What is the evidence that sound travels fa:wj5**t4 wk 4 ujutbas a wave?

What is the evidence that sound is a fwpj.s2ivcwh c( g.6, form of energy?

Children sometimes play with a homemade “telephone” by attaching a string tcmg, ;emz(5wyk 8zs9u )-ygod o 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 the sound wave travels from one cup to the9mdy,uok)gcy z (m- sz5w g8;e other.

When a sound wave passes fro bd fwaj 0rw7vs(ns,0t3/.yvnm air into water, do you expect the frequency or wavelengs0n7 0wb/j awv vf(st,n.3dy rth to change?

What evidence can you give that the speed of sound in a7un0+w d(nlq b8rw3r9a znpt,y db7j-ir does not depend signific8,+-u dr07 t(rw w3bnn azp9dbyj7nl qantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitche 2wkp2kovs/0dgsm:85 vt f- jsd. Why?

How will the air temperature in a room affect the pitch of organ kvo4b7 -q:hiyc o1gvyr46b: c, mu8f fjt-+fjpipes?

Explain how a tube might be used as anb*qzys a 9o4: filter to reduce the amplitude of sounds ioqs9y: 4*zn ban various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethe 6sa8 4x0k;qrfghr6rpr as you move up thex4 r rsf6q; ar6p8k0hg fingerboard toward the bridge?

A noisy truck approaches-fcpg;)5 uxxj pz2t)r you from behind a building. Initially you hear it but cannot sp)x)5tg 2zrfpcj; u- xee 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 said to be due to “interference in space,” whereas brxb(yc;yn7d e:8lk v8nv:r*e: :guqreats can be said to be due to “interference in time.” Expvre legknq8;(:d:b ur cy 7vr8*x::n ylain.

In Fig. 12–16, if the frequency of the speakers ku+cd.36a8 iybww9 p;nf7 geazd9d+6eaoh h 5were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart orady9b357.dhn+eu gw8pfwhkz ad + a ei96;co6 closer together?

Traditional methods of protecting the hearing of people who work in area phw9i5h5gyj+ rkz68 yn ats6q:dm16g s with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reach516ah ntdyk+zr856s :iw6 m gjgyqp9hing the ears?

Consider the two waves shown in Fig. 12–31. Eacaza bkpv8 ol0*f/q3 b7h 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 cap3zkb *8aq7l / v0bofomponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and y*)n*f*s .ckcvhsxf 6observer move in the same direction, with the same velocity*csyckhsf*v f.x ) n*6? Explain.

If a wind is blowing, will this alter ao)nds3 dhr(tjr2x ;+ the frequency of the sound heard by a person at rest with respect to the source? Is the wavelen2);arnddtjh3 +ox(rsgth or velocity changed?

Figure 12–32 shows variouv ftqx. ad t2k ;*21k1(ejslu30h oyugs positions of a child in motion on a swing. A monitor is blowing a whistle in f;yl. 22*1t oafk(g 3tuejqk0du 1xsvhront 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 jg :at4xxaj6)phktdu,1 :5 u6h.d yoqby listening for the echo of her shout reflected by a cliff at the far end of the jx6t:udh u1p6d:h4 xakytjaq .o5,)g 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 hears the ecn+kh 9 rzna 34es2zio9ho 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 significantly with depths49k n+ir2o za3n 9ehz.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20e()1a lo/ uk x+qn7lk,mznm )sna7v hud;4k t6 $^{\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 juscb:/zqtmmzd,8i)ek e y/+t4 ut above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time e /eqb :)e,8y 4cdkitmm zu+/ztlapses 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. Tk (+)l;; (s)gcyiu1cz h yqhnmhe splash it makes when striking the water below is hs ;ykh)z(qh1n ym) +g i;ccul(eard 3.5 s later. How high is the cliff?    m

