What is the evidence that sound travelsjwxws27ro.n-dt0 ) la as a wave?

What is the evidence thac6g5f76emn72qxjz wep t34yt3skc 9p t sound is a form of energy?

Children sometimes play wij 7gy8i2pjps/ th a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how th 2p7p/yg ji8sje sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expec /i,w0h 3ugxntt the frequency or waveleiwt, hgu03/xn ngth to change?

What evidence can you give that the speed of sound ir3 f06a+v 2ngvqx/pc vn air does not depend significantly on frequen p60rvgnc2+ v/av3fq xcy?

The voice of a person who has inhaled qd1y s,os;o8qc v 1+lbk+xl js1uy14hhelium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgs*y*v:xc ii8 ian pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundwn,61j4 vq36mpxk w,l yc qwuw0(pm3ls in various w1 mw0w l c66ujpnpx ,mwq lvy,3(k34qfrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1/ gh*l1cuhenxdqvw i/ *+; ;rj2–30) spaced closer together as you move up the fingerboe+*u;hw;/xq jh*i/1 rd gvlc nard toward the bridge?

A noisy truck approaches you from behind a building. I;dm*que l:4fvsa/ 2g9vp8sya*c htw4ao6 i o:nitially you hear it but cannot/aa 2sips y : 4o:vuemf4d*vl qt;o9w6*cha8g 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 Section 11–15 on diffraction.]

Standing waves can be sx-d3pu 4irdh6o uh*ux 1sqt/1 aid to be due to “interference in space,” whereas beats can be said to be due to rhuxuhoxtdqs4 /- 1u3di 6* p1“interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakg0vda- 94 o2n m.kdsrgers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart ormvd4.r d-k2na 09ggso closer together?

Traditional methods of protecting the hearing of people who wor r +v1x:c 7m*jm-tfvuc:n ,(lt*rkwqtk in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, wvj+xvc mtl* 7 *n(:tm:1r, ktqr-u fca 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. 12–31. Each wave can be thought ofkp zs) neb bkc4/5.wg4 as a superposition of two sound wavpsng.5 bck4zk/b )e 4wes with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction,wr6fuvrlwssjm x )89;8* ywf .vn*aq1 with the same velocity? Expl8v18 .9wl) q y6**s rnj;fruvwwxfs maain.

If a wind is blowing, will this alter th3x*e47 y le a+qs9jobge frequency of the sound heard by a persoj9g7eya+x be4 so3*qln at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a cz7pn.y;a t8u,6jjil child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sounpcz6;iaj7yt . u ,jl8nd of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her 0i-sa7wpsm 8 bshout reflected by ai8bss 07ap-mw cliff at the far end of 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 below the waterline. He headgt evh/z-l3(rs 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 (Table 12–1) and does not vary significant v /l-ztg(deh3ly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20hk53in.d.k as $^{\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 driftb3//u1zrl nazing just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig.zzlabr3n1/ u/ 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it make6h9v natmy-6y s when striking the water below is heard 3.5 s later. H-vy6n t9y a6mhow high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pav,a oc1yuqb 3j7uem;3jement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impac31je qy;7ucauom b3j ,t occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile ofdl1j1xqv+b1bzg 7 lt7khi. j0om h6/z lfg, 2y distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatudxft ,zogj+7 1hiv hlz1b 7/2lq ljg1y.60 bmkre is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at them48wtzaas(x19 j(ic n 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 le hpycj8sa/)1r s(l:oo3zz w 2mvel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 6nakhb/s.x r /c.6 y-2abbdqtpbh7/0qyj5fl dB when fired simultaneously at a certain place, what will be the sound level if only one is e 50btb/ph dy lahcn - bfx6.sqa/b7kj/qr62y. xploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nr8 : ij+dyqy / lzzkm(yc.-;hcoisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person jmlz(.yky:8;ci/ d qc+ ryh z-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-noise ratio ox-hir kh;e,4jf 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities ofehih,r;jk x- 4 the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power / iuj znn 9*p4:bvnqd6output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound sprej6n:9*bn zuqi /v4pndads 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 stru-6fpfz: wt9 o:sjebmiltv05 4n 4a)gikes 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 mowp g85vsaiej(dv1a5 2dest amplifier B is rated at 40 W. (a) Estimate the sounweapvs2 5(5iavgj 1 8dd level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of e.)e1+fj c b3j) zket1f 0xeosa loudspeaker on the stage.fcf e11j kjtzbx)e s.0o+ee )3
(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 deueefqbex+4 ddkq,4sis + 7)3g j-g*nt tect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levelqg4, qie e4)fnb*3g+ksedt u- 7+sxdjs differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a c 5mwdpzbo22.odk m 7*sound wave is tripled, (a) by what factor will the intensity increase? Increase by a facwz*7od 2b c2mmdkp.o5tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal disxatd0v8e + m1iplacement amplitudes, but one has twice the frequency of the other. What is the ra8d+1t i0me xvatio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thatz2amd v l2m1t0 corresponds to azd v 0am212tml displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-v6-qy0uz pc9/jll p8y u6cn+n Hz tone that has a 50-dB sound 6 -lynjpy 6ncpqc+vl/ 98zuu0level? (See Fig. 12–6.)    dB

