What is the evidence thiq :j9 j c1c*ep9qyuh6at sound travels as a wave?

What is the evidence that sound is a formades uonj +: u*9av4;1p 6d*pj1jgrlc of energy?

Children sometimes play witru6++uk oj k2kh a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clekok+u 2 +r6jukarly how the sound wave travels from one cup to the other.

When a sound wave passes fw hk6hx.nm m4ik; v,c.rom air into water, do you expect the frequency or wavelength to chim; hk,xcmvw 6 hkn..4ange?

What evidence can you g1g:i vcwi f+r7svvg 51t:9e utive that the speed of sound in air does not depend significant:rg iwvvc7 ts59+ iv 1g1fue:tly on frequency?

The voice of a person wh6,/knvs)1 sq jgry7hpo has inhaled helium sounds very high-pitched. Why?

How will the air temperatur/,c53 orogrto e in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sound9d+zja aa*o +r7/xvaes in various frequency ranges. (An example is a car muffleaaozdr++ *vx j9 7aae/r.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together al):a s9f j3ejis you move up 9) j f3jeasi:lthe fingerboard toward the bridge?

A noisy truck approachnchq(r6 a8l .ges you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain hg68n (.larcq. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spa9 7nm nr0meklv0l mh;(ce,” whereas beats can be said to be due to “interference in time.” Explal evn0h9k;mm7rlm 0n (in.

In Fig. 12–16, if the frequency of the speakers were lowered, would 5 v8c1b7x*l tcl*qvaqthe points D and C (where destructive 8 qll5qxa71vvcct **band constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wv8h u+nqu/*cenn6l 6b ith very high/bl86u nnh*enc 6uq+v 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 wy(wlm 7dn(nh 4ave can be thought of as a superposition of two sound waves 7(dn(n lm ywh4with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourcyz* p-:o89q p 3/f+jo4c vue psuiov(f-mz9gwe and observer move in the same direction, wio mz9gup+98ovcwi -qfv *:(/3ofuyz sep-jp4th the same velocity? Explain.

If a wind is blowing73* qn4+rmj txv 1q2)vzkb urm, will this alter the frequency of the sound heard by a person at rest with respect to the*tbq rj+74q vxzm k1 rvmn)u32 source? Is the wavelength or velocity changed?

Figure 12–32 shows variou, nez6jyzu1a 7q;ver; s positions of a child 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, will the child hear the highest frequency for the sound of the w; u76r zy;1ezqvaej,nhistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shoutv 6/3wpv1x3s.t 12qy v qdacgj reflected by a cliff at the far end of the lake. She hears the echo 2.2.q6dvgat3vw/ 1 px v 1sqc3jy0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jrh+ ev: (cec-must 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) and does not vary significantle(v-+rc :c hmey with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air athg0hk+:lx 3 1pqtzs2f 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 d;:17/ jshuij+,krgyze wb3yi rifting just above a school of tuna on a foggy day. Without warning, an enginejy , +e:bki 7ih/gry u1sj;w3z 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 to l/6,prsz+6ma9xz zwbp of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the czs l9z6p,zmrb 6w+/ xaliff?    m

