What is the evidence that sound travels asi+g*4es97k /+x+qa4weyy qvlp d sj2m a wave?

What is the evidence that sound is ai*c;nj r*xuk 1 form of energy?

Children sometimes play with a homemade “telephone” by attaching aazb4 .mv28 bai sa:env,a/qa39y n;wb 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 cles9b qmiy wanaa8.4a3 e ,/vn;a:vbb2z arly how the sound wave travels from one cup to the other.

When a sound wave passes froob9y:zf p/n7ym air into water, do you expect the frequency or wavelength to changez9pnof b/y:y 7?

What evidence can you give that the speed of sound in air k v,5 cb1djyb+does not depend significantly on frequenk dc b,5bj+y1vcy?

The voice of a person who has inhaled helium sounds very high-pitched. Whya9.ec jfjt pyc6ws 3 r-rh -6wr31zj2q?

How will the air temperature in a room a :334z:ncf 1fa-tkj aj6rz2c9nm xr aoffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reducc w.ogo4 p/ vk18mx(bbe the amplitude of sounds in 8(/wbpk4ogvm xc .o1bvarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mofu6 +6 blopdhx 3rqb-,ve up the fingerboard6+h -ob36rpbd,qx luf toward the bridge?

A noisy truck approaches you from behind a buildu /gohm64,ami 1vuyk1 ing. Initially you hear it but cannot see it. When it emerges an/am,ug6io4h1 y1 v ukmd you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” where y4cya xjpcl o*3b ::6aa2-f*tb )eh(xhjri-sas beats can be said to be due to “interference ih r :fj)i:tcca6 jyb3*yhe*o (x 4al-axb s2p-n time.” Explain.

In Fig. 12–16, if the frequen:q,8im :p( 3xtiluyikcy of the speakers were lowered, would the points D and C (where destruqlik(,i8m3xy: :itp uctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work ucwy.hv (:wxoi/8lml4*m*jm 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 to the headphones in addition to the ambient noise. How could adding mo wjic/.m(x*wu m*l mo:48lvhyre noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thoughey2a0 i1cv 3g7 jd+llk+kvw( nt of as a superposition of two sound waves with slightly different frequen3ijyne+w7c v1l +kdgl 2 v(ka0cies, 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 mi7dp5fdal/b-sf j q) ah621jwove in the same direction, with the same velocity? Explain d2)f7/hi-1jaq j wlsfpab5d6.

If a wind is blowing, 5er jy uqwtc,zn...x/will this alter the frequency of the sound heard by a person at rest .,.e rxzn5 /tqjwu. ycwith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monito3ksusx3 b5oy4r is blowing a whistle in front of the chilsu 43y3bk5so xd on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listeim(yw576f 2wcj2 b phbning 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 (5y2mfj h bb72 wpiwc6of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the watewcf0 r f(a5 rtb0et7g6rline. 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 0fwrttrcfb5( a70 ge6 of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavev1iw3ae9 k ph39 oodr:lengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is dri v/.jz vyf:8lufting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on ano:8 l/zfuyj.v vther boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes 1nt0a x,kek j.when striking the water below is heard 3.5 s later. How high1kexk.tn j 0a, is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the fcplk:( t-;xf 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 s apart. How far away did the im:k- cf;t f(pxlpact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of disc-97t oekgk:h tance by the “5-second rule” for estimating the dgkh:c7t9-oke istance 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 x7xor,7g a/xkthe 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 wcn txsy47,v+u hose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously ao 7txk3-pd6h ,zig 6ocife3z 4y ;-jkht a certain place, what will be the sound level if only one is exploded? [Hint: Add intk-hp ;e i f-6jt63xoczozk 4yhdi, 37gensities, not dB’s.]    dB

  A person standing a certain distance from an ac,h n4b ,+uq* nshqp*gk 1zm7g*)sbhbirplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, notn7**c kb1*qb) mqps,gh,bh +hg u4nz s dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for ij5b,vp6fu 1w 1w 8d nnx0 r5,cva faajo6,nq)a CD player it is 95 dB. What is the ratio of intensities of5nnji1 nuw 0,qbv,wr8xap 5 afo16v6, fa)cdj the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a personrmdybone;5nn rcqe 41b/, bwf f,)1f0 speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centeref my)1o4b; 1brnfn nqe,dbf ,r5 c/0wed 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 strik tj5t3f+dx +:rrgf ,yfes 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 thev+7gk(jh 1x9 so vl1oq more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expecg+s9 lk17(hj oo1xv vqt at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whemi(4 9k zzxolr)frm)un3d4 n9 n placed 2.8 m in front of a loudspe)(o34)xnmmrk id9zrulf 9z 4naker 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 devwkl g kxm.49)*rd gj(tect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectio(km xgvg9j) lr. w4*kdn 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inten-t/5/kg kml 5u:+k2 quaeyyf isity increase? Incre /ay kl2e+/kyut :m5i-q f5kguase 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 twic:yr ec3u 3za+pe the frequency of the other. What is c3: yu3rpz e+athe ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corres3o5llq a;ehy. q/ (mq;zfqs4iponds to a displacement amplitude of vibrating air mo/l;4 l e5(isy qh.a3 qqmq;ozflecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sepb ;jmau9*6crem as loud as a 100-Hz tone that has a pamuj9crb;*6 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear cnh5s .fk*v cpr 34vlc.oi;5utvr( 6suan detect when the sound rsiv sf35.ockuh lt nr(p5 6v;.uc4v*level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of s.l l pz0i8we4dound levels. What is the ratio of highest to lowest intensity at elpdw08 .lzi4
(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 r 61re 8f )2mg1sn m 8buq+ctlxdbay*1frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35bxsr)f+8rt8qb*1mmn ud11gl 2 a cey6 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and 1gc p3,t(is uh)mt)ju arv7mfp( lq44 first three audible overtones if th()uvaftc q)374stiu1l m(,mp hg 4pr je 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 bxw+ (r7x0r5 7*fhpm:p a6h2d b*m mds7zepvb hlowing across the top of an empty soda bottle that is 18 m mrd*h zw*+(5ams 2eh 70pxf h6p xrbp:v7bd7cm 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 hw).15x1l: ylnxrl oj5jf7su pipe organ with open-tube pipes spanning the range of human heari 5l1:y lujn7)1jhsr f.lxxow5ng (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic.* bw ;cg(jpzy: What will: cb;(p*zwyjg be its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 0dd qs2n svv)/m long and is tuned to play E above middle C n2dsvs/vq0)d (330 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 le98ygqnzsx6dh t)+x8) ioionw7 .krs 9ngth of an open organ pipe that emits middle C (262 Hz) when the temperahzyko8x8g79qsn9o + nriits6.dw) x )ture 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 9hwdaie. /ur1at 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 t+k3)cvc1. ic +(ln:dyot 5nihv otdz 4he hole be that must be uncover+5i43z1dc. khcvtn +oy:t)o vinld(ced to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, e7o. m 1cuzj+/zxi q.-uo*78tdwvp xs440 Hz, and 616 Hz, but not at any other frequencies in between. (a) ip ew8mxvqdc jusu*-7 xt7o+./1zo .z 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 l2e vardxr /d52k9j6lboth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What akr9dlxerldj265 2/v 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 zuq6 p:5jqx.2delzj5mim+ :a$^{\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-m-long orgam79s kn hk:z*39ybhhh n pipeh9y7*h khh:sb9z 3 knm at 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 outs tee 9-vzt(dbfs7ng 0 sn8vr3.ide and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer .f(te3 ve097tn ssbzrg-8vdnto the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beatcm-qbpqqe rrzhq j85.12r :vtc2um* , every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency cmr21 85b q*2mrh:-eq,rq.q p uvjztc is the other string? ±    Hz

  What is the beat frequency if middlew/pq)k3f7gt e 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 njt-jibi.46uo vou 9/k f/y)c23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simjfv)iju /b6okn-.9 /c 4t oiuyultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tu. gixmv9wgwb154ou7 zning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Wha.wwo7g5vi1 m xz 4gb9ut is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequeno p;1vgp5)aee pdf7m-cy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequeae )gpdov;pe1f- m 57pncy heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play midx) dt j/se17(kw+6iavuafs*t 2vwx l; dle C (262 Hz), but on 7vlw( 1+dv ;iax)s*et/2xa6w ks fujte 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 frequ,* l/4gc wfn2 zvy)avtn( a-ceency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequenca(n/awf)24yl ,zevcn-*g t v cy 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 s4ny7e/*bfmn y s3vc a3tands 3.00 m from one speaker and 3.50 m from the othery/3 nem c7y 4fbns*3av.
(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 ,o: s kae6y,iompu24q a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mustp,2y6koaem4:i sq uo, 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 many beatv0/acv53 xcq r uo,o(6fb r,dys per second will be heard? /uq, oa3dyv6,xo(bvrc cf5r0 (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencyn4lou+09kvzu bid:)d g l58 zt of a certain fire engine’s siren is 1550 Hz when at rest. What frequek:z8l54 )d+dbuitz l9 vugo0n ncy 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 engi6 vxtv98llo9/an n9/s zs j7 hwxn-lr/ne whose sirenx jslso/ rl8h wnvn9 99/x7n/z6-tva l emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Ho* zz rv/k uxsa:3l06wk+jh4nz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exa r4wh+*:klvk 0u6zxnj zaso/3ctly 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 frequenc,y5ldwkmpf:,a2 l,v cy horn. When one is at rest and the other is moving tp,m, flclw 25vk,: yadoward 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 at 50.0 kHw+dxp ru*u -bkza :)4jz and receives them returned from an object moving directly away from r-u* buapdz+ w4 xjk:)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/s As it flies, the bat emi(. dnum71dz66bvn alsk -*ow qts an ultrasonic sound wave with frequency 30.0 kHz. Wh6bs6mqon1.l*awz d 7n -kv(duat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original0h1. yido0fl-e 20u 8si 1i ;mmypcaaz Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone whi1h8u1;a.2am0lmiz0ycy i -0 iopd sfe le 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 usqnkm.rjks9 .1e *qz/x es ultrasound 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 frequenr 9 mnse.j*./k 1zkqqxcy if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrason -+.mytfvc 8zoic 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 sou cjrmib*rm-s78b6rxb 8pd 7+xnd of frequency 570 Hz. When the wind velocity is 12 m/s from the nojbr br+8rc7bs7 *p8 id 6mxm-xrth, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an objecq05xiqj a ,p6 1,vrpdut moving 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 /fls)oh r/v .fyfh28 0cg zx(mm/s (a) What is the angle the shock wa f0s)fxv.hr(zo 8/c2fhym /glve 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 of a planetcn z))h1rcj)r 9gxjr)kmrcl7e ,*)s b where the speed of sound is only abou 1cx7 , nl)rbskrm)jcgjrhre)zc 9 ))*t 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oceanw: zd*zf.sa :0lxs2cz. Determine the shock wave angle it producesflszx:. 2s:wcz* d0za
(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 /ux;tga69 as c$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and apx5t(px6/rs(t3i k usee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By thki(/5 t x3(p6tsap ruxe 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 sends 20,00f:* 4.rf pp+)f jfmqyq0-Hz sound pulses downward from the *:jf.+pqpfy )fqf mr 4bottom 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 oc ob5+h68ep cwgtaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony39lnzhf; .noh . It consists of many plastic z;9 hl3ohfn.n pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound closepaskoh t c..8p87 f8ir to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mopat si7 .8fh pr8ck8.osquitoes?    dB