What are the lowest pb qz9g7:0 x 7rukk( akyo6lt4and highest frequencies that an ear can detect when the sound level is 30 dB? (See :7glka6(z0 4b9pkxrqtk7 uoyFig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. q n.2f5u3o. 3oub;wrd /vqxg39hbmkgWhat is the ratio of highest to lowest intensignb;5k/3gxo9 u 3d23fb roq .vqh. uwmty 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 frequ;)jwo1qc 5x rnency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string5nj;1xcwro q) be placed?    N

  An organ pipe is 112 cm long.x,i:jj 5( mr5dpa ped8 What are the fundamental and first three audible overtones if thrm5p5,pdiajj(8e dx :e 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 expe 3d7 httlkj,hl *vaq3l4r sc:,ct from blowing across the top of an emptyl7jhqtl 3*, dh4ka, cl:strv3 soda bottle that 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 t+j6e7t 5)wqezo.jfaq he range of human hearing (20 Hz to 20 k jzw5).aoqe6+ et7jfqHz), 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 g(oi fqh64wt7has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengt(6 og7 iwqf4thh?   Hz

  An unfingered guitar string is 0.73 m long and is tu :y dje:;3( lau;idwwfned to play E above middle C 3yf :edl;ud wi;jw(:a(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 an open organ pipe that emit p8p5j1s9b6jxt fjp1 cs middle C (262 Hz) when the temperature c81 6pjj t xb195pfjspis 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 2 2z.7g.p wdvtd0 $^{\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–ugf +fc w6v7-xg jpa9:10 should the hole be that must be uncovered to play D above m wuv7-faf:pc +ggj9 x6iddle C at 294 Hz?    m

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

  A particular organ pipe can resonate atyp;ed 5 h4vp4y 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betve;p5 4ypd h4yween. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is o;k ui5u chgdax,e5(/b3xqzj8pen at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hqhk z ,j35gc8ab/xud;iux(5ez. 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 as.a;sq7pldgnq1t +0 $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audibrj ( f *5 eam3i7(mkgs xxq7p6uls1b;lle range for a 2.14-m-long organ pipe at m1l;sfr* ((b 5lj 3pxkm 7ex7gu6a siq20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outs,ue )ukda-iqz1i 4h a.ide and is closed at the other end by the eardrum. Estimate the frequencies (in the audd ,a.4ui-haz ke uq1)iible 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 la*c4x39 4u9vjvvwohs when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strino3v v*4lx4 ucj v99hwag? ±    Hz

  What is the beat frequ-n 6i+fx:(xvl joitpoq4 :ooj632psyency 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, while another (bbzi:p- 458 6 rpxphyf3yg9jxarand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate t zbgpa8: x3 jpi4hry9f6 5yp-xhe operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounowzq(b8l).q93d yluda8 g-g1+gwtx i ded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vigq ldw8 8iz 1(a.wgo3 q+gxd-)9bult ybrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The ten .ru)zz+abhd( +3wlc nsion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played t3alurwd( .hz)z +nc +bogether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eacj8yb yy qbt0+/h try to play middle C (262 Hz), but one is at 5.0°C and the otherqjy8t + 0bb/yy at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. rix5mke-ps9i398 dqwFork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What be ri wqdmis89x 35e-9kpat 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.ifayc;q1s /(jpi;j q apart. A person stands 3.00 m from one speaker and 3.50 m from the othi(py/jc; .s;i q1jqafer.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piancrtdj7/ 3)csjo tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratinrtc 7j3sc)jd/g 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 +wvz,n(x4k vo air. How many beats per second will be heard? (Assume Tvkwo+vn (4,zx = 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 rmt3e 69ho:b cof hb osj(qd*- 8rd.)foest. What freque hdod(-3mc q6ojb9 for e*o8sbft) .:hncy 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. Whatjf74:3zxho hq frequency do you detect if a fire engine whose siren emits at 155xhhf:z3 o4qj70 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 y+ib9qm ne,)o t 1+snl2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 9o +mi),qn1stn+yel b 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 swc4oi;lkn m- (ame single frequency horn. When one is at rest and the other isik4c-(wlonm; 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 ultrasonifs 8sm2awmsxei3 b 5, k8l/w6pc sound waves at 50.0 kHz and receives them returned from an object moving directly aw5s eal6mmx2 88wp3, /s biwsfkay 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 flies, the bat emits an u-;wdic3taq00p6wa( 2ip n aa um3)f sbltrasonic sound wave with frequency 30.0 kHu;wbpastp acd0w6) miq033 fia(-2 na z. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler7lem9d5.(m r xunsov-6e0 xhw experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if m5. -ehuv dxmle s7 on09r6w(xthe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoundbl0g9c /bdor .wrqp(5 waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound roq/0c9br d(5p .wlbgin 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 fn24gyoio fdn udp*/9.requency $2.25 \times10^{ 6}$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 thej;f lkxw b qo gwc;8t3;3wrmln,k;8y7 wind velocity is 12 m/s from the north, what freque;ll ow7m kbx twrg, j;3k;c3w;f8nqy8ncy 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 lt 4e y/-y-wrh ei8dklceg;j:o, ;jb;nand 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/s (q2odb mbgd4; vk;6 4u3lx6aj ma) What is the angle the shock wave makes with the direction ofgdakd2mol64m 3x4q;;b6b vju 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 wo *7 kv 3k7fy8sjekxm-here the speed of sound is only about 35 m/ vk3s x7 kjyfmk7e8-o*s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shoco p;fejbg5 )z-k wave angle it produc;z p jeo5b)f-ges
(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 y 18ho/jcsh t j7bk/cd47g+tjwg1- o x$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhea-e0:x :elc at v dhy6(fgdd1a;d and see a plane exactly 1.5 km above the ground flying faster thadg a1(d;v:6-edhlxtc0 :a yfen the speed of sound. 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 that sends 20,000-H2bvmdp: q,8nfr.j8v d z sound pulses downward from the botto8 mq,d8vfrnj2 dv.bp :m of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in1m: hn. *vcjsg the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphon* l ;oz zh.xm0sz9:7f1 rq5jv cosbxf;y. It consists of many plastic pipes of va1q97zhsxmx0;*;vjoz. 5 :zlfsb crof rious 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 5.034s yl2(kr cep m from a person makes a sound close to the threshold of human hearing (0 d4(3k ply secr2B). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultane(;e 3 dacsach7d)651tv w vzlt sound level when an 82-dB sound and an 87-dB sound are hear 3 edw (5;lt)hzd cv7v6aac1esd simultaneously?    dB

