What is the evidence that sound t6wa2,w1- jw84o bcdmh6obys travels as a wave?

What is the evidence that sound i(1:vy*pe yg9l : n,bn mulz.fbs a form of energy?

Children sometimes play with a homemade “telepho5(.c et19ylay;vrn xene” 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.(c5vr ta19 yl;x neey 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 frequency or wl*nr)o o/s 6 es;8s2 bcu+fpw;jhc4jw6 ;ozxhavelength to chans+z6 up n*lsso /xhjwc4 orw)je2 o ;f;b;8hc6ge?

What evidence can you give that the speed of sound inwz:vglpk.n is+;,tg.o4 d4vq air does not depend significantly on freq ; n,.+dig 4 .ogpskl4wqvt:vzuency?

The voice of a person who has inhaled helium sounds very high-pitched. m,dc;bp((vd mzesj var8;)r) Why?

How will the air temperature i imp gv3p8i):.hmls8gn a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the -ik-m/ b68 :lrptanxwamplitude of sounds iai r:tkx-b8-w6p /n mln various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closf632,na qi 9rt4dwyoto z-o-jer together as you move up the fingerboard toward tt- qjod9wo2 o,r-n3i6ytz4a fhe bridge?

A noisy truck approaches you from behind a building. Initially you heai24qjlx .hog:tja 6 m,r it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear mo6: 2xmtlq a ,jgi4hoj.re of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spsgh8;ui:qrd1hq7 i 2( p(sjdz ace,” whereas beats can be said to be due to “inteih(g1 ; qdq:(s2r7hszju8diprference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poinj3ogk5vn0/k ets D and C (where destructive and 0k5 gjvnok3/e constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hea *e4d -t2b:hqk2rqx xvring of people 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, inverts it electronically, then feeds it tx22*x 4kr :d- eqthvqbo the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves sdpw2+sjg t (q/ d,bk5phown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with sli5+sw( pk2 qt/,d jdbgpghtly 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 source and observer move in the same directiostc)(5vd9bs hn, with thsd(sb 9ht5c)ve same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a perz*eopsim(e7 if:q25 nk;:k8 lov vkalk-2sf. son at rest with reei(*s.7 2oeiksklm2k;qla z-ff8o:nv p5kv :spect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on 9r6 5cb :f4cnftcwr,g a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through crt9rfcbng f 4,:5wc 6E, 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 for the echo of08u rine6*;hzo iw cc-s q1 yvob-v2d) her shout reflected by a cliff at the far end o*c81n ozcshb ii0 )6v eydw-ur ;2vq-of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes thex3* g*j sigm:n side of his 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) and does not vary gjxgnm*3 si:* significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aiky cx.f1d+0rbr 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 justs-s rj9 9ist j5)h5dqh above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0h9hs)q5 s s ij-jr9td5 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it ma-49 u d4rwhg2ju 8jbr- vwdq5qkes when striking the water below is heard 3.5 s ub qj-- jwvqgr drhd48u95w24later. How high is the cliff?    m

  A person, with his e3a vc+g; occ5-gs kq(jar to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the -ac3 qcj+o kvgc5s;g(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 mad*xke8 w3s2 jv.n 8yrr.qgh1y4x ,srgve over one mile of distance by the “5-second rule” for estimating the dist.y sngy,8 jrsekq1 xwx rv.v4gr*3 8h2ance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at*ows8yvmb2 2we,) :x4dbvzh gzz0)fx the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensityy)r5 txfe( e,q is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when yzwls5z;.-yssxf z28 fired simultaneously at a certain place,2z.zylsw ;x-sfyz58 s 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 with four equally noisysl7 phby4xcl;jy sa 29* . d7,jop(wqr jet engines is experiencing a sound(2 ;jqyl7s4b ap7 , j9s.*ocxpdrhywl level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to h2 sn*fmddogh/o3drub;6 0k r)ave 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 background noise for each device? 58 dB = *3n/r2drm d; h 0uookd)sg b6f   $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of s/zj / fu(gr;l4;qr *sxn cdnt5ound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rougugxrl /;t4r*nf nc5s; zq d(j/hly 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 striejg+ (3zq8 0fslbd s4ykes 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 tg2,9d 8mh c ,3me.z5wmxskkblhe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from amxe 9wgmchm 5s b,,kd.l 328zk 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 rj a+tku0+()kvt oi(zmegistered 130 dB when placed 2.8 m in front of a loudspeaker on the staziov ku)k0 t+ ja(+(mtge.
(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 lqz )w (pjb32 qh2ctxe6sd v*x6evel of 2.0 dB. What is the ratio32 d x zpqqx6b2h 6c)(evwt*sj of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by y;ct2sr3/ kc*s fq hfj(2tx.,t -z,kb fds1skwhat factor will the intensity increase? kh1.s/2s ;k,fft t *rbqky2f-xzcd st3j( c,s Increase 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 fr3iagyh k o)jf h.zw*+0equency of the othzh+3fya)i wjg k*h o.0er. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in c sre9 h3-j(hlx0:u niair that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mljc(h9sn-x i3hr0 : eum at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lofu07n; h(6f)k b o kkikyf0ac(ud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 1o)6(icnkf0fykk0 7 khabu( ;f2–6.)    dB

What are the lowest and highest frequencies that an ear can d, z pqz75e f,niu1e8dmetect when the sound level is 30 dBp5 e1qf ,7u8,nidzez m? (See Fig. 12–6.)

