What is the evidence that sound travels as a mik:i b2-.jl iwave?

What is the evidence t )1xtau,lgq 4( 2oapqo ks.7ythat sound is a form of energy?

Children sometimes play with a homemade “te8 ocm;v:y u sd9adw2wpq.k a1-lephone” 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 ot d-sd1q;8 w yaow9mp.auv2 kc:her 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, exx m8vqo7 34odo you expect the frequency or wavevm 7x8o4xqoe3 length to change?

What evidence can you giqw op+ ,ezr9o3qel/36-zm z,ls(ehu sve that the speed of sound in air does not depend significantly on frequen,3prssz-+,oho9ewqu /qz ml e36 z(el cy?

The voice of a person who has inhaled hwudg 6s a/9;he/u 7oxm/o+x inelium sounds very high-pitched. Why?

How will the air temperature ihn p*ey8 cd.p)yj 9g0kn a room affect the pitch of organ pipes?

Explain how a tube might be used j;u,bfmqo; s) as a filter to reduce the amplitude of sounds in v f,sq;)mj;u boarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spacof5c0q1fh)e.c. vf06m de afgk6p,-,cag g hked closer together as you move up the fip6ge5e-kf,.6.k fdv ,hc0gm fa qh1cg0 fo )acngerboard toward the bridge?

A noisy truck approaches you from a* sz0gurdtq hy7c9.bs5w10d-p- rlibehind a building. Initially you hear it but cannot see it. When it es uwz0b-p9qcdl01dsr*. 5ri7hyt g- amerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in wvpr4z40iv ox)-8mz gspace,” whereas beats can be said to be duev rpzo04gv8) -imxwz4 to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woudhm4 b .t5 zg0v1.p2wojlpi;mld the points D and C (where destru movd w402;pmt..l1 gih5bpz jctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work0bnbheeu-bb vk5 ).7 :mj7 s2mu2goze 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 more noise reduce the sound levels rebg :7o mz )vb5b-0 s.2enbe7kej2uumh aching the ears?

Consider the two waves shown in Fig. 12–31. Each wavet 5:hb +huovvfh qol--:qk9yd k8+n6c can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of th qoh8kuyh-ctd 9lqbvnv: k5- h6+o+f:e waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler sm nnjx2;++.d( ccyg:hf hzl5 fhift if the source and observer move in the same direction, with the s.;l5 hz:fmg2 +fjxn nhcdy( +came velocity? Explain.

If a wind is blowing, will this ahrmm9,0,y,yjbyb of9 /d igcq:ey mq r3 5(f(flter the frequency of the sound heard by a person at rest with respect to the m/bm5(jqy ,9fyhc( 3:m9e dyq ,,igrffy0 bro source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a sc0s *y*in ia/ksbsoos/au ,5qf j 9:i9wing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound ofqioau/ 0:sioa9*, n9kf* sss/ijb 5c y the whistle? Explain your reasoning.

  A hiker determines the length of a lake by jnpzh de24) mbp-5su/ listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.05d nmpb4 /uhez2pj-)s s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jtk9/d3jw qh*af:*yj 07udbfyust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deephwuj 37ak9dd:q yf/* yf0* tbj 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 in air at 2f khq :hs:rl7h 9gk/h 3 y3r0iah.t)kv0 $^{\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 a school of tuna on a foggy day. Ws5 k:fuqsr5m,efke1 3 ithout warning, an engine backfire occurs on anotheke15 s5fem ukqf ,s:r3r 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. Thehv 0l8l3li;yo splash it makes when striking the water b;il yo30vhl8l elow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the6a 60ghqys6 zt 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 didaygs606 tq6hz the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one l .2mvam9. d-gksg,eu mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a).va-s ug .gm dk9mel2, 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB?ndei9 k02c*n/ qil1qk 8yxvi 3    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 i+ aa6qxnqu/q2ntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of m,( c*e v8u*birs il(z95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hm, s8 v(uicl* bzr*(eiint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an wop*f7yt51z lski*.x airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experieyfw **5s zpt7oxil.k1nce if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sign/7,-xgnx xw s6yy xoq3al-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratnxsw/oxg,6yq3-y 7xx io of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power;nyx5 g8ybfbhya n4 9c-0cooh(q4ws) output of sound from a person speaking in normal conversation. Use Table 12–2. 8;)yqbs5w (0f n-4 ync 4gyobhhco9xaAssume 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/o g-hwe6.6 km4cl pgdls,*fftrikes 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 rat/xtkfxo3w) q 1e*a)fp ed at 250 W, while the more modest amplifier B is ratedwo1xf)*e )3pa t/xkqf at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in qu54av6q8d s20qmu tm3;pfx i front of a loudspeaker on d3 fqq siut4xv826m;auqm5 p0the 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 typicallya- rvl;m*u w eu7-jxg6 detect 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:*eugl 7wvr-ma;6jx-u See Section 11–9.]$\approx$   

