What is the evidence that sound travels *ph+r 6jy om*:f hxg+zas a wave?

What is the evidence that sound is a f j mgu+ .izx+.eps1q;oot;m ;yorm of energy?

Children sometimes play with a homemade “telephone” by att8vn6-hr10+xtj kfygh aching a string to the b ht8hg-j1yknrvfx 06+ottoms 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 travels from one cup to the other.

When a sound wave passes from air into water, do you expect the r)(bf6nd kl.v+i2l:w k4g-idzq1 , 2ryozfrn frequency or wavelengtl , i1 l 4z-)o.6(v2nkfdrkqiryw:+n2rdg fzbh to change?

What evidence can you give that the speed of sound in aizmn)7/e ccb8 zr does not depend significantly oenz8b7m zc/ )cn frequency?

The voice of a person who has inhaa2mm: a7b usvhe:q693)2rsjb l.r zffled helium sounds very high-pitched. Why?

How will the air temperature in a room q6yho j- ye.8gaffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplit3 n3te4h v57z8l n85kqdzmnip ude of sounds in various frequency ranges. (An examplktenlz88nhpzv d7qi5354n 3me is a car muffler.)

Why are the frets on a :z gjve 3t(js,guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bri ev ,stjj:3gz(dge?

A noisy truck approaches you from behind a building. Initially you hear it b7syjjhd2qt1f4. a1cbut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noisf1.4ab jdqht1jy 7s2ce. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “intd) ouy9u9t2jnu :(gv merference in space,” whereas beats can be said to be due to “interference i(9vtn9 2yojm): gud uun time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would th1jne9l4.c x hle points D and C n.ejl419xlc h(where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peoplewxm/wn 5w4 wbqh,x95o p(ss(a who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, invenw( mh ,9wpwswb5qa4xx5( / sorts 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. 12–3 vy* ati3sb(/kv,eupjosoy 10o vw (/*1. Each wave can 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 freqkyyse1v(v j*o30sv /pbo(a iwt/*o ,uuencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directw9f. 71-m14 jltgmefpp,uv pr ion, with the same velocp ,1w up7p. 1 mjfrevflmg9t-4ity? Explain.

If a wind is blowing, will this alter the33n aq jx3 zs4so0gzcax u-2o* frequency of the sound heard by a person at rest with respect to the source? Is toasno q4 33z3 0u*agjc -xxs2zhe wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swiufesteusb52*96 nt m4ng. A monitor is blowing a whistle in front of the child on the ground. At wtmfe6e s 2sub95tn u*4hich position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengthfme1 r+s1v(gq 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 the lakeeg (vfs1mqr+ 1. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side off1rj9amt f/.0cwwj. v his ship just below the waterline. He hears the echo of thea.mtrwffj 9w.v/c 10j sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ing3 bof2su 5r0eogf(an(k 9w(j 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 ajf -3dbc f,n*v school of tuna on a foggy day. Without warning, an engine backfire occurs on*df3nj bcf,-v 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 makesty-yf4 3zqjhdg.t vy;c7-r ( p when striking the water below is heard 3.5 s lateqy p (4zrht;y73vgt.jd--ycf r. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge n.0ypscxa,6 fxwa u(dvk--/xi 5z xt+ 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 concre/fvi0 . nsc (y- ,xtw -uxkpadx+azx65te, 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 errorhtf7lb /)kem 0-wc 9sj2eds-q9 bgc +s made over one mile of distance by the “5-second rule” for estimating the distance from a lightning s-29bsbj+s-whf q9t k7/m cl)es 0dcgetrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at p hz. me,p4 p8jspftoe:p; 4t3the 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 ) uvr4ky (,dee-o q ;vtz3mht.sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producz (2mk/ ljpzh53qwse2 e a sound level of 95 dB when fired simultaneously at a certain pl32kpm( /sq5zzw ejh2l ace, 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 airplan,32 :micu6 6pm(9f ezhjd:fwvy l km;fe 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 alf2z 6i6 ;vjfwyd: c 9p ,um3k(flm:ehml but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to/;- n-livo3sf 5p +qetjmk )dgk4o yx* 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 an kg5/eox- +msptl3odiq; k-*n4jf)vyd 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 n sly( ;g-bpc,sormal conversation. Use Table -;bcys( g lp,s12–2. Assume the sound spreads roughly uniformly over 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 s-: p 4y)w v 8uxpd;wu/jwkml)dtrikes an eardrum 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 amplifier B)5j p wz4 e1xycbrcp8; is rated at 40 W. (a) Estimate the sound level in decibels you would expect at arby 48 cewpxc5jp;z1) 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*g :83glfeufi3) wpu37x3 nwg8fhkxg meter registered 130 dB when placed 2.8 m in front of a lok8:g3fg7gx f*3wu3glphwn uxef3 8)i udspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level tvp:)(h z1os qub5s2d of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?qs15 z:) hptdu( ob2vs [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whatlr: ccbg*1v 9e factor will the intensity1*9rgce:lbv c increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaceme++gmjc7)9hxy m:ttzy 2 a0kzunt amplitudes, but one has twice the frequency of the other. What is the ratio of their intensit):zj9act7yh g km0m t2y+x z+uies?   

