What is the evidence that sound travels as a azc93;7:,f6uydza nmd .epxs wave?

What is the evidence that sound is aisrl8o tuqo54 myp(x5/+s )ru l(twj6 form of energy?

Children sometimes play with a homemade sdh,9y1cdq x4 “telephone” by attaching a string to the bottoms of two paper cups. When ts,hx dy dqc194he string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freqip/.ybfz0p kot(yg) z:z:ejk.-z d2quency or wav-oiqzppf :t z/ kz )k .yje.d:20bzg(yelength to change?

What evidence can you give that the speed of sound inuu mhl(sm( 08msu3s *n air does not depend significantly o0ssnlmh su38m*(uu(mn frequency?

The voice of a person who has inhaled hec)8rosl iq )t036gl/vqonbk 0q y)b +ulium sounds very high-pitched. Why?

How will the air temperature i.px8/ vjyxdv* n a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the 2y sd2 mndoio2kz /+c1amplitude of sounds in various frequency ranges. (An example is a c2i2/n1zo sym+kdd 2 ocar muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethp b8m7ht-4 n 5ws ,uj2yowqur1er as you move up the fingerboard t 14jbos2wqw-nr8m7 u ,uy5tph oward the bridge?

A noisy truck approaches you from behind a building. Initially youmt xnyp91;y(k hear it but cannot see it.(pntk;x1m9y y 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 beats ;ppb lik w06q2hd1gj;can be said to be due to “inti kwb0;g;qp2dl6h pj 1erference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowere;hu/me fx wb,:d, would the points D and C (where destructive and constructiu ;w :/m,exhfbve interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people wholapq+x +0+cou work 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, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones ol +uq0a+ x+pcin 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 wav ew)2gqa;he+z 06lpjfo*6 p lae can be thought of as a superposition of two sound waves with slightly different frequencies, ael 0a662j+pgl*ozfa q);hweps 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 sam-hw9t 9 g a8lpt(cu xfc8s9g op7xe*d0e direction, wi t8cxfg-t89 egdcu ah9*xwl (0ps9p7oth the same velocity? Explain.

If a wind is blowing, will this altero,o 7;efbv3bt the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changed?;eo37t fbbvo,

Figure 12–32 shows various positions of a child in3 +tyq-qe0bmi motion on a swing. A monitor is blowing a whism0tqi-eqb +3 ytle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo oiq n0(s0kee)d f her shout reflected by a cliff at the far ene()eq0 k sd0ind 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 hears th nvn4d3ba vpnq -8lyi5:j.xq8 e 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 doeb- 8q3pn8iql yv .jx4a5v n:nds not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airhsy ):0n ehiq2rzrj,. 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 abov(nxrzn2.crvn 2j/:ytg v;.s s e 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 erv.: xgn nsjtz r(s;y /2.nvc2lapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frbkfgvq ldk6:m1 r+ 7-qom the top of a cliff. The splash it makes when striking the wb76qkgv-d +lq: rmk f1ater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stv h2vtno0fdu pj ,58/crike the concrete pavement. A moment later two sounds are heard from the impact: one ch vv/8ufjo,2tpnd05 travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distan/ yc ,dv -vbw*xjcr//p5xgv*hce by the “5-second rule” for estimating the distance fro dxc gp*y*v5-vvhr /c/x/w bj,m a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? 7+ 0mg+vysk0;q mnwgn   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 sb dt+7nd+cd+ uound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers ;gr)woa, )+facmn4 a:62grqp) vkbdh produce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound q:))a2f;d+wgc, r)marka6ohbp v 4nglevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nooa, ,y5yyca d8/dt ih8isy 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 onedao8,/i tacyd85 yh, y engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to lfwjx*6h3 0+nv d9dg ihave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is th x*d930vnlijg fhd6w+ e ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nb(,h qb*7 uiivormal conversation. Use Table 12–2. Assume the sound spreads roughly univq u,i7b (hb*iformly 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 whose area is flf s:jg9j*y3b -c 6clrpy o5:$5 \times10^{ -5} m^2$ (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 amplifi/ i i3rbdlhh)4er B is ratedhld3ihb ir /)4 at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn 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 metdy/g:j85gc+pg2mi lder registered 130 dB when placed 2.8 m in front of a loudspeakerd8j:2gip/+dcmgl y5g on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound leve10q ..g*d :rbye*t qfxo)qmbx l of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by bm*y*b.d q) .ogr qt:e1x0qxfthis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intenszgq8vjzi6wm 1c cg ),y6 dysa4bo/g(*ity incrzd8/gqyia wozy6 v4*g6bmjg) 1(,sc cease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplp*xu.pid6 s,5soc cq2itudes, but one has twice the frequency of o*ux,ccs56d.qpp2i sthe other. What is the ratio of their intensities?   

  What would be the sound level (in d./ao+ ng;v 1o ,f5a1slt kghdoB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm a+al 5d;g.k1o o,hn1 g/sato fvt 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lo.4d kpy ijasrt .t/:tanr6a7r5mi0/h ud as a 100-Hz tone that ha7d: ap 64h5mt. /rijaky/tst.arn 0irs a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highe2). eapg7)su 1)swh mqafcr.ast frequencies that an ear can detect when the sound level is 30 dB?7 hmqc2gsrfs)wea.)1a u)a. p (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound r 43 ,.yvsp (ij2jmn9w g:tvpvlevels. What is the ratio of highest to lowvg4 spn3v,9 (rmjwp: 2yvi.tjest 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 fr55f gyv +nx k)to;*qw g b+hq8hxh)qa3equency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tenv w))hnq ;k q ++tqof8xxa y*g35bghh5sion must the string be placed?    N

  An organ pipe is 112 cm long. What are the9i:*w/kzlp g)c*n4x g pr h+vz fundamental and first three audible overtones ix9vg l+z*i*z )p:cr/wpgknh4f 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-4x,; ux(jyu u2bjkp/ + lxsmj from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clyuk jl j2s-um;x/(bxxp+4j u, osed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of humb9ngm0j l d8/wuz8l e1ms-+yc an hearing (20 Hz to 20 kHz), what would be the range of the ly8/s9jl0 w8u1- znl mcb+ gmedengths 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 hakn er(r/js,q:/wyx*d rmonic. What will be its fund/qnx y(/d :k je*w,rrsamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pb )s qs; fu3ajw+35rxdlay E above middle C (330;x3d3a js swufqb5 r+) 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 op1zt3hl/ukn/q iist 0-(tz, yaen organ pipe that emits middle C (262 Hz) when they/30-l(nqzