What is the evidence that zt hg5iux36czk4 7,ij sound travels as a wave?

What is the evidence 9fsqq24 ,ksnvthat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to t4zlfu72ulmqm k hv:c1 5: ukv5he bottoms of two paper cups. When the string is stretched and a child speaks into one ufk7uc4lvk5l5q: 1m: vu2 mhzcup, 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 fr6- 8gg i a,.g.1yoay9eu7 rm;4ntmvvq yfxx7lequency or waveleqygu; glmv .e 4gtoyax-,fx1y8.7iav6n9 7 mrngth to change?

What evidence can you 397m/k)mvy ilotvns3 give that the speed of sound in air does not depend significantly on freqm/lv 9vsn3)o ki3ymt7uency?

The voice of a person who has inhaled helium sounds verdlczl)j7-)3vsj3o xs . dmmi 2y high-pitched. Why?

How will the air temperature in ah82pdwpp1y f l n1,:c3us5suz room affect the pitch of organ pipes?

Explain how a tube might be usep+ zob*kjvdzzq6v6 ,8d as a filter to reduce the amplitude of sounds in various frequency ranges. (*pz b6q+ovz,jv 6z8 kdAn example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yu),p z8d0e;ipxc *hz you move up the fingerboar8) xpepz yuhi ,;c*0zdd toward the bridge?

A noisy truck approaches you from behlwwcpz 8d*+: zcqrz)- ind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sclr*:+zz)z8q w cpw-d ection 11–15 on diffraction.]

Standing waves can be said to be due to “intel3/m+c1f mjq a wl-ys-ypf*2erference in space,” whereas beats cac21wa *mllsf-e+ m-yj/f 3 yqpn be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were)chx,+fbt 2-fz(vfey 0 j5hky lowered, would the points D and C (wx,f+fy cb-)k 5tfez h0hj2vy(here destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wipp a.v j2joxnj1od e jl3 -+:71cko:clu1ndh ;th 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 dvp: h dl+1jxdoj 2jno;uce. n:3 7ap o1-1lkcjetects 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 reaching the ears?

Consider the two wavesu4cg2 -pfaxzb o(0xt9dl s.)w shown in Fig. 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 frequencies farther apart? a sl(x )gt0c4zb29 o -.dpxufwExplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obse8fprn ;biy+xhwb/ + 9s.t y)mmrver move in the same direction, with the same9 b8w+f/+im nbhm)sp rxtyy.; velocity? Explain.

If a wind is blowing, will this alter ln ./ek0xcr) uthe frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or el.x u cn0/kr)velocity changed?

Figure 12–32 shows varhzkqk 7 1tw-fhbyo7) 7ious positions of a child in motion on a swing. A monitor is blowing a whistle inz-yo kqw7h )h1kftb 77 front of the child 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 br .4wnmyh/y3 f8 e0)rn.hdwey;p mx0gy listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoutin4hw.y pm)3nf0 n/.xd yg reew 8mry;0hg. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below thet7sy:rs e ntt oo13:tm 2d25oo waterline. He hears the echo of the sound reflectys:5 mo21roo27t3dtt s:nte o ed from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelen+ x1ag8k8elnzjz4w o5vt8 r -sfx6,sggths 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 drifting just above a school of tuna onen-l0l* )c 7 kagyd.mh 2ehc qnpu:j0w(;)tdd a foggy day. Without warning, an engine backfire occurs on another boat 1.0 k.0e*)kt u ydlh7h(-cd dnp ;wejqcg 2m:n0l)am 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 osjmzgqjn -0(3f;) lc a cliff. The splash it makes when striking the water below is heard 3.5 s j0m-jfn3zg qc)so (l; later. How high is the cliff?    m