  Your auditory system can as ps0e.ry: x- ix:lgo4ccommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at sx lr:px4- yo.g s0:ie
(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 rxy9gon x w1*pma84 8u7laz.p44 ck afof 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the str1ola9xwug 7 m4rpc *a 44xp.yza8 nfk8ing be placed?    N

  An organ pipe is 112 cm long. What are the fundamental ag1fwu 8fow05 kz ki.(dnd first three audible ovegu.k8wziwo( d50 f1f krtones 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 across 7/pzup*(2re)0ydsr7eldl v t1vnd- g the top of an empty soda bottle that is 18 cm deepreups7py- 2ez v(drg7 0dn) *l/ldv1 t, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the31bm12sw s 9okkf;gr a range of human hearing (20 Hz to 20 kHz), what would be the range o3 1fbmrgsk2oa1w ;9ksf the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hwpw 4*v;)of;md vk) mxa;a3szz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% o;v*wvo3 akwm4mf ;zxp;d)a) s f its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E ak d eqm,ox2q;9bove middle C (330;k ,me2xq 9oqd 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 openo) -fr27amr4t fn ou1b organ pipe that emits middle C (262 Hz) when the temo-nm1 uf4 )2rt fr7aobperature 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 ws gl ,z:4jvjh i(9gu-ko-yl9 glx1r7at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the holeoi;s j q3t/.mf be that mustt3qmo /;js.if be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate/y-plro z1hguj4** m t at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show /pjutgly*z *4r o-1 mhwhy 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 om9ia, -xmej4sfz:dhl -jd 14xpen at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What ,xdd a9x1s:j-fl e4 4zm jm-hiis
(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 ( 3)hkd i.(j ne0wo8s ip-uhyr3vfzb8$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-u0t,e cx y4, pe u+5upzi*yt-om-long organ pipe a u 0c4xe,upi*t-5o etu,+p zyyt 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 tu -,z rwrhny710)3 farp cjudr) ue p)+.kjoq,o 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 answer1p3e )n,f u0) w)rjzrhkc,7ruodp.ryquj-+a 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 xh.ai)j3zqrh klzeswj5:dc (9o c1y5 d /+*pqto adjust two strings, one of which is sounding 440 Hz. How far off inz r 1+: / jodaecs. *qhk5w)cyd(5xjhl 9pziq3 frequency is the other string? ±    Hz

  What is the beat frequency if middlas2 :k-pppgq9r/ :b hqe C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates ao5nm0co p.n wr (*nfr.t an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine ofow*0.nr(om ncn.5 pr f frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soil-n7lv -q pp 7qu(z9lunded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tunpvq7l-z9(-7 uqpl inling fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings arehwh), mj/u*wt tuned to the same frequency, 294 Hz. The tension in one s mw,hw)/huj* ttring is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fli2h/i hk tewc1w s,0b5utes each try to play middle C (262 Hz), but one 21ie,i hc5t 0hwskbw/is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and ij1f ,qt ; uf/mlm5.agC. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together,it jf,lau1/;5mmf .gq 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 stanadjg0f/ go)o96:mgn*tumt3u q ; zy2ids 3.00 m from one speaker and 3.50 m froai90uy* 3gtz onm; mqfu2 ) g:doj6gt/m 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 piu d j7h:+wcmkg+1fp2fano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, whatgjm+huc+w pf27f:dk 1 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 nx7z7lery b xs;o)f+25 fii-84c ofmcin air. How many beats per second will be heard?7iffny75+ifo;)x m2o z8 rcxc4eb-l s (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren(-vp fsq.:ocy j6bmh)ux(/n g is 1550 Hz when at rest. What x(c(pf:.hvm )os jgq6y /ub-nfrequency 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 ,. /n)b og -aurhnf5wba fire engine whose siren emits at 1550 Hz moves at a speed f5 habw-gn r,u./b)noof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20pp-c n.ce,8he.0bup2lh/ 6s x e*tryk 00-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenc.p.8ee tx e2ur-0h, k*pplnc/csh6yb ies 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 the same single frequency horn. When one is -b)ywa v wj-0lnu7c(4yk w5br at rest and the other is moy y klw(v)jbbca- 47-uw5w0r nving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves a*1e-n3.oms- dm3d gnios5 xeyt 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound 5me3o -1 ydex.*dmoi-3nssgn frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an kr785 wrw7hmm7azo w 5ultrasonic souw7rmw5a78w r5ohm z7k nd wave 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 tuba was playe) jxiui j9eqy+se:d6/d on a moving flat t+iy/qj9 u)jixs:d e6erain 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasov jls05v.u:jv ad rkcl7nj y,yi(/n)(und 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 arteries at 2 cm/s directly away from the soundci,(yju0 sv y:l5v(r jn)/ .n7k javld source?   Hz