  If the amplitude of a sound wavergd oknz00dk+c6b99p((rwgw is tripled, (a) by what factor will the intensity increase? Increase r pkg c(9ond6w0zw+g90brd k(by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but bx*e 99 :b eplb j.7j:u1djyjjone has twice the frequency of the other. What 91j .b*xe dj7u::bjbyp je9ljis the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave inswp6k..uqy*5j : aez s air that corresponds to a displacey*ja5qz6s.p u k:. swement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levelrz l+jd ).cv)a-k4rr ymoo*c . to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12 yl *-o)rr)mk.odcvj.ar 4cz+–6.)    dB

What are the lowest and highest frequencies that an nc4 4+w7djp3 zjfz; tzear can detect when the sound level is 30 dB? (4 +dwcj7ztzz3n 4jp;f See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lemap(,ip3;qq+z, uq*a .qkmjq4l0 zw vvels. What is the ratio of highest to lowest intensity at mzw (jp m0uqp4aqv*i3;qq q ,ka ,l.+z
(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 frequcpu:d3c *f3xe:akhl7w dx92,b kbwq7-+ bduc ency of 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 string 9:xek ckc2:,xw3bf7h7 d+pu3* d d-lwa bcubqbe placed?    N

  An organ pipe is 112 cm long. What are1.6) l:fr yuqe4xtpuc the fundamental and first three audible overtones )64fu1ly:c qpx . retuif 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 freque,;h9sodxic( mncy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, mo;cs,hixd 9 (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 the ran0a-zeuy3sy*ukr-4ix20vy i e ge of human hearing (20 Hz to 20 kHz), what would be the range of th*ez0v i20--u4xreyi s3ayy kue 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. What will c,f/g 7)oryyz be its fundamental frequency if it is fingered at a length of only 7zr )/fycgy,o60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long alo/ rohb25g78oyricr rp 2v4 .nd is tuned to play E above middle C (330 Hz). 2rlro7ic45gp 8r o2b/ .yvr ho
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that eqlg s x,;:d+phmits middle C (262 Hz) when the temperature is 21 gpdqxs;:h, l +$^{\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 atmecw wp q2e 4ov(;x23q 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of tf /.iz 1r vwx9mog54ula vl0a)he flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294wv l091v)5ux az.mgfoir a4l/ Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hzwrux -s.h 8isslo1g92 , and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open osslg8 s .o9h1rwu -i2xr 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 resonates at twkoo pe5 m2u7c:edq2-mu.3r3gs vc qx/o successive harmonics of frequencies 275 Hz m- 2 ecu3xdrq q/ 3g7o.5vm2kospeu :cand 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 wsi 5o s0t:yp7gu.q)h$^{\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) n:lx)c*yneyz qvvb gg/ j-9. for a 2.14-m-long organ pipe g9 vy.zqngvy)- nj/e:l)bcx * at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lonctqsahc)+3e v-t+ wz/g:f r1kg. It is open to the outside and is :vse- wkfac3t +1qgchr/ z)t+ closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to 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 vk)av5tu 9mp 9)84znuah, xbfs when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stria z95n m)bktfuaxp)8 9,h 4vvung? ±    Hz