  A person, with his ear to the ground, s +e q;;ejlar;tees a huge stone strike the concrete pavement. A moment later two serj;te+; l;qaounds 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 impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ovy n01y49x urmoer one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatureou4n r1 m9xyy0 is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pci wrj m()3m okf8obo6/tfi( ;ain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity i7r w-/b0 olebbs $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level 6 czx.n;,wbuwwswq d3,6+jpp of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one s6w u 6,j x.wdpncwb,;z+qwp3 is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equazd xw+(*xl9bl vzb.1elly noisy jet engines is experiencing a sound level bordering on pain, exz dv 1bx blzw+(9l*.120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noi45/cc5bexulnrg(wx rmc),(h se ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =,g)4x n5(echm wc l5/c(rxur b    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person s8u;(cm u/h izwpeaking in normal conversation. Use Table 12–2. Assume thw;uz iu/c 8(mhe 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 strikeuex)u,p 0rk4ys an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is ra-2fk8i jtsw 329xuj jated 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 tox28-3w9sjtu jaki j2f 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 whenkvox 8b0rr 1+:p.sa og placed 2.8 m in front of a loudsp1 8b v pxg0o+r:kros.aeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. - *ewu .f8gmy bb(q) mcty-53pi+rxoz What is the ratio 3)zbwfiyem- u5yocpm x.t+(gq*-8 br of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what f+eu- 2 4ojmc xy5;wgoihv+ -pfactor will the intensity increase? Increase by a factypxo --u+e4+ 2gjfvoiwhm; 5 cor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampr,2 wo4 rog0 awanlyustm9dk:5s 193nlitudes, but one has twice the frequency of the other. What is the ratio of their intensa4 s 90rrdw,tosg5 n 1uamo3wk2y9:lnities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds toy29 z:md85gv z f+halhr nz.a9 a displacement amplitude of vibrating air mzfn9dhygh5v 89 zl.m: aar z2+olecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that(/m7pr gy.j(/x7 h vbxty5p fg /y (r(t/ bx7yfg5hpv .gmj7x phas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wh wpbvc 3tt2jiw; n7r(0en the sound level is 30 dB? (See Fig. 12–6.)brwj7cw n 3v; t(pt20i

  Your auditory system can accommodate a huge range of snimpot8m 2q +k; 3)a4rmj mtm+ound levels. What is the ratio of;mjmm ) 2t8 3+r+mnkioaqpm4 t highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length ofzs7:uoj; p, . neenwt9 the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension muw,pznte:eu;.7 j o sn9st the string be placed?    N

  An organ pipe is 112 cm long.0kj8 ozrg+6.vr f,kco What are the fundamental and first three audible overtones 8ko+0gz. kj c6vofr, rif 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 the top of an eslj 5byj7t 7b,mpty soda bottle that is 18 cm deep, if you assumed 5bjybjs7 tl7,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 yut qj; 5 vx+t1em+l n.dz)d+cof human hearing (20 Hz to 20 kHz), what wouldt+z;u+. +j d 5n1lymqvec) dxt 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 l axj(he.8h,v; ps illon:4 y9frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60%l j vl,e (x;ilh.n o8spy9:a4h of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abzqr/0uee :k b:ey2+o)6lr ddgove middle C (330 Hz). r+l:edyg uq r/z2ke)db0eo6:
(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 -tx8ks76crr d0ja:y:n 7: qq x o4i4gtwqtoq)an open organ pipe that emits middle C (262 Hz) when the temperatur78q y-:q)xtjnaow4os kgr7 cq64dx:t0rit:q e 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 zwov8 n2u/mm.at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in* m6iw+.oo0pn(tk wj;gi f+cg Example 12–10 should the hole be that must be uncovered to play D above middle Cjwft6m (c+ i.+ikn g;wo0o* pg 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, gfw+c/5gad*y2u1jfz 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an opefw/a+g5dfyg2 jc u *1zn or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It iaeh;.i * pqjlmb1/z 6resonates at two successive harmonics of frequencies 275 Hz and 36q*/ai;plb1 hij.mz e30 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 ppt; hz (m1li3$^{\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 pres7cz8daal-ox -ent within the audible range for a 2.14-m-long organ xl z8dc7 -o-aapipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm locm18tym.ba qwfm9s05 ng. It 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 the relationshi8 mcms1y fb9tqm 5w0a.p of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, onllw 7j9yzs5f8zwpnkv r77qia:999pr9ij/ fq e of which is sounding 440 Hz. How far off in frequency is the other strinrir9q y99jl :i7p79fwlafnvz9j57spz8 wk/qg? ±    Hz

