What is the evidence that soundyf:j u 5y+tka6+ zakn5 qv:63bcw;eae travels as a wave?

What is the evidence )j*kn kf/qo7bthat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thxn7udz(f2kl 9 e bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29).kzd2n(9xfl 7 u Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do qus7c9o0z 4bl.xwx7 iyou expect the frequency or wavelength to chbc9qzx7l4 ow 0siu7.xange?

What evidence can you give that the speed of sound in air does not,ja0y9chf3 s h/y/mzt depend significantly3/fm0js, h yyzh/tca 9 on frequency?

The voice of a person ha.r- v,b +up s3t)maewho has inhaled helium sounds very high-pitched. Why?

How will the air tempe7x1qz+(k43aw ho ojgerature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce thebxqc1;p)xf b*5 r8vn pph9k b3 amplitude of sounds in various frequerx3bh9;cqp)xvb k n1p5*p8 fbncy ranges. (An example is a car muffler.)

Why are the frets on a guitart 58l)0jwa thc (Fig. 12–30) spaced closer together as you move up the fingerboard toward thetc0jh5wlt) a8 bridge?

A noisy truck approaches you from behind a building. Initialuli4a4g u(sz +c:tj j1ly you hear it but cannot see it. Whls u4jcg+4 t :z1(jaiuen it emerges 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 space,” 8texg1 xgsn ;2whereas beats can be said to be due to “interference in time.” Explng 2 xx1;tesg8ain.

In Fig. 12–16, if the frequency of the speakers were li-cx9(6efub c5xt*b/o w+fx xowered, would the points D and C (wherxc x( *+5xouic-9webtx6 f/b fe destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the h8is sdorz::e1earing of people who work in areas with very highrdess:o1: 8iz 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 reaching the ears?

Consider the two waves shown in Fig. 12–tzq o wu-0)s3k31. Each wave can be thought of as a superposition of two sound waves with slightly different frequen03wtqkuz- os)cies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift ik7r( o ,qx,xsdf the source and observer move in the same direction, with the same velocityq,kx7o x,s r(d? Explain.

If a wind is blowing, will this alterv;ga(r kvt6 7w the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocityt vrkw( ag;7v6 changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mokjay i )b9g tc+m523zonitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear thea+j9bkzmg)3t cyo 2 i5 highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening ts y,z)u(f3oi for the echo of her shout reflected by a cliff at the far end o i)ou,f3ztsy (f the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belo /f82nnedfv t0w 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 (Tv2fenn /d8tf0 able 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthspdct;k6 i*6f-9q o lcn 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 scwg/*lm3k:j e6 p 58dwjx-mzeahool of tuna on a foggy day. Withgmaz w jjw*e5x-6d:m 3e/l8kpout 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 tbj1s3 (+n 5(yja kerluop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is51ls(j( jnb ye+3ukra the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete ue)xc(ou s-yh 9h35z zpavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did tyzcxoh3-)(hu s9ez5u he impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second r mm; +u/*tpbiyule” for estimating the distance from a lightning strike if the temperature is (a)b m+t*/;pmiuy 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at th1vt5 ++oai,zz ws; bnse pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a apu/w:yb0g b*l vvkq- c9, -h pwtzq68sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prb v u9/y;tw +bl 9x7tvjxg0vl9oduce a sound level of 95 dB when fired simultaneously at a certain placebj9vl9; g7 tb x0vwyvt+l9ux /, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certau( qa-,:a zyfain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one eza,f:qyaa -u(ngine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratiomot6 xa5aeo:i8dt.8b w2fv *p of 58 dB, whereas for a CD player it is 95 dB. What is t 82omavtaew85 b:ft6*dpx .oihe 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 fr,np;9f n(x . jisbxtf3om a person speaking in normal conversation. Use Table 12–2. Assume thx , jf;tps.nfix(b9 3ne 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 strikes an eardrum whoss;rf+itl.qy3 e 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 j(ia4j9 3p(f* kzatnyamplifier B is rated at 40 W. (a) Estimate the so zn 9a i(jjpy3ktfa(*4und 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 plac f,zsgs2ma3;e/ w ) 5fphzse/wed 2.8 m in front of a loudspeaker on the stage. wsg)3h e m;za2ep/,/ssfz5fw
(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 d eo,5kq,kfli6cy+-fj.k /kgsound level of 2.0 dB. What is the ratio gk6-5+ ljqyc.kif,de f/, okkof the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sounw.z 6/djorf9y urbix79 b5y.d d wave is tripled, (a) by what factor will the intensity increase? Increase brwj yu9z.dfr 679/diy o5.bx by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have e9q6nvr d-x1saqual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitiq6v d anrsx19-es?   

