 5bserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone i9bw(u, y62ylfq- c lcyn 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 0.34 m farther from one source than the other. What is the frequency of the sound2y ylc c(y,9wubq6- fl?   Hz

  Two trains emit 424-Hz whistles. One train is statio apzv95s9 qoa rg7s/+jnary. The conductor on the stationary train hears a 3.0-Hz beas qza9v p57j so/+ar9gt frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 c+p11sn8gi f :p h zwnh*b/hd.Hz. After it passes you, its frequency is mewf1 h*sz h p+cib nd.8/pngh:1asured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate t/yfltf1j*+wv wjht3e)x- 4ewhe speed of cars just by listening to the difference in pitch of the engineewhwtj* )fje 3 1 ltwy/f-4vx+ 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 bea n 4hl-9ckaf-vt frequency of 11 Hz. The shorter one is n fc-lk9vh-4a2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railc4 --u gdhrzv)road car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–d-4)zhv u-rgc 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 ingzm4by9k ed 2g.qj)npb,i.: u the aorta is normally about 0.32 m/s what beat frequency would.pdbgj4z n.,qg:k y)ib9e2 m u you expect if 5.50-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 speed 6.5 m/s while the moth o q u 0)6(ey04p*uifo8in kyxil;k4l ois 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 that wave reflects off 4u4 l ii)e (l0*iq 8kun;xpko ooy06fythe moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a m 7 vf6 vu-yj:+ow,ndrcoth. 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 the echo from one chivvfj-u7d 6w r+ :oycn,rp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals,i /zb(w3e7:k-kytnnn 8bjcy from one Alpine village to another. Since lower frequency sounds are less sus n nbk3ykt-n87/:ze ji bc(,ywceptible 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 open tube.

  Room acoustics for stereo listening can be compromised by the nfa5mjs-r z rx7cs.9 *presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m79 jaz* m5fn.s-rcsxr 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 long, slemuq+2;gk. vqtd;h 9sf nder aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing .qg mfu9k ;vs2q thd+;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 yh3he j2k-6,j e .dvrohearing for the human ear at a frequency of about rdykv2 -h ej.hej,o36 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 a0rue v0k/oh0ek ; (g2rllv b+tt Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the planvk(r2oekl0u0/ 0 r etvb+ h;gle passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1.tn yhm b4:yag,2 nfdt5qv,3z5 $^{\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