  What would be the sound level (in dB) of a sound wave in air that cow,sr; (*mn5zivplr w -rresponds to a displacement amplitude of vibrating air molecules ovw ,n;5i z rlrw*(mp-sf 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to vn,6 z,vehwj f0fd 2n+seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)f,0 n6jvfz2 wde+h ,nv    dB

What are the lowest and highest fx(9keb*p /:pei*hexn requencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)/pip xk** he(:nx e9be

  Your auditory system can accommodate a huge rangece++,b mmq : a-i7;nnsr5ue ql of sound levels. What is the ratcm -q:+n a le smi57;,r+uenbqio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The leng nhrh9l)/sto xok()/rth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension /krlt9xrhohno /(s)) must the string be placed?    N

  An organ pipe is 112 cm lo- jj1j tt6gny;ng. What are the fundamental and first three audible ovy jg-j1j6nt;t ertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency7 0 (x ysg:jh-rdmikx8 would you expect from blowing across the top of an empty soda bottle that x hxdsr0m8:- 7j(gi ykis 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe or 268a:k-ih05g orrohda wyofv( pod 1.gan 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 reqd 6 w1 kr0ofgp.vod8h:o ia2r5h a(y-ouired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strinv5 h td-t.ev:og has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at-vtd.o :te5 vh a length of only 60% of its original length?   Hz

  An unfingered guitar stringj)z ftz, /obh6 is 0.73 m long and is tuned to play E above middle C (330 Hzt 6, jho/fb)zz).
(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 ok4riw2(v/4c0dl: hgcj lq ft6pen organ pipe that emits middle C (262 Hz) when the temperature is 2 qhgd4:2k6 t 4(wvcl0jir/lf c1 $^{\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 sztwc u lya4um9kqt+wh6b3d,2-ic4) at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shoi0mj+ tis563 0zyah lxoy(u n8uld the hole be that must be uncovered to play D abov( y m8t+5xlz63 ijos0u n0hyiae 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 piplf./dun m8nk:; lcag4 +yv:p xe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at alnkd;ayv8mfgup/ x 4ncl : +:.ny other 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 long is open at both ends. It resonat f,9m du+fs 64dqim0ya zfu.+hes at two successive harmonics of frequencies 275 iz,a.4yd0fd f sm uq u++fh9m6Hz 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 xut5 -9q1 a :lwvt0gmzx*szq6$^{\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 pre gfz.4h+tbd:xd2moa+ sent within the audible range for a 2.14-m-long organ pipe d 4 2mdogf:z.++hxbtaat 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 tzh3ax2 2hg9:ekc cfjnz8 6 l7bhe 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 zf gzl2c96kx 3n82hjc :heab7the 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 nu2ljmhnn f-qw* 9fp1.) h +da/ die3vto adjust two strings, one of which is sounding 440 Hz. How far off in f.v p h9l 2n 3nqfain*wf)me/d-1+h dujrequency is the other string? ±    Hz