  What would be the soo/j0 nv- ut oqzxh0)r4q7*a oeund level (in dB) of a sound wave in air that corresponds to a displacement x0zqe4a/h0 rv7 o- jtoqn*o) uamplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hard yp.e u+l+wddw66d5ve what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) u++w e dw6.l5pddd6yr    dB

What are the lowest and highest frequencies thawk , /6nwprxb 75oxxy;t an ear can detect when the sound level io/knyw, ;6px rx57 bwxs 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range/4bkghb lmktz-9qlyupe:+gto *8 9tz 0 -ogq 2 of sound levels. What is the ratio of qb gbp9yok zgqmle2k- g zh0489o-: t+/*tltuhighest 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. Ther-1(o g ;4xm-v. 6s.sxx74 xebpazjnrunvoi2 length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stxxs2.u m;r44 .zoj1x6 e- n povg-svarin(7xbring be placed?    N

  An organ pipe is 112 cm lon1p b 1p5tpf)zp)q5k bi7ve8 -tq8ji mag. What are the fundamental and first three audible overtonesq zb1me)p7f5 a )8tp 1j-i8ptik vbqp5 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 exjiq ytt 8z;x21z,0b flpect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube,xt ;82j0qzibylz1t f ?    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 spi,if bz-v2.mwanning the range of human hearing (20 Hz to 20 kwmv2ii- ,bz.f Hz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540d8f5 zj pypwi 288vqd+ Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original li28p5 pv8 y jdf+dwqz8ength?   Hz

  An unfingered guitar string is 0.73 m long andb)d,qlz3nbl y,5ic rz4h;m 7n is tuned to play E above middle C (3b4 incm l zb;yl5),qd,3hn7rz30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organso840 pc3fw9k g 4wgcx pipe that emits middle C (262 Hz) when the temperaco g3k4 f9xpc80sgw4w ture is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at r6d 8)l* arj 6fw26 aq6qjtkik20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of t. l3bo6sj4 wmghe flute in Example 12–10 should the hole be that must b3j bwsl4o6gm .e uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resoqy clix6sf 82r ol*rom4u4;p,nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a6l*lq ofxums pr,4iyo8 cr2;4 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 two suc bcp8(m. ennz w+c*/yncessive harnz/n* (nce+ cb8m.wpymonics 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 aq8jmxta )3 f3$^{\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 withhhr +syiwg4vy-: +hp7in the audible range for a 2.14-m-long organ pih w+vspigr7y h-4: +yhpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is e+n/lk3(yijc:gbkn f,f0 lyj*x r8d q u);wy1approximately 2.5 cm long. It is open to the outside and is closed at the othe8kj;(c wg0j,:)n/u ydflrnekb+ 31 fqx y*iylr 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 s when trying to adjust tw i biq5vk4x l8)..ldeso strings, one of el5ixil4 .)d.k sb8 vqwhich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and.3 k:f;b3mhr )co21hxybrsnl $C^＃$ (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, whilmf1sj0 ,o ij4*kl tpt)e another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously,kt osj)lj f1m4it*0p, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundedpaujg);;3 wpj with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationa3ju;w; gja)pp l frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequen vgo;q awmauqw(9+*9wcy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recalw vo*gwa9+a w 9q(;umql Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eac+d,6hja sqnvv ou67b/p4 n 1toh try to play middle C (262 Hz), butjo,p1o4n6 h/u v6+ dqbs7atnv one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequencygfg;tctsj o9+24f yk 6//xn vw of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded ff9ykx ;t2gc//tnj6 +ws4vgotogether, 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 stands 3.00 m from one spx2 .ld4)(xk:pnf cswo eaker and 3.50 m pf:4(dox2wn )kcs xl. from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibratinyfvm+ ir 4icb6-v)/uhll :dn/ nsu3d7g at 132 Hz, but a piano tuner hears three beat l:ndm)- u+u 47//lhfcs3vibv id6nyrs every 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 in aiutcds 7e9/n uz430yv6rt-dvo r. How many beats per second sd -yvz d0uu/ 9vc6totn34e7 rwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire *l5b5k zgy p+lengine’s siren is 1550 Hz when at rest. What frequenclgk*pz bl+5y 5y do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sirempor70fw .on7jj(gb 49cf8n t nnn.otco g7ff4(9 b0mj wjp87r emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in ff; (o5oqrc+f drequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving towa o+of( ;cd5fqrrd 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 one is at.q ( 3xljkgt,w-j zehj)(mft5 rest and the other is moving toward the first at 15 m/s the driver at restwzgt e( hj3)lktqmj,.f 5x-j( hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0d-o37 7db9jn- a ggdqy kHz and receives them returned from an object moving directly -g9 jd-nq og37b ddy7aaway 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 As0hmco4) 5tfj7( nmfq.:porpi it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear i5pn i jhcmpf(r)t:m.f7qo o40n the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on f7/u, g wqgvr:ey.ygosivz67 ()zx :h a moving flat train car at a frequency of 75 Hz, and a second identical tu (w zo 7)7/f yv6qigyr:gs,:gx ezvuh.ba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spe iek/n,vyfl dl(u+r 8ws;a:1 reds. 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 lara1rs; f 8i(:yu+dek,vlrwnl / ge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonicq ej. 7p)cmfo)d f0ca1 waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity 0ykoo a8h6cf- is 12 m/s fry0 kc8 -faho6oom the 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 land if its swo10vh.qcac 4 (fx:rspeed 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) Wsbug 2o1-hmmfy.5 1pmhat is the angle the shock wa1 1.-2bfmgpuoymmhs 5ve makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters th:xd)rjmqx v k)4nd 3w*e thin atmosphere of a planet where the speed of sound is onlyxjw4qdr v:3mkdx *)n) 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 8500 m/s strikes t7yqv *d/6 kk9gwh*eg- f9t pfyhe ocean. Determine the shock wave angle gtwy-d hpqkk/9yg796 *f*e vfit produces
(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 / d0v4cwsmzhxu 8znrmbsb0 ahj* //;3$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheaa. ,fael1k+bn d and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, tna fek+a,lb1.he plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sou4,bezb,y:plinfl tt m4n0 :t; nd pulses downward from the bottom of: ,pe ,btyil;4l40t nmtzb :nf the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are pzni)eakl4 z 8. .to7w bli;k,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 consists of manyes9 3d2v(spq u plastic pipes of various lengths, wh2d( s3sev uq9pich are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to thvx gm- m*v po42ked(:ne threshold of human hearing (0 dB). What will be the sound lev(pxe* :k- go 2dvm4vnmel of 1000 such mosquitoes?    dB