  A person, with his e vb*5 k:ev0ingar to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air ande5b0k* g:ni vv 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 over one mild 9qdp*ofssf283yxi .e of distance by the “5-second rule” for estimating the distance from a lightning strike if fqp2s8 s9x*df3o.yi d the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1dd*a(kx.lri120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level o1b7 im81i df3uz3zm kwf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers xd 6r.rl;yop27cb-fwproduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Ady.7cp -;wfrxrdo2 bl6d intensities, not dB’s.]    dB

  A person standing a certain distanc no y to yb*c4s4mbb;(qu(,2j4uv2 cgie 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 engine? [Hint: Add intensities, not y 2qu(y t4o(,os*bu jicbc4;2g4 n mvbdB’s.]    dB

  A cassette player ise sjfat)bjapg;6s;6 4ls3fwj im t0, / said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgro4 3ts 0;aa )/jjmlg; 6eibpft6 s,jfswund noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sou6rw8 fe1 ts-g1l8 pofmnd from a person speaking in normal conversation. Use Table 12–2. Assume the sound spl11r g- w8 ts8fmefo6preads 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 earhn)1: ;*bg) m ea0whf)f hljatdrum 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 z,8:m 6pfv ga/t vqk-crated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudf:m8azc-gtv, 6 k/v qpspeaker 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 req5n il9 vz1 :avm6mx5tgistered 130 dB when placed 2.8 m in front of a lt:i xnz6 m91m5a vvl5qoudspeaker 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 soqy* 7/puc 4oi29 zddhtund level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 1 /29hpd * qtyid4cou7z1–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor w6gw*/; zjxxmpill the intensity increa6 pm;xz/* wxjgse? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but oqp 5)kqgduy+k:d8 c1g9lpv0 yne has twice the frequency )g9v p dq1k:y+ykc5dpql0 g8uof the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave w28bainm7r w/4m xur (in air that corresponds to a displacement amplitude of vibrating air molecules of 0.8br4aww i r(nx7/2mmu 13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what ,dh dsq8;f8ikmot+: njuc;+h sound level to seem as loud as a 100-Hz tone that has a mfs h8jn +u,i;kc: 8t;dh+ oqd50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect :szd 3f*akm )xm00u jswhen the sound level is 30 dB? (See Fig. 1sm km szj3*:d 0f)a0ux2–6.)

  Your auditory system can accommodate a huge range of eaa,2 ag/ -udlrqkf)+ sound levels. What is the rat2d,akru+afla) q e-g /io of 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 h-:phou 5nvl f 1pz7ir8as a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Unviznu8-ho r7lp5f :1p der what tension must the string be placed?    N