  What is the beat frequency if middle C (26lm6r4t. fv(rc 2 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 (bran7v o-u9 3fatst+byr. hx;kk8r g:f2j nd 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 simultaneously, estimate the operating frequency of br2f rh7r fo9 a k.ngyku:x;tsv-3tj+8band X.    kHz

  A guitar string produc0 cp o*7swy27skb 61pdu m44e yjawm.ues 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when d wsu7 7 1ujyp2 s0bm6ypwok*4emc 4.asounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frehca/:n1 vbx)gm r +:tsquency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the tw: xsam )1cnt+rg: /vhbo strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mid xd0v9kcnf6 x,dle C (262 Hz), but one is at 5.0°C and tf0xn6dc9kv,x he other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B h:j8 7/rianh yog8x z3wtp i/1gas a frequency of 441 Hz; when A and B are sounded together, a beat frequencyzjt3n1w7/ih ro/xy 8 gip:8ag 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 standc (pb ltd**c/ 9qpjd.ls 3.00 m from one speaker and 3.50 m from the oth djl*pl/p.d9 cq cbt*(er.
(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 p/g* ejrr5zy3 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating atz erpy/ g3j*5r 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 maoc2 l.u;ud jfk7vx-onj7op :) ny beats per seconv)- j;f7xocd k: .ol u2junp7od will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencep i)3n yg-c0,zfgrwqm/ya n srl0 1;+y of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m//n)zyfp3m,qe gr1wly0s cnra i- g; +0s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sir +wd;9ytcirefg4z n) ry-sx.:en emi yzet-yfrwri49sx;g) +c: .ndts 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 ag-gyv2z. rqqn 9 t1+vc 2000-Hz source is moving toward you at 15 m/s versus you moving toward it a- ynvc2 .gqg1vrt9q+zt 15 m/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 equippede-fqyck8t* . d7ruxm1 with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency8r1xkq*td.cuy em7 f- 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+(( zl7y-6skq dw hd1jltxv4k.0 kHz and receives them returned from an object moving directly away from it vhs xqdk1k4- l+ d(7wly (j6ztat 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 i ; sp qd8gk mqpx28imqz5k49w+t flies, the bat emits an ultrasod5i pm x9gkw2 4z88k+qs;qqmpnic sound 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 experime 5babw jo8aq7(* 4pdscnts, 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 while at rest in the railway station. What beat frequency was heard if the train car approac b8(psjw 7a aq*o5d4cbhed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound c22- i8uugp whyyemn2 6la swa. /7g0hwaves 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 cphy2h . ye 02g cna7u682 wiusa/-gmwlm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves 4vy+ mj;b)2pgxqv4fm 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 Hz7 u.dvircuqi;6d 6:od5m vx3h. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest,xi;cr 6: v7 d3ddqm5uhvio.6u
(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 land if its syq;ah v ahd.rv3zh/k*14r st e 9zl3a4peed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What e azias7*vj/k6 iqn7fdv4.u. is the angle the shock wave makes with the direction of the airplane7/6f vks. .iqea ji*zdvau47n’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 planet where the sphcyv *h7o;.uf ae0ev16;l qff eed of sound is only about 35*oe 7lvhvaufcfq 6 h. f1ye;;0 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 stlgmxd5 90ge8mjfr9n;nap/9m rikes the ocean. Determine the shock wave angle it prod; pnfm0 gd/e99nlra g5m8jmx9uces
(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 4dcr 1339m3wuvvq+ r:nruz bf$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km abofidc z-b39 ryykn*+4d ve the ground flying faster than the speed of sound. By the time yok9 d yb3+ zcf*4y-idrnu 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 devicei,o4+y)dr4mrw yqs rd:d5 wo1 that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If ymis +oo q dr4wr:5wy),dr41dthe 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 ab ek9n 44ge vhe*89gxaenav0n+n+ d7q re there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It f i mi6a-odqk- l nqt/5z74s ow.)f.epconsists of many plastic pipo mpfzlf .-tid 4.an7woq q e5s/)-6kies 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 fro jvpdz5) 03rww+d*k )l;h +-zfkuyet/qz)tg om a person makes a sound close to the threshold of human hearing ( k 5k zqeu+w-l+t*)z))jv h3d0fg zrdtw ;/yop0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an2:zhq 8wn2 t vz o.ybkv4pf,q* 82-dB sound and an 87-dB sound are heard simultaneou.oqpvh8f*kw bzyq 2 vt:,42z nsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opsm6 8s aoof92 vr+ode8en, is 105 dB. What is the acoustic power outpum26soe+sa8 9dr 8oofvt (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpuxxbxu ,wtdcj9 7;1k5lt at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wat,d7 lxu; 9bk5x1cxjwtts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective d 1 juufy8bx-j1s *za2ievices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power i i2z 81*-fs1xjyabujuntercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, 8uccglgf*9e6x 8h8 wz $\beta$ 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 g zek 28g0xk-qis 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 hfs+l 0m9piucla4db)g)0tn 6between fixed points with a fundamental frequency of 440 Hz and a mass per unitlg0at6cifdb+ 9l hn)4pusm)0 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 tubehi )ewth:i- k3i 3s9xe 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 ise:ti3 ihx 3w-ik)eh9 s heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 i 6b -0g7cjc1o iz)f q8bkcb*lg is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in i6 bjc0f*8o-gci ) qibzlb7 ck1ts fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate 9g,rh )hglvx, 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 rang1zn8f bfhtm-i;r.,l.38xhjxmeqr(a e coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sotrar 1zfn e8i(l.b3xhq-h. j;m ,fm8x und?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the s(hpzxu1 yn2 z4q4fij0tationary train hears a 3.0-Hz beat frequx y2zpf1(q4zhj 0ui4nency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After 60 p-cy f70o ;oukd zoe1bub:bit passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocobue c-b1o boz 07k6uf ;:pyd0ity)?    m/s

