What is the evidence that sound tr(0ehm) ly /lpn :zi;bqavels as a wave?

What is the evidence that sound is a form of ene 5:v hu4xmi:kzrgy?

Children sometimes play with a homemadtm,- dta ;rcy-e “telephone” by attaching a string to the bottoms of two paper cups. When,c-my;dt-a rt the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency oryz(;)9:z nzsyt. j sto wavelength to cy:yt n)t szs9ozzj .(;hange?

What evidence can you ryht)c*hn0 adxy /v-e(8hhc4give that the speed of sound in air does not depend significt4)* dcny/vxr0h(ecyhh8 a -hantly on frequency?

The voice of a person whp;c z**v;qugk6 zm gut(:s0)krx5dpk o has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect z4;.vbpfu1db d/)sl; ls,g*lwg;wtl. :r ydi the pitch of organ pipes?

Explain how a tube might be u+0 zibpfsyh,l..kw;v;v m2 pnsed as a filter to reduce the amplitude of sounds in various frequency ranges. (An exampleki;vhm. 2b .fnzpw,0 ; +ypvsl is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) sp k0bs;* +:ef reyu/nylhmee1 wplo888aced closer together as you move up the f+8rw:nke ;elh e*oy0fmse b1 l puy/88ingerboard toward the bridge?

A noisy truck approaches you from behind bkz:h (7v1xbnwb :fv4 ew-z 2qa building. Initially you hear it but cannot see it. When it emerges and you w-hxbv4fvebznk b(wq721 ::z 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 saf a1m-a/kn 5wrid to be due to “interference in space,” whereas beats can be said to be due to 1knw-rma a5/f “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers k;mb,zzc96 qke u gn:03ns9lj were lowered, would the points D and C (where destructive and constructive interference occur) move farth q6zz3csnu mgk 0j ;9:e,lkb9ner apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wm1c p6)o(pf b sb8b7jvith 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 avbm7(pc j s) pfbbo681mbient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 5 vl,:vhl5,jzndkpz6 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component fre:vlnhz6lz,5 v,j dkp5quencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obse 1frs1 9gsfp4ga5lq.29 pe:kttz-naurver move in the same direction, with the same veltkn esz1:-spu5f r49. 1qf aag2lg9pt ocity? Explain.

If a wind is blowing, will this alter the frequency of thw6kd0 j450kpf; a7c 7d fnhekie sound heard by a person at rest with respect to the source? Is the wavelength or vejknd0 d747;0acf 6ikw 5e fpkhlocity changed?

Figure 12–32 shows various positions of a child in motion on a swir l;mr2 7jdl-pby0q )k2cnig 1ng. A monitor is blowing a whistle in front of the child on the ground. At which position, A throughrpjl0bg 2qkly ;n-d)1mrc2 7i 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 listening for n;z1n 9*app16u2 izj9xgz+ 4 dq hf nq7fl4rclthe 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 the4 l9 nnu21cr*1fqhnzz6x igld4+7jz pq9 ; apf length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hiwuxv:/3 8rd.tz)c; u7ayb cmxs 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 (Tab8zy 3;/c:dvuxw) 7c bmrua .txle 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20j0yei : yq4)vb $^{\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 schomqzdzc(v -7 -q7z5uieol of tuna on a foggy day. Wit- z7qdqce- 5zzvm( 7uihout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Thbd t*mf kf:cv:7u +n5le splash it makes when striking the water below is heard 3.5 s la:5n*c+tfd7 vf ulkm:b ter. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stri ,coxe;q3d ux5tnh;s5ke the concrete pavement. A moment later two sounds are heard u5x; hx3sq5dtoe;nc, 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 impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent 9c qye(roqkppx,t+wl /1qp9 7error made over one mile of distance by the “5-second rule” for estimating the distance from a lightni+rkql9q9t o/ 7( yqcp x1wepp,ng strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1 :rb.-gqw lu0c20 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levedcs q mo 3(3,6vasdd50n:buwil of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously 4a5x9*vaa+ smjlb3yk at a certain placebk3a54a v+l9ma*xjy s, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a z+ 1:r9em uuxfcertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What rzux+:9uf e m1sound 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 sai).z nhee/( flj scn8b*d to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. Whacjn)hs.(ebe/n*f zl 8t is the ratio of intensities of 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 person speaking in me 0hry*hlbdzx (:00f normal conversation. Use Table 12–2. Assume the sound spreads rodx*z l 0behyh(rf 00m:ughly 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 strikes an e gib64: qd, c2uwxtb+ngonmv *u3c9o 5ardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modesli (x f ahmog1p8u.4e4t amplifier B is rated at 40 W. (a) Estimate the samhe o48gl (x p1fu.i4ound 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 1 )f1.wnan vsp ,bbk5-kfs5 evregistered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. fs5)f5evkns w1n1.-, pavbbk
(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 differencerd(i;oz(dxy bbk1p - ; in sound level of 2.0 dB. What is the ratio of k xdp1iz;d(( y-o bbr;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 what factor will thew/ d8yw-k(4ibr7swhx; c g(fpc e8 oy; intensity increase? Increa whsb;occ;rxwd f7i/yg4 - y(e8p8( kwse 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 tkx+0r x)i35t,s yy zelhe frequency of the other. What is the ratio of their int 0 5xzxylkyeis+r3,t)ensities?   

  What would be the sound level (in dB) of a sound wave igufh1w(*qz /j1 x5 nr6xw8 ji.; iprgbn air that corresponds to a displacement amplitude of vibratiz/irxh1.frw*w;ng6b1jjx 5q p 8gu i(ng air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loudd z pjqmr5w):*9)xpgo f 20rht as a 100-Hz tone that has a 50-0d xw)ppfho5rq2tj: z r)9*mgdB sound level? (See Fig. 12–6.)    dB

What are the lowest and higqm))qd4w/ ero hest frequencies that an ear can detect when the sound lq)wq rdoe)/4 mevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommoda,2a5vfx a) 4i gltyig8te a huge range of sound levels. What is the ratio of highest to lowest5fv8iat) 2,ly x ggai4 intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a(m4y:e 9k0k1l m 0knmtzkl 4cmc i9fh6 fundamental frequency of 440 Hz. The length of the vibrating portion is mkmi ykft14 ke6mcl c00n m9:lhk 94z(32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and);yhv h4gyp6dg: c) wc first three audible ov;)ychp6ghg cwy :d)4vertones 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 7ey nd-y2q .2 c- ;ojfjxw1zjtthe top of an empty soda bottle thajw.o tyc2 d1;-zf27jynxqe-jt is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of huz1 dv9lj31op0 -ehg1e he p gs08ogyo2man hearing (20 Hz to 20 kHz), what would be the range of the lengths oh j ps yeheool011vg1 83 dg-peog290zf pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540k6nkq h0ld82u:( x ryi Hz as its third harmonic. What will be its fundamental frequency if it ilx d n2k ruhy:(8iq60ks fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above midd qpc0/a3hhto4lewl 9( n fi(z-le C(c (q3zh0iwla h9 l-/ t4ponfe (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 length of a y(msi6jf.o8ckz9 i,u n open organ pipe that emits middle C (262 Hz) when theo(c8kij9.sz,uim6f y temperature 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 at 21tk;x 8ix0nt2 zz0faa 0 $^{\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 hole be )dj3uwcdbowf6t7pe n7- f;wf40/bz zthat must be uncovered to )nw;wd60pt zb zu37d7jw-f4f c/ efboplay 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 rej4lq b0mwac 7s .v.)x6vms) c bg*cp6osonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (mmcspcg.wq*js)b .607l oa c6x)v4b va) 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 1.8i7fxu.qiqd 6xh;w, hl or ((0w0 m long is open at both ends. It resonates at two successiquw x(r,(;x d.iow60fhq7l hive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 vk klx,v(3mi ())syxq$^{\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 ;cpnj8;9 g zmv4eqgd9 within the audible range for a 2.14-m-long organ pipe e cd4ng89;9zmqp v j;gat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. I78 na p4s-xgxst is open to 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 p xs-87xnas4g the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s wh +tu65bb .y beh*,hhjfen trying to adjust two strings, one of which is sounding 440 Hz.*jb5 ., y6hhftbub+he How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hujvs8*p .eq*xzx g-/ zz) 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 operyd9a5l zlr/b nrj10.r qftuj8 2um i79ates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played5ymj.92/t7jlql fn1u8au9r bz rr 0id separately, but a shrill whine of 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 sounded with a 350-Hz tuning fork andfs4 z/,iis 5xq 9 beatsq xisi/5,z4fs/s when sounded 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 frequency, 294 Hz. 4n 2i(zf5 u-yaao8la du9ii)/vi suh.,gmzb (The tension in one string is then decreased by 2.0%. What will be the beat freq bsn8a )h9 (iu-dayu2z/g i4li(v .5a iuf,ozmuency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicajoy oaz6cq/)k)3o43xu 1pdoml p(yf 6l flutes each try to play middle C (262 Hz), but one isyczofpjd (uyp a)3xq/o o641k6l3o)m at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; wh:g xbz-+ z+ehi1:h gmren A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are gi 1m: eh:z-++gxrb zhsounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m x w)a nik66u5pfrom one speaker and 3.50 m from the other.akx566ui wp)n