  An organ pipe is 112 cm . pu 9kgtbcn5 x6(,xpalong. What are the fundamental and first three audible op a bx5pug69nck(x,t.vertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acxp 1yhxwl: rm9 yhx:-c432m vmross the top of an empty soda bottle that is9wm:cm3p1xm:x2-4 yxhhlvy r 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 orgm-p-h4s ow6) yt7df epan with open-tube pipes spanning the range of humaes7o dw-f4mp yh6 )p-tn hearing (20 Hz to 20 kHz), 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 540 Hz as its third harmonic. What w*ngpfx- lb :llp5-dyqo5zft 2jvq,/9ill be its fundamental frequency if it is fingered at a length of only 60% of its original l-l*bfplfod n- 5 :pyjl/2zxgqt vq9,5ength?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E rn b7kyg*2xwbf -krt km 30i14above middle C (334ftng0-*2y b1k7rwim brx kk30 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 emitpm.6+ojub3 ,tc:rqf ns middle C (262 Hz) when the temperato m,3tpnuc: 6r+.fqbjure 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 20i*7 xe 0184s yfnqkowq $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpie3+kqa 9l. l1ljl(dwj 0dssu w09ar5qhce of the flute in Example 12–10 should the hole be that must be unco q 0l9(d.1dl sq ujl5wj9sha+kwa3lr 0vered 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 resonate at 264 Hz, 440 Hz, and 616 Hz, bu:m)zeu5 1zuls, mq:pvt not at any other frequencies )mml,zvps eu: q:uz5 1in between. (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 gvf12:gcr2m k k 1yvs +wfh,g+1.80 m long is open at both ends. It resonates at two successive harmonich,v1rg++gkfsky 2mcfgv 1 :w2s 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 ktzlf1/6 ua,g )nvakc:r *i.t$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long organ mdbn ihvhr)2*k49c4*dn4 mu4p- jeqc pipe at )q* juid 2p *-mbv94c 4cmdn her4nhk420 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately41x4tfq 1)l)l2uk 6 wtferv xl4aww8l 2.5 cm long. 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 relationship of your answer to thuxt8l1)4xw4l)6vqa w1w2t4l kf efrl e information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every j,iql tf7sxk+v24 uo02.0 s when trying to adjust two strings, one of w 0qji txlus2 vk,o+f74hich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andpjau c0uh9o*i - i0y:r $C^＃$ (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 ophpng4 2om+fz vqhv;o( +:qj0lerates at 23.5 kHz, while another (brand X) operates at q(0o +gjp v: m fvn2qhh4lz+o;an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sphmiu:v( z;*e ounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 35uh(:mev p* ;zi5-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tun(er;pr 0t f((zv5vzl 0yljt: eed to the same frequency, 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: Rt:0;r ejfr(lzy 0v( l5e(zvptecall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each trykm/gwpsx)6w1 7 bw *dv to play middle C (2621pwdkws bmx/vw*7g 6) Hz), but 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 frequency of 441 Hz; w7eg if(ks 0q um*bqc:a0o9 6xshen A and B are sounded together, a beat frequency of 3 Hz is heard. Whe0sqx:6bg f o (cu ki09qa*s7emn B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apa nzb(a.swdm- p:a a4+ort. A person stands 3.00 m from one speaker and 3.50+ao n.-4s paa:dmw bz( m 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 supposehab.k.q .r 6izd to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when th hqi..b.6kazrey 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 air. How manoyj crgy 1fxpk:9.l 9 ud/-u+xy beats per second will be heard? (Assume T = 20 -. u+x9k/y:gyo9xjrd c1p l fu$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at-jnjxo+3 quz 0;rwk/l u)eoe) rest. What frequency do you detect if you move with a speed of 30 + kn ;oqo)x)ejl -jwuu0zr/3em/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect le : us-,vbc;uif a fire engine whose siren emits at 1550 Hz movel:u cvbs,; ue-s at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequu-j5gr-ce92 xe.mt e:-s9n xo u.e otnency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the s.nc- g5xumx9nteee.s2e:j-t 9- roou ame? 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 thuq0trlzx:no- /ysl(6thi 94ne same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hear lno/-:t0q x 6yi(shn9l u4rzts 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 50.0 kHz m,pux+d m jt6fi45txvnix)c o ;u2n40and receives them returned from an objecm,f2)oixnp5 44mxv0cdx t 6ntu; +ij ut moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall atdcs9nhigw75,kf : 9yn a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does 7g,h s9k:ncyd i59fnwthe bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playj6 co +mj*i;*e, lordu(bwi z+ed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same * o(++j mz,e l;cojdu rw*ib6itone 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 speeds. Suppoo 2 4ve.-g9xkh5+lxwpfmm p+vse 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+9gp xfpmwvv+ekx4.lo52m h- ected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usj, pe-4ev0rvy kq,rc*ing ultrasonic 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 gm ;v-ya0 np,lfrequency 570 Hz. When the wind velocity is 12 mym,l 0-pa ;vgn/s from 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 speeblbi4g:: a e/7j ynt2d .onc1ud 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) What0wygz0 c a7/lrvp8n8v is the angle the shock wave makes with the direction of the airpla 8gn08l azwr0v7 yc/pvne’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speer+(bbf5 3zx1z*p czs xd of sound is only about 35 zp5z b3xcb(szfr 1*+xm/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 strike nrca* 9y b7jqdwv+ua: tcu777s the ocean. Determine the shock wave angle n*aj7dy7:tvqwb7 + ruc97uc a it 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 t*)xr+st6m9x+/mmjb vtz s )h,5 v pgg$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above thewgy83awp( ,fz ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane g(w f8pyw3a z,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 sound pu l:0 czzyrkh*:lses downward from the bottom of the boat, and then detects echoes. If the maximum depth for whi*0:z:ch lyk rzch 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 in the hum8 u,sobjk1jl ,an audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calle vcsat5hg1 4us* n6kj06w/pbwd a sewer pipe symphony. It consists of many plastic pi* n bs64ju/0hv6pgac 5swtw1k pes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makep(s4t4zv3t4 e fxl na(6mk750)ru5n z h cdtsys a sound close to the threshold of human hearing (0 dB). What wilc4(a4uy trtm pn(34n tf50h l5zxve6zd7)k ss l be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level wnrimt9 s/s.ycwarl ) (;l6o-yhen an 82-dB sound and an 87-dB sound are heard simultaneousrylw;9yns.i-als)m(tcr/ 6 oly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wis8dj 392qvmi8n jdg5hat is the 9in5id8gsmdj2j8q3 v acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output w8 n vacpm 4x4.zu7zo1drops by 10 dB at 15 kHz. What is the power output in wattsan c7 pz1x4.v 48omwuz at 15 kHz?    dB