  A person, with his ear to the ground, se gr)27 gwddb0s te8jn3es 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 0 2nsdbg87r 3wed t)gjs apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent m*usroot ut pd1)5 /(qerror made over one mile of distance by the “5-second rule” for estimating the distance r pdumuot1)s*q (o5/ tfrom 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 pain level of :v6c;a 6tsch-e+e ry*h,dtkc 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 intensity ip5f7sip ,x1oy(- wgrx s $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultar.u;waaor7wiz/oe *+neously at a certain place, what will be the sound level if only one is explr eiwz+ura7wo .* a;o/oded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with ar5wo br3z.3o6it ;h uy*hxrqn3q;9 ffour equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experie9h3t ruqbw3y5xzari6* hr qo3.; fo;nnce if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is 6,f ony 4h)v.jphf 0arsaid 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 back h4ov0)rh.pj, n f6fayground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output +omglv3su0eo sr*88 25m opto of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere2o0+ 83oomv *o 8um5tselsrgp 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(u) f- wys;vnijqk i8;p74ckv whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier5jb+qk wq0(x tb y)sw( 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 connectj(q xk0wb)(q yt+bs 5wed 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 regr/2dj8 qgzl1*h3 c*u gfhym k0istered 130 dB when placed 2.8 m in front of a loudspeaker on the sta r2hmkcz 10fdj/l*3y 8uqgh*gge.
(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 sou9zsntx8rdt a, )1 owqpa0o1*end level of 2.0 dB. What is the ratio of the amplitudes of two sounesz1dar tp n *ot0a8,q9ow) 1xds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whqqq4wbm5pm2 65 .t hmudo yc9cv*4m4msmw + v2at factor will the intensity increase? Increase by a 4m25s2qmw .b qcp*64mmmqh 4do9vm+c t v5 uywfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal d tal vy 68-je9a990+qhpcsmqaisplacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities?a+ ayqh98 v0tsmjqap -99lce 6   

  What would be the sound level (in dB) of a sound wave in air that corr,g frf7z7l:ghesponds to a displacemengz7f,flgh:7r t amplitude of 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 that9wf.jl8 j b:wq/jo*ff has:9bf qljff8jo*wj/w. a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that anlbc66l fd*a 9p ear can detect when the sound level is fb66p al*l c9d30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge ran m,fnix2ju9 cy3cu cv.r2a 7+vge of sound levels. What is the ratio of highest tocuf2 ,ac7 +9uvmv ciyj x32n.r lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lent-s-saune b )o3 nq73ngth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the st -sotb373n u-eqsna )nring be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thrx hhws,, y/ 6q0g/ezuaee audible overtones gqz6,suha/,h e 0wx/y if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acrosk.rwxj wb0hd( 97 7fu 7ffmab*s the top of an empty soda bottle that is 18 cm deep, if you wfa *7j0u9bhf(rkfdx7 7b.wmassumed 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 pi n-e:(q4po,o tsy -kxape organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes reqn k-,:oxeas4ty op(-quired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harvjyc8.bisf ,- odr( h;j3hgj) monic. What will be its fundamental frequencyfj y(8) ;jh,obiv-srdcg j 3.h 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 Ed qk , rvoe6fj t5-.s)hkh+yzg)h, apsl,4 0mk above middle C (33,0p4hoztkm5.f,6,v)y-hekr d h g )sqlks ja+0 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 onks*k ;yh,ikrcozt u27j* 3,a f an open organ pipe that emits middle C (262 Hz) when the temperature ii,;kc s3y nt *ah2k,r ouz7jk*s 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 3suyx q h*q qznm.3 e22eq-ca0at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mou )wa 8+74nppvsgf rd8./kimq k5dg 5ldthpiece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middl4apkwpqk)d5 r /d .f7+8vg5l ms gdn8ie 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 ath0/xl yr w,ii6 ay0mf8 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this ymx,8h/w0a lr f0iiy6is 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 resw0;nmw.0(323hgx fuu ent xa5ka3ay sonates at two successive harmonics ;tefnkgm2h35n0w3 asw xuu aa03. yx(of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 q. budpe)80-1je yuh3m: jbkv$^{\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 aud2vrn.+yc ai:2,v won uible range for a 2.14-m-long organ pipe ata 2cw,iyn+.ornv 2:uv 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 outside and4l j7-vyhqs;ks uwah,:v-:tj is closed at the other end by the eardrum. wuj ,sq-hh t:4y 7:jvsla;-vkEstimate the frequencies (in the audible range) 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 two strings5 v01re vao.e3r,eek; fwwo1 x, one of which is sounding 440 Hz. How far.e;5v,e1 ewek1 o for x30wvar off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and vyx++x cugft4*( zb; u$C^＃$ (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, td 9g6jvh) ee7while 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 Hz7 get6 )evhj9d occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 ggt:/ zzaw (jm*7afg +beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Expzj+(gwg:/ *gz7ma tfalain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in f btg- 3f:*njucq :nf rx8sc,q l;*tq,one string is then decreased by 2.0%. Wha3-:s fbr tl **,8ft:gcc,fqnxu qjnq;t 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 tr6unph0; ec pr;y to play middle C (262 Hz), but one is at 5.0°C and trpup c;nh06e;he other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, 1 9 fwwi sjo)b-/ptmw:A, B, and 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 togethew/o9 wftpbjw : 1s-)mir, 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 elj4bme(x 4 8*9 p/u9 lqmuzznn-xrk81.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other.q* k88pnex (9u /njue 9x-r4lzmlz 4mb
(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 vi;prllusk u65hzx4yt 1qy /4 )*6dapzsky7 2ucbrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 13*s1/prud2qsy z h6ut;476kp5 yl)ulxyaczk 4 2 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 angqx.*: 7 m7acfcdzsgbj g,;6qd 2.76 m in air. How many beats per second will be heard? (Assume T = 20 xqca7g .jq, ;:gf cmb dz6s*7g$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eng m npu 1oa4c2+-rbo+gsine’s siren is 1550 Hz when at rest. What frequency +ouo+ac2 rsm4 -gpbn1 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 *b73ifhu6+ (fw lhdtufrequency do you detect if a fire engine whose siren emits at 1550h f7di6fwh3 u b+ul*(t Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift ij r7e:(.ediwli4yy-fs. ,kxo n frequency 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 th rky:-( 4,iiw7efsjox dye. .le same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the sa)ne 0-a 16aosryq.w irme single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5aeasrw01y6q ino-. )r .5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and roto0em)tw35 fk4 ng (ieceives them returned from an object movik3teo 5gino4(m0 w)ftng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a qjt+(n nce o;/p*6ij/qk(clz wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Wh(ki tjccn p/j;e/z +6lq on*q(at frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubs;g2.wpk ce(ya was played on a moving flat train car at (wgkp ;se.cy2 a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. S:xm4/c)+ y4er ekrcw wuppose 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 arteries at 2 cm/s directly away from the 4cy4 mw r wcek+x:)er/sound source?   Hz