  What is the resultant sound level when a2mwoe+ .l u mcjz,*sjp2,mj 2wn 82-dB sound and an 87-dB sound are heard simultanej sjz+2,clm ju2ewm* pm.o2w,ously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is59sn/ d7hmi 1hdyy) nm 105 dB. What is the acoustic power output (W) of the speakeri y9n7)s5hddhn 1my/m , assuming it radiates equally in all directions?    W

  A stereo amplifier is raik+1s1htdez 3 ted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What i zihk+s13td1es the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prote9-jx fr bfpvi,h2b4orha +d6 7ctive devices 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 ha9o dj,r h4ffh2 6pb7+br-ixvas 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 syk 41njfk(wk3wk 3 q )iuwmqv0 8kha,2istems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequenc9( jl0 op6l seago:-iey 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 6txo-8j5q 9sgte6+xe er2ol l32 cm long between fixed points with a fundamental frequency of 440 Hz and a metqexj l r8ose 9lo2x5t 6+6g-ass 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 ab0t: fgz . f)kzv7f2ml*.mamppove 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 toa0 pm .7f .*):mtfp 2fzvkzglm 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 menj mm h-h) bvp475le8ass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension shouldveh7mm -nb)5 4 lhj8ep 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 vf mw69rw;ib)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 puryvd 7r ,0s5seve tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant 0sy5evsv,r7 d 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 sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on tht0h*fgrg(9d cc -d7zde stationary train hears a 3.0-Hz beat frequency when thecf9c-dg zrg 70*(dtdh 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 q8l0 64mq5o+bcq yhka 538 Hz. After it passes you, its frequency is measured ahkbm+5ly64 q08 cqoq 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 just by listening to thes /n sbok0f4l4 difference in pitch of the engine noise bet ssl4k 0b/4nofween 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 rp:tpap hdgu(q* +7l,of 11 Hz. The shorter one is 2.4+gdq:uppt(r* l, h7ap0 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car4y6er+d ro+ sz 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 positize +6r dry4s+oon 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 aortdbk6 ju eu6,dra2n,x -a is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with xn6d6, eu r-d ,u2jbkaa speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mothy/i 7/d9u y xrbff16wk at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off th17fwx9b f iy6/r/yu dke moth?    kHz

  A bat emits a series of high frequencyoy *a-/ /czvxogad)e0 sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about) evo/gdoz-y/a acx0* 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 use6v1s )ork6 yx; d2agand 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 as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonatyd2)o1k;s axvn6 ra6 ging. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of s5 0 yg6 cucst95kqjo,msdg1e ,tanding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room. 0g u5c9eq6 ,ydgm15kjt,cso s
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods;ivi)lxeonx.a * w, /u,” involves a long, slender aluminum rod xxv;/nieliw, o*.au) held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, 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 frezk,e1s:f nd0 bfz)a9 f/dab z0quency of about 1000 Hzn zfbb:/sff,z1 90d ez)ak0 da 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 2.8 de4a ik hedox751ad 67cny;s0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s aly6d8 oh;k7xane ae57dc1di 4 stitude?    $ \times10^{4 }$ m

  The wake of a speedboat is r6am: yz3 di ae,rw-gk+s5ch1 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h