  At a race track, you can estimate the speed oopgd6 c4: ecw )ctto -09na:pxf cars just by listening to the diffep:td ) awo9g:c- nc4o6cxpt 0erence 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 of 11 Hz. 7: lr-5eiurtwo, ;1 qhfrr a(gThe shorter one is 2.40 m long. Hr1- h errao,f(5; :iwqgtl ru7ow long is the other?    m

Two loudspeakers are at opposite 4-jr2k* f/arhxmom 1eends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fif rrm2j 14/x*aheo-kmg. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is norma vd12u;lx d2:wgb yxt1*uhn4dlly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were ;dhnxulx:2 2d1uwt41 ydgb*v directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward the t/p vrahv8q9815eom o bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the b/o8v 8ro taep19h5mvq at after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approace2u/x6ypd ..47lsat9b 6fbjgj9xyoy hes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitt4b j y xpu9 gj/2fy69dts7eyo b.a.xl6ed?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Acx8pryy qh5 m7t *4s:rlpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When pyxy 7r *p8:r5t sqch4mlayed 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 listerqj15f9 7nb +jgeeraj/1yo 2ining can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of thrbejejiy/9 aq 21jfg o5+7n1re 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 in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, caluaz24 xvc1b g/2d( iviled “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. viacb2zu 1(i 42xdv/g With a little practice, the 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 thy* 7abii28 wthreshold of hearing for the human ear at a frequency of about 1000 Hz is w8hay*2i7 tbi $I_0$ = $1 \times10^{12 } W / m^2$ 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 2.3z-5 3bsqzwha4l1cvm1xh m s-0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alhlz1w5s3m-3b 4zc xs am-1qvh titude?    $ \times10^{4 }$ m

  The wake of a speedboat is a1klfjd/ kd8 23 lop9x6,o csc15 $^{\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