  The Doppler effect using ul) zuijta zt1( m.7az(yi*l k-ctrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. cl rc8./a:(pi m3/r b0dohmxe When the wind velocity is 12 m/s from the north, what fre(3lpci08xa c e /r d:ho.mmrb/quency 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 moviqtyb u/2f6ux.bppu 86l4vh0v x5 ,cxmng 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 M :mmf pqbchcxc 1;/p4 81zjr2zach 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 :/pm4b1xz1jf p r2 c8hm;qccz 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 4:4fb ,)r2vqqqvb;ii .dypnnfv) m(othe thin atmosphere of a planet where the speed of sound is only about n,q;b op.y4mi2q(fvv vq:nib4df)r)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 shoc0d4-ge b mml4,v e (qyd vvk8oc3c16buk wave angle it pr(v103mudlqvyo 6e8v kc,c dg4m bbe- 4oduces
(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 .tp(:uj wap *4iyem a-$/theta$ 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 exacto ws1h5d sh2/chi ;uk9ly 1.5 km above the ground flying faster than the speed of sound. By the time you hear thw;sus1hdhh25i9k/o c e sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses down-nn:mbj hja.) ward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what inh:nj- . )amjbs the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human ( 4x1w 6xq9ojo yw2hloaudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a se ;dpas 49wntc++f3 p0qjuyy/cwer pipe symphony. It consists of many plastic pi+pwp4c3 dcsuq0a 9 ynjt/+;fypes 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 0 i av1fj7qz2drzl/k7i1j1 r nm from a person makes a sound close to the threshold of human hearing (0 dB). What will be t/d 1kq7 r vz7if2j0ja 1znril1he sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB 6,:xxt*3 : 1u0trzu*tnsz rb*cx winw sound are heaw1,nxrsw*x6xzctb*:3*r uin:tzu 0 t rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placj00 bwt4bn),l24mgdf ae lh g3ed in the open, is 105 dB. What is the acoustic power outplbwm3telg2f)0 4dg4 ,anhj0but (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ouslzd; 8vhyvg 1m3-uz4tput drops by 10 dB at 15 kHz. What is the pow vzmzhy31l s;g-48du ver output in watts at 15 kHz?    dB