  What is the beat frequency if middle C g-eobr9auyp6 ,v6zj,6 r .rml (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 23.5 wr k y(z1h*xkzt9j8j )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 fre z( rx)kyh t*1j9j8zwkquency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3z*46n3c0oc nrukm*v 7n; md cx50-Hz tuning fork and 9 beats/s w0ko7;x num dc3 *rc4vnz c6mn*hen sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tunedm;k +j(q+ sm 0fbb+f30ve wqyp to the same frequency, 294 Hz. The tension in one string is the (sq ;qm 0m+p +yjwbb+ek0f3fvn decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flgow5r3ll7uh;ze kgqt0 g;oq3n z9; r ,utes each try to play middle C (262 Hz), g 7 uotzl3e qoqhz; k0r;w5,gnl;93rg but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz;p r- umllqsm18t9+gs:gb-uf - when A and B are sounded togsu-m1:sb -t flu9l8pq -rggm +ether, 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 and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one s rl7o.nr2ui,yeb+1 q epeaker and 3.50 m from the other. o2iuee7rq.l+1n,br y
(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 supoc/ytrh *v: s)posed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratios*)yr/ vhtc: ng at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How ms/7 kphf:1fy sany beats per second will be hea/f:71sfy hpk srd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hzj;waz 3n;oe1f when at rest. What f3w;e1j ;zofan requency 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 do you detect if a fire engine whose9tkag *0(zb t- h9xufb siren emits at 1550 Hz moves at a speed of 3*k utgtx0b(b9z- h af92 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you qs dl,.76 gpmrsol.a.at 15 m/s versus you moving toward it at 15 6,sd.op.mqr . lal7sgm/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with th.3 w+5freytl re same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver arw fryt.+l e53t rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them rej ,hs7abd )ma75z8veoturned from an object moving direct h)s ,zm7e5bj8adva 7oly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/ 4 qaxljpalz(n6:m o46s As it flies, the bat emits an ultrasonic sound wav 4op6alzlqn a46x(:j me with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tug ugrr/9 ov0w)40wb ofba was 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 frequency was heard if the train car approached the station at a sp)r0uw9r/b o4 v0go wfgeed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound /sf(h+rm2j gq6mf3 b uwaves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human t6 u3ffq2/g(rsm +mbhj issue 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 /*1mz lbufx szi /a.gt2hip5: ultrasonic 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. When the wind q uijo.o-q) zf08ejlnceo*4 ;velocity is 12 m/s from the north, what freqfn4z )eo-;ijleo ocuj 80 qq*.uency 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 lan2vmz j8+8qv)t x(alh i1u1 rrjd 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 qy, - sjls8qw62d roe;of sound is 310 m/s (a) What is osyes-qjl8w6; r qd,2the angle 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 atmosphere ofqr 5k9-fza0kmp- j 59alz5lhc a planet where the speed of sound is only about 3k5p-amz5-jak q9zl9 fc0lh 5r 5 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 std d *.zsgll1 zg.u5v:vft ;6u(zil 4qdrikes the ocean. Determine the shock wave angle it pro dqu (zvvfld;g 5 1l6:4 lzgtd*..ziusduces
(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 hbpx2/tae7 +m$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a p1o-y ;lsn,hb13 fjam5kdghw 4lane 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 hoyhwg 4;jm5ab-n, sdl3ofh 1k1rizontal 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 20,00t t1wm3x m3 8lpdx)nq+0-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth + l3qtxtnmwmd 18p3)x for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how man-emuvap ob;w -f-x7bkwn ,eo:,d* 9on 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 symp+-od ou n,2bdshony. It consists of many plastic pipes of various lengths, which are open on bou,d-sobdno +2th 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 gz* vd168 arg3y o5cyemakes a sound close to the threshold of human hearing (0 dB). What will be the soun5z863voc*e 1r gyayg dd level of 1000 such mosquitoes?    dB