  What is the beat frequens rt 86dtvks475 wxt)pp1y3b gwh5z:gcy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, wlcby9fe0f s/ 52cbm9rhile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrilfbmlr9e c25y/c 9 fbs0l 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 and3apdt.a*/j.xdkbxg uo d6z5: 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of thd*j:dtx /d 6.uz3g.o xap b5kae string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The toq2/:g zlx/;2c upyj b.2efntension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13e22 p. xuyzqnlof;/jt g:2c /b.]    Hz

  How many beats will be heard if two identical flutes each try to play middle Cys0jl;l igoeng b+. 87*m mn6v (262 Hz), but one is at 5.0°C and the 7bvm+6gg.s8;i me n *n joll0yother at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44d6yj xlg z1wt21 )r(amtm9fe31 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 frequency is 4 Hz. What are the possible frequencies of A and C? What beat fre w3ta9l1(jd6y mm2)rgzet x1f quencies 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 a0fo/ y*xf.l d.6 gwxyt1ovvo-part. A person stands 3.00 m from one speaker and 3.50 m from th/foy61 xwvd -*0.xvtyl.fo goe other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 13eey q avv38;v47v974 khay obh2 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency ofvva7b;aq7o 3984 h 4 yevkehvy 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 wavelengb b xq0ogoc -ln:qq(+8ths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assooq 8 - n+(xbqg:lbcq0ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at e g,mli4/0bjmrest. What frequency do you detect if you move with a speed of 3 be4j /0mg,lmi0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose s(nge 9ixjicx 8w a-y;c)+r3y oiren emits at 1550 Hz moves at g3)axrcx nijco98; +(i- yweya 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 bbckjh hlk) 8-i yh. 9 eut4ax3c0l2(jis moving toward you at 15 m/kax.hj l20)3ke cb h -i ty98hl(uj4bcs versus you moving 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.j)b+00nrtvxgfxpxft +w60*3)cu;9 kkvn ha w When one is at rest and the other is moving toward taj0* nxbf0+k6r + ; wf n3)v0hwptxct9ux)vgkhe 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 wavesq7q m pa100e 0g:)hwd)ilw3 + gnjvzck at 50.0 kHz and receives them returned from an objec hlgqegw:1q z jp0)+k 7cia wm030v)dnt moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fli)a0 n:o)3wvbg.djspx5 mrm h ;es, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the ba d:brs05mp3n;jo .)mhw)v g axt hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a ni /e/;wr jtl8tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the stationw /ei;trj/nl 8 at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Sup8c pxjs3x9b+ .3fx,hg;kssqg)u bc0ypose 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 exp b3 qjyxfcss +0.sg3)9px; k8hugb, xcected 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 :ta4x u kn2h;vhddu id*3;j3m 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 emjnq qv/*4 ky 7ye;z+waits sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear w4y kwa;/ye zn *qvj+q7ho 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 u-l(lvl(/9 z symyu9f 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 8ur a:szpxa s;x51x0tb;5r ubk98dpu Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directiub5zux kx1:bxdtuar8s p8 p95 a; 0r;son 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 planet whe/ ikkx01q br 4haf h v3on;7m3cocwu33re the speed of sound is only about 35 wvfc3khq3rubxh ;o 1a7k o /3 m04c3inm/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/ r 7 qqp*z/3jac1uru8qs strikes the ocean. Determine the shock wave angle it pro7qqjurpc* /qz a3u1r8 duces