(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-rr9l3m mcom+n) e- e+m mlet2 supposed to be vibrating at 132 Hz, but a piano tuner hears three beats e2l3 c-m lteeemo9nmr r-) m+m+very 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m ij0) v8birm/mpn air. How many beats per second w / imr)08bvpmjill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550p 9mzs cm ,;qet- :sds(mr3r5l Hz when at rest. What frequency do you detect if yoc5spd m 9;r,es3rq(sm lm- zt:u 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 rxh d8m3hwv-n* .zv1rl,ri2y do you detect if a fire engine whose siren e32hl 1y,. -riv*vzwnm d8rxhrmits 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-Hz source is mfqp,fyxx2pz -u y d.(4oving toward you at 15 m/s versus you movin x pufx4,p.( -yz2dyfqg toward it at 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 equipped with the same single frequency horn. When o vzucg rfg lf2f)x all*9m(:.4ne is at rest and the ot)*ga9lvmclf xfrl.z 42u f: g(her is moving 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 ultrasoni4jw;qu jynd8*wkw / e0.(hsu rc sound waves at 50.0 kHz and receives them returned from an object moving direct; hedwsn /8ur*qkj .j( w4uwy0ly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a w kg* 3z/n7cvrhall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0gk3r7 nhvc z*/ kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler yicl0k:d 1ujna /l4(hexperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played tn4 a(ki lclhyj/0u:1dhe same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measub4441si wp g2icd,vds re blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the pw sids2,cvbg1 i44 d4speed 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 sound source?   Hz

  The Doppler effect using ultrasonic waves of frequen4r4 xx:t637hazi bsmwcy $2.25 \times10^{ 6}$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 velocitsmi/ee( j0papx+b j)dg.hh5f u -,n7w y is 12 m/s from .gp+ip-d,5uh jan/7wf ( es b)jex0 hmthe north, 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 object moving on landqp)8sghehr;e w.lz9 5 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/li2w3joo v.m-s (a) What is the angle the shock wave makes with the direction of the ai-oil.v3j 2owmrplane’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 speed of s r l);du8sdfc5ound is only )5dusc r8lfd; about 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 85( hsq6jsxonw )/s 1s;n00 m/s strikes the ocean. Determine the shock wave angle it prods xsqs) (o ;sjnwh61/nuces
(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 tzmkx3, x3c; 5lmu 2ww$/theta$ 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 above the gr; :u6ensx r,fpound flying faster than the speed of sound. By the time you hear the sonic boom, the plane :,nfspx; 6ur ehas 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 so*l;7r k n)yfwmyyc;/znar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is d;/;ylrcnwf 7k* y)ym zesigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hu : 4ss16.j1yzpao8z6qo qhxrrman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consistssaan(as+p/ow. 5bkv ( of many plastic pipes of various lengths, which are open on/pk(sbsw n .a5aov a+( 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 make ubyzhy( n lzr5*1l65fs a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoesby*5fh zz6l5r y1n(ul?    dB