  Workers around jet aircraf46tsi( i7 0mjm 9impf8b6o ngut typically 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 eb gn49 s0jiit m6fp7i6o(8 mumar at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain,qmv c 267dndh (oape.y1i k7k+ $\beta$ 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 gph +lf 7fn-dp8p+; zsto 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 f0vl-kbz :lts5 ixed points with a fundamental frequen5stl lz:vkb 0-cy of 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 open tubefbrok) +9v* n zbp7+jq filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube akzv+7fqjbnob+ )r* p 9bove 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 2.10 g is near a tube that is open at o6xhjxtw, t s34cp e9q0ne end and also 75 cm long. How much tensihp csq0,9t 3wexjt64xon 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 ww)bb+m 1a6luy as observed to 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 ran( ;dunb31yscj-p 2 cnege coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequencyuc 2cysbe-n(3;n jpd 1 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 stab1ljw f6y94wky;. *,zbj2fe dgrz v0mtionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whatw g2yb0l 9yje;zbkf w.fvjzmr1 *4d6 , is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yotdbo;3y)v )mxo f4hk1u is 538 Hz. After it passes you,)v)yk x;f1bdo 3h to4m its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can esti 0hn s0uw1ckq0mate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding c0 nqkw ch0u10sars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of k (kqam0f:oo1cr .) z 3a4euuk11 Hz. The shorter one is 2.40 m long. Hc 0zaueqkk (kr.fu)1:3 oom4a ow long is the other?    m

Two loudspeakers are at opposite ends of a railroad co;gd9 z;i p,xwar 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 po;,dzg; i9xwposition A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about)a ; ydoxp*ez/ 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 blooepz; y)x do*/ad cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5yr n21z/p59 fa+rv igo m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sou 1/9gaz52ofv prryin+nd wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approacheqhb19 fg4t2+ur8gp yy,zw(df p1/dors a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chi, tr yg9 d21g1z4qr( /byp+fu8hpowfd rp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used/i3gc yznzs0 / 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 f/cn 30sygziz/lat) 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 to; dbtyl3z,mtu . xd u 5m4xp*2sg67unhe presence of standing waves, whicmmg*o uztlt.u ,3p4d25b 6 ;dxxnu7 syh 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 demonstration, called “singing rods,” involves a loqu6.f juc6c eb/ lf.s*ng, slender aluminum rod 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-./clc f u*q. 6sfbuj6elong 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 frequenc.l c4 7v3ozxqey of about 1000 Hz isocelx 3q7v.4 z $I_0$ = $1 \times10^{12 } W / m^2$ 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 observer on the ground 0dtu b7v5 xs:lhears the sonic boom 1.5 min after the plane d btv:xus07l5passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbj9-a2bc/ ihzw*qx1x /a8fe yfoat is 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