  What is the resultant sound level when an 82-dB sound and a m7sgl(u 0zk:bn 87-dB sound are heard simu7z0s( lm u:bkgltaneously?    dB

  The sound level 12.0 m j+ o46tcvz0 y(f pwu8efrom a loudspeaker, placed in the open, is 105 dB. What is the apfty60v+u 8z4c joe(wcoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is ratrbbl35edk xre.rd1v y41g0h- ed at 150 W output at 1000 Hz. The power output drops by3 rhd.b v l4r 151-0ybegekdxr 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their :.s x s jo:)(i2tjsndgf zb:t/3je-zxears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. Whas) :z::-sz .jb/f3(dtoin e j sjgtx2xt 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 gai)e, lzpsac8:wn, $\beta$ 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 vioeddub0( xxq9xz58i p;lin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with vieu-15 wowi;d9pd 8 na fundamental frequency ofonw9ip1 d uw8 v5;id-e 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 vh.lnm ,7 nc)uyv)snx9zlr2*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.z.l ) ,sn 7xc9vy unr)nmh*l2v What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is n9tddh i8/ go4o9,ixt0jvm4q :zgq ka-ear a tube that is open at one end and also 75 cm long. How much tension sho gz940gxtt4: -/had9km,oov dq 8jiqiuld 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 re*gpo 566v)ahkm oj6mlsonate 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 wy*q9p(.fdl eyd-x1 vthe 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequy*w9f (1qdd- pvxe .lyency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the gp mgo xx8b;76stationary train hears a 3.0-Hz beat frequency when tho m8g p6bxxg7;e other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whist3mfn/hf. mo+1 5mhpaw le as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume cons 1 +3f whpm5af/nmmoh.tant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lis1 )dso2ckkukc2 q 2c3utening to the differencec c s22k1okuk2cdqu 3) 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 going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency omq*wtvy25;la* cu9 pi f 11 Hz. The shorter one is 2.40 m long. How long is the other? 59* *yt ;clwqp vma2iu   m

Two loudspeakers are at opposite ends of a railrocz 7c2u81h3ehtmo6 m iad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies 86tm1io 3u2 m chez7hcof 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 e firwsz qq+3o0 0 f7qjuys.1)normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and refjuqyzw. 1o7 si0)f qq0f3ers+lected 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 flying toward of*ot 1osl15 ij7e-xedzlp: (the bat at speed 5 m/s Thepeszjl1of oo:7- l(ex5*tid 1 bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. T2.s3 lx nlfnsua 22kh*he pulses are approximately 70.0 ms apart, and each is abful klna*2 x .2shn23sout 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 /y zs(g+- z9ye/yhbaqsignals from one Alpine village to another. Sinceza- sbeyzg+ y /9/q(hy lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pres qwe9f2 xw )w-qlsxy.:gr-jd(ence 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. fel9sy rwj-x 2wgxdq-.) :(q wCalculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods) b5,zw ;b-ove6dtfz:qc;v v j,” 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, z eqw;b5d:);tcvo- ,jvfbv z6 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 o;*x;ztf uwmgb-b.lrl2 jx3v7f hearing for the human ear at a frequency of about 1000 Hz2bv-t;glb.3zxrw; *mlfxj7u 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 sow:u7g2dz/ evl xw:9mny9b .t6(ryljm nic boom 1.5 min after the plane passes directly overhead. What is the plane’s2m wy:r9ljn6gd (l 7 m9/u. zbtyxv:we altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is j- o,:z h;. c jkwvm04szqp3id15 $^{\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