  What is the resultant sound level when an 82-dB sound and a:j+ skb0b ,eisdx*4)yxxbcfna vpg1 2ow 2v9* n 87-dB sound are heas+v*xd ):cpn9a0k ,b x22j sfbgbv*y o4x1i ewrd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opejhn+r 03cz un3n, is 105 dB. What is the acoustic power outpuc z3rnnjh+u30 t (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output ds lhzui2a0v7 -rops by 10 dB at 15 kHz. What is the po lua0v i27hzs-wer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deviceslgyah pngk :75 g2p;unt7bt83 over their ears. Assume that the sound level of a jet airpll2a7 t3 5 ;:bppgk8ung7gnh ytane 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 systems, the ad e2gj 7h)d6egain, $\beta$ 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 isj 0jub)jq(85s5xvc mj(n6fe j 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 cmvvl b4bjn34+ cmv(vfta 61pg3igjr /- long between fixed points with a fundamental frequency of 440 Hz and i3 mnjv4v-g+b(1vfcb p6t/ j43g vlra 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 intk o6) rw/gw5+kmyf;fj o vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of f56 ry)wwkk g;mj+fo/ the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tufz(t.hr d+h,xf r72 r(oi na7nld/a )xbe that is open at one end and also 75 cm long. How rah/.7)ddarnrx,2f+(tohl zx ( 7f in much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

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

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Them1gg9uo)9 :hjhj ajdp, kxs8pz,ort.p8+. zp 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 t+p)8kj z.,hgrp1zu8x . 9sjp9otam, ghdjp :ohe frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the a3dj(lsddet 6mi6.8 mstationary train hears a 3.0-Hz beat frequency when the oth.t63di ajm6(desm8 dler train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approache yz/o h)35n 0qb.gzhems you is 538 Hz. After it passes you, its frequency is mea y3z50nhmbz/.geq)oh sured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars juwb+w/; f,rky(g xg7fcst 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 straighb+r/k (;fc7w ,gxy fgwtaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The8iy(jrc: ui4 yg+; xvd shorter one is 2.40 m long. How cduigv4:;+rxyy 8 j( ilong is the other?    m

Two loudspeakers are at opposite ensps 6u.gz7; d2.rp lozh q+cz4ds of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have 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 speaker+;c2g.sppql o7 sz uhrdz6.4zs after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.zx3b j-i,gilyb.2m a za, o0x,32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the 3.,axma bjgol,20 bz-xyzi , iflow 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 tha) .m s2d0pqr sa.xkcemnt nhh)j1 296e moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What iest)xjr k 2da)m0 a1.6h hc2nnmsq9p .s the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frnqi47 ho+* xmhequency sound pulses as it approaches a moth. The pulses nqh 7mo+i4 *hxare 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 emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpin a.8nx6 ik2shdtl:m pv6jx*, ze 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 6,nmpx:dhj.6vz8 2lxkiat s *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 the7 d(3z ;+ qweyfrwyg5o presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure e fw7y;3q go(y dr5wz+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, cal:7qzwzxo ct6fwcn7n/ah) 6 qs+wdl1 2led “singing rods,” involves a long, slender aluminum rod held +1lw7c zwoaz 7wnh2qdn)c/:6stx6qf 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, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the humanl ylj- (k3j4x/pe9clh ear at a frequency of aboup jk9yl/ehx c3j(l -l4t 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0.n o.5gzzhk t m;,.e-otpfvh*)9n 9esz An observer on the ground hears the sonic boom 1.5 min after the ps .9.n tn ze)9vh-fe5o,zpmozgth*;k lane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 /-jc mmvg6j +rjih q0zydp5 1f7.kkh)$^{\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