  Workers around jet aircraftjx:/z hy4 85c7qcqq.g yy6lwy 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 tc/5g7hyq 4yqw czlx.q:y6jy8 hat 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 engine?    W

  In audio and communications sy7m6ll9j fmj7v 3 cfzto(e)3gmstems, 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 frequenc hxxeu gs:w)n. dv( jfz)lj/78y 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points w9xtxt z:9brm2 0lxm+tith a fundamental frequency of 440 Hz and a mass per unit l0x:x9+tbzxm lt2t mr9ength 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 tubect gw.en 6ec*mh y.h- i)iv.(w filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequencmwyv-*cgw. c )h itn. (h.eie6y of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that ifukersusy79 pn )zs (vo3+-i3s open at one end and alnf9p3u(si 3v y) u -zek7+srosso 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 tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one l1ncfd59d 0 k6c3jaqcj rz n14full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in tk 1- w*mepd-rtl n)o 9uzqlpol9-i9c/he 500–1000-Hz range coming from two sources. The sound is lou 9oqlm tpz/ik-lpewrd1 9c-o-9ul n*)dest 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 whistles. One train is stationary. The conducd z ,a y*wf1pr30/yzq rz/7ctator on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movinz trq 7zrf3/1*,dya 0cp /ywzag train?   m/s

  The frequency of a steam train whistle as it a m9aar st.8.iplid)ua06qgl , pproaches you is 538 Hz. After it t .aim,s 986il)lpg.q0d auarpasses you, its 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 * m+po7z2tvw0 ic-fltp/tzm3 cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Stmp 3tw l 7c-+ v*fz/2mzo0tipuppose 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 frequl,7jqm9;dt/)ec y.mln g (c ocency of 11 Hz. The shorter one is 2.40 m long. How . oem/mclg 7 9y,cjcn;tdq(l)long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mov6ky4fb(/2db)vmft bkhr(y :sd0sh d 4es 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 bsh6y d y f0 dd ((kfkbv244)/m:tbhbsry 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 ilm* as.x8zd. perw ;f*s normally about 0.32 m/s what beat frequency would you expect if 5.5.z*l fs wmpd;x *r.8ea0-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 is yu1yz +)q arl:flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequeq)u+:yr za 1lyncy of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequench cypl5 2/pk9vhi2d o;y sound pulses as it approaches a moth. The pulses are approximately 70.0 ms ap;o 9hpy vi h522klcd/part, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 1 7z+q, sk h2ssay guk*sb2/i+1bi:qly2–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less suscep u ki2z7+qs s2yi+qk/: sb,b*gy1lsahtible 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 ster lecg4:hr/ becrg*i //eo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the st/e/i/gc: * hgcrbr l4eanding waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “s582p c)te mq 9oocvuu+n*1d3yi0ntau inging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or em ucnvo)9nt mpadi*u05c+oqe 2318 yu tit 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 hearigw0q s44i.tm tng for the human ear at a frequency of about 1iqt 0g stm4w.4000 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. An observer on the ground hears the sonic o(wdjk hw.6i0 boom 1.5 min after the plane passes directly overhead. What is the p .0djww6 k(iohlane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15t hbiayozl36- /yq qn ,3l/nv: $^{\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