  The sound level 12.0 m from a l nwqy7i iy2zf 5ek8/0uoudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dire k75uf/8 q2ywi 0znieyctions?    W

  A stereo amplifier is rated at 150 6g 7ivvr( -rapW output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powervv( ga-prri 67 output in watts at 15 kHz?    dB

  Workers around jet aircraft typic3*64kfx *ik+k/pgiygp9lpv;i :-s sfpep:uwally wear protective 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 has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a dissgp *-fys4i6/pxp+k p*igvi ;fpwue:3 :k k9ltance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the dl*y r2)7rb. b+ zgitigain, $\beta$ 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 jnd,/ftaa++nq+rpvqq -g r-2 h,ba9t4 a4xf rfrequency 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 loo ckle80j ytip 2m.p4z95m*p qlpq4o 0ng between fixed points with a fundamental frequency of zp ll p45qkc9y0o e4*q mij 8ppt20mo.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 a mjwdfk9*vq 43hd )5yobove 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 theomh)*q3954dwjvd kfy 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.zc z(hen7gnbad-9i 37 10 g is near a tube that is open at one end and also 75 cm long. How much tension cz9n gben3h7a(z d-i7 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 du h:i9/+fgdgao7lx. resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming fr-xh +cfld: 4* p3iajiyom two sources. The sound is loudest at points equidistant from the yi*i p+ h4-xacj:l d3ftwo 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 u zm rm1:z/ol c0/aua5the stationary train hears a 3.0-Hz beat frequa5zurulo /am z1:m0/cency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a ste+/pte7 ywk;bki8ha(rzvjq. ii 9rh2 1n54zbmam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as/i+ ahkbw9 zhnpqj28 ib1z.i7( r4ert; kvym5 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 liseq buan.5 .mxiare09v -0ir+utening to the difference in pitch of the engine noise between approaching and receding cars. S iixa .0ur5eb+enuqv a.-m r90uppose 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 v/tazzd 9zw 7ohsx8.hz96p3 cbeat frequency of 11 Hz. The shorter onoxhvsdz89hz. zz/7tp36 c wa9 e is 2.40 m long. How long is the other?    m

Two loudspeakers are a *vdsc/s;4z(cte/u ib t opposite ends 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 f/4siv/csb*t e(ud;zcrom the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blivb ob rksdnk,zj4s)pz/i.x,l9. *8 zood 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 that the lzzo,kibjrb)z*./k,s9i v 8 d4np.x swaves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towarz3 ck2ojg+( nhzv8pp z2fs07n cf.*n pd the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHg pf+8(hp ovcnsz*73nfc 0n.zjz2 2 pkz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series ouxz(d:08+ , ffadcib a61hfok io;g)yw3o t/qf high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms l (/tx) caqu,oih0f8 fo a bg63wkz:f1+diy;doong. 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 uerjn6+e( *vcz;o z.ib*un5wl 2i(ko. 12–38) was once 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 as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to .c*;nzilkne (e6v2 r+ uoz o(bujw*i5F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereoy 5llh3* w,avo listening can be compromised by the presence of standing,o5 la3lwhv *y 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.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrationeq)w2t vy*3gq-dqt7 h ik6( xx, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. -3t( egyx2qq 6q7k*i)h xdvtwWith 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 frequency4wgqm/tid 3b ( of about 1000 Hz qb/(i3w mtd4g 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 observf7t ess 2hgd+ ji*9b4qer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altisdthsf*b+g7 e9 j2i4qtude?    $ \times10^{4 }$ m

  The wake of a speedboat is)u : tcevt3-lt 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