  The Doppler effect using ultrasonic waves of freqkgo;sh0 asmd 2 ph/p* o ko4ws6))t1pn;ctof :uency $2.25 \times10^{ 6}$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 velocity o,euet:t.wk0 is 12 m/s from the north, what frequency will observers hear who are located, at rest, et u ,ew0:okt.
(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 moving3w c5q(4 v)jxs.+;ro( f-mgb vez sevd 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 (l*z:f a9r2a,x5 er*rzw jl6fua) What is the angle the shock wave makes with the direction of the airplane’s motion?56,ezaz r: fja9 u lrrxlf*2w*    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet whereu 1 md,a+oz*g9vy7ag t the speed of sound is only about 35 mgaz 9+ ,t7gm a1*yuvod/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 8500gf:aj xdui) c)/z:uxwo;*u s5 m/s strikes the ocean. Determine the shock wave angle it prod*o) :ducaz5/ wuxj: )fs ;igxuuces
(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 ju ).w l-hi)vr$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a p46hq p).7 hppf3tee nzlane exactly 1.5 km above the ground flying faster than the speed of hpe7p nq6f 4p)hzet.3sound. By the time you hear the 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 seih-sjs9seq xn 0t96+1wwsqo/nds 20,000-Hz sound pulses downward from thwwq/so+sins0 x1 q9j9st6eh- e bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are th:*u )brm+j chwere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe syhfwwmvl-b0fd r*-u;l,7gk y r +w(;hbmphony. It consists of many plastic pipes of various lengths, which are open on both; ,vwwdb0r-hk; mlb f l(hy g*-fu7wr+ 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 from404q 3khhlyot.ukdb i 0pp0g9 a person makes a sound close to the threshold of human hearing (0 ibpp0dqgtk4 hh0klo90y3.4u dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soun z jx3q/kr7n)gd and an 87-dB sound are hear)rzk3 gjx7qn /d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, ;nu- 6m;e. l. xflpcsris 105 dB. What is the acoustic power output (W) of the speaker, assrnpl;m6 xf u l;.esc-.uming it radiates equally in all directions?    W

  A stereo amplifier is rated b n4qzyb ,wvw 93o;1ynat 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 k;qyovynnww1, 3z 9b4 bHz?    dB

  Workers around jet aircraft typically wear protective devices ove.vo jnix xx35 kvvx-)8r their ears. Assume that the sound level of a je n3kovxj-)ix.8vx5vx t airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systemjeo t*llq;: 7u y,lh5ns, 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 x785m7 zpnoaw 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 betw.kizakf-9 92j9 l zudmeen fixed points with a fundamental fm2 z9k9ki-.jazld fu 9requency of 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 tkw .hw i0o cveh;2q+7wube 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 openin2ichew;wq 0w.k+7 o vhg 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 qjk7 d)9udvkf+ez2 y cqh7i) 6that is open at one end and also 75 cm long. How much tension should vqki26j 97q7f) ue c)yzkdhd+ 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 reb 2ljd*i -:1zlwxsr /esonate 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 ,,g y6zvmpd; jrange 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 ovpjz, 6 y;gmd,ne source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor onvfa *)kgrcm6q nmx fns0pm 7kx f((08+ the stationary train hears a 3.0-Hz beat frequency when the othe( s8m pm00 *7kr)mfxkgfnqx6 (f+vacnr train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as i9gtf0rflhv:, t;l bo.g9, f3 sd ifm8mt approaches you is 538 Hz. After it passes you, it t .0mlmhro vfbd39f;g sfli:f9, ,g8ts frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate thq j/*r;cenr q0vzox/ 2e speed of 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 drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it goiq*qv 0 zo ;erx2r/cjn/ng?    m/s

  Two open organ pipes, soundizn; i2sajoec.5 eww+hb)h() tng together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. H)whe .be)ho t+n5s(jci;zaw 2ow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pasti)3nbs.bi jw( 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 fi b j3wsb).(inrequency 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 th76k2lyrm2fh 5 k (h d(vkf;6 uc/fhbade aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed ou7f2y6/2fkhk 56vd rfhhk m;(dc ab(lf $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth 9:jto3lh ty (sd6thi;at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the fre(toj6 lts: ih;9hyt d3quency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sjrg/8s i83hkg g2z,kpound pulses as it approaches a moth. The pulses are approximately 70.02jkik gp3/r ,ghz8gs8 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 chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used tyk2se.c+gzpt aq o4-*o send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a 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 4*pka2syo tq gz- .ec+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 9iw +n2n f4e+,zyc wxtpresence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Cxnc2+t ,wifyn4w+9 e zonsider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, ch9ed:.v k5-en hr emr2alled “singing 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 emit a clear, loud, ringineh9k r r:en5m.dvhe2 -g 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 hearing for the human ear at a kp.e3 6iuev :nfrequency of about 1000 Hz i.3en 6pe: kivus $I_0$ = $1 \times10^{12 } W / m^2$ 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 lu 5ptx6 i* evp:-qam6-.f v5wfia8c cthe sonic boom 1.5 min after the plane fvv a-i6x p5m.f plia t8-e*quc:c5w6 passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboaan i8(c eih1g7t is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h