  What is the resultant sound l+ng0 +s/tc 5c9zknxvrevel when an 82-dB sound and an 87-dB sound are heard simu9rcx5+n+z0t cgns kv/ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.u(qasnqeb.wxz. mq)qk 31i z9 l7ui:8 What is the acoustic power output (W) of the speaker, assuminxa s qqwq zn1(b.zu .iu)k7q38l9im: eg it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pl(clic2nu cz *nr l6)/ower output drops by 10 dB at 15 kHz. What is the power output iz nlcnl6(lu*c 2r ci/)n watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over cepgn 5 ezj,.n13og8 xtheir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average humaengep5 3n1zxg8,o.jc n 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 systems, the gaif;9 :6afra*fpvh 1i jmn, $\beta$ 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 ta81-hq (mf zxgolrt9.3ul c s*o 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 cm0f kg9 7ashi+si w 4)pkq+hib* long between fixed points with a fundamental frequency oih9s+gf p7a*w+)kk qhb 4sii0f 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube;2 i s2pyixvo6 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 thy2; vpioxsi2 6e tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube th1;h -r/,vmro7vj 8c edgdgv vo6b:gr3at 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 v:gc r-;mdovr bv7g 8oeg1/ vh,rj6 3dthird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonax8k,/1 hch csste 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 in the 500–1000-Hz range coming from two sources. Thjge 4t+2*jqr d*ublf( e sound is loudest at points equidistant from the two sources. To determine ex*+f teulrqg(d4 jj2*bactly 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 stationa)y)*aod1jojb+ dr*y ow ,aat8 ry. The conductor on the stationary train hears a 3.+ ,tj8) aaor*wd*1y)obojady0-Hz beat 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 approa 8r()64zr:liplih y xtches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constantp:8(iy h z4lxi)rlr 6t velocity)?    m/s

  At a race track, you can estimate the speed okt;kzrb4 jx y9,2lc1xbu.ooeo0e 50vf cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car dr2oxb 5o,z e41u vrko bl xy00jk9;e.ctops 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, producilf4(xoeigs5: 5bag l)a/ lw3e a beat frequency of 11 Hz. The shorter one is 2.40 m long. How bgexg4 5siia3al /) 5 lflwo:(long is the other?    m

Two loudspeakers are at opczw 8pu*2hh1ke4.z rrq9g 5dpposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identieu gw.cz2pp h 14k9d85r*hzqr cal 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 /tg. b:pxo+sr),p jtpwhat beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bloodp+t/tsjg.rxp ,):b po 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 flying toward p5ca zw0zimf+ og/2x+nadm 14 the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequmi nza 52+ox0z a4 gpw+cfd/1mency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound puls4zaq3kedebx zj:c) fs+ t( q/5es as it approaches a moth. The pulses are approximately 70.0 ms apart, and each ib(s+qecet )3/a jzx:4f zkdq5 s about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alntjsyce9 4s/-ydl0v 0pine village to another. Since lowsyvynj0 l/ -4scdet 09er 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 open tube.

  Room acoustics for stereo listening can be compromised by thecpn+n t, p.vb+y)i a;p presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves i ab)vpi+ ,ny+ p;.ptncn this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involv90dww)jgpm +i)-5c3p7k) ye yqro d pjes 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, t5cmp7q)+wypw ) -0y )9kdjdo ierjg3phe 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 thresholdx0kyf7es*h 1f3utu v,id:b z2; +rv sh of hearing for the human ear at a frequency of about 1000 Hz32 hk+*vh , d sfuztefvi7 ;0ru1xsy:b 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 xz)qd 6z.x a fh w32,jgu6x+ibboom fxxgx ,qwh+d63 ajz 6bu.z2i)1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15r (2mmj5bxjhz-04lnt: ;tgh q $^{\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