(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 ty4nnck; 8zd 2z)s6jlfi sy-xn+fg, 0 $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plg jve+jx) jzth4 +,r(.e vfho*ane exactly 1.5 km above the ground flying faster than the speed of soundv t(j,xfzh *vrj++ oj e)hg.e4. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device th,47/3icq k :cmgej9gwyznoy 9at 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 designed to work is 200 m, what is ,kqme9w 43cyi:7j/ong9cgzythe minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the huo e fr:;(p7irkxql95tman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called qund qax; u 56je17h.hivkw:/ a sewer pipe symphony. It consists of many plastic pipes of variousuvk /e7a 5:uqij 1w.; nqdx6hh 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 sv6 qgy6m(yi4 t a/rrn+ound close to the threshold of human hearin/6 +i qv6(gmy4yarrnt g (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an iab2 ub+ 9tow;n/ak;z 87-dB sound are heard simultane;bub o2a tw ;n9/zik+aously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,d.ek yn721hoya1g ym 5 is 105 dB. What is the acoustic power output (W) of tydym gkany1 e751.oh2 he speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 10t3rcc vdkm19;ifn.-8gn 7bol 00 Hz. The power output drops by 10 dB at 15 k;f l8g3-bnoinm9 cktd71rc . vHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devic, zhhh (5.lyzc jrc;) gau1j+zes over their ears. Assume that the sound level of a jet airplane engine, auz+1hccyzgh; r j,5z (.)al jht 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 systemir3h3 .z ewe7rs, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin8:gt+n sd n)ier: g/pb 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 poin;byg*bytsy m -unr*, qj ,6;nyts with a fundamental frequency ;s ,bnbn*6;m*qj-y yr,uytygof 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 o;odt8 xd-c1 xxpen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it do odc8x tdx;-x1es 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 the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10ns)s-g24 ttmk;vvbz11 pa6 :etkui; h g is near a tube that is open at one end and also 7iz6 s;ak 1 k :mh1t);4 t-gbptuvsenv25 cm long. How 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 one full lowfwvsy m46s5 6)pisb(op ($\frac{1}{2}\lambda$) 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 fromb7c 2wdbuim ool wbk/8 35vf0x f13w.a 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 tho.27fim1bvww 03 xob lfkac b358wdu/ an the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One83abs:a --uv3fyoryw0 9 ca am train is stationary. The conductor on the stationary train hears a 3.0-3w:o-ua ym - 3rabsvafcya9 08Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is32lz-g0e2a i 8(rpuhs9 l2nq pdm/b cue5el*c 538 Hz. After it passes you, its frequency id8eu5z g- le(sm0r l2/up3 cnlci2e qpbh92*as measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of bbn0a, gfdys ,b3r3(wcars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of d w fysb33,g,b(arbn0 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 bee)n*w88 tebyi at frequency of 11 Hz. The s*en)ite8 w y8bhorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad cfpg saj,9)99;b ibhciar 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 th9fh 9sc ga9)jp,bb ;iie speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of bkn in4nmz (-pzhlqnxrw; - ,/2lood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume thatmn(/qp2rnn;xzhlk-z-n4 i , w 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 ij qk 8c0+h059ugzjo9aji.ql ts flying toward the 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 bat after that wave rjt0 9j jlih .9+qqao85kgc z0ueflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Th- m1s1y z wp9w0vtjtw9 j2 7rf;a9yn,dy8oxtue 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 rzsxwfy19,oaprwydt 1j99n 82w 0-;ty7jvtmueturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was on2kmwd57z +dobf5.gs k cu zoe-w1n.a)ce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played ad+fwd)7g -em skko5nzo.wa.5z12uc b s 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 n : yjmtea-+2w*j-rsi, xzbecsu 6,*kbe compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider azwti 6-j,sarxk+-e je*y2csu,n* b: m 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, called “singing rods,” 19rh9g 1k uahjinvolves a long, slender aluminum rod held in the hand near the rod’s midpoint.r1h jh9ugk91a 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 human ear at a frequency d5nn qyf3;zm( of about 1000 Hzf q;5( mnndzy3 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 observe apf3 :g9sqnx: :2ppugr on the ground hears the sonic boom 1.5 min aftqgf px3an : 2p9::pguser the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 151tqi :xqdo)44n v7y wvq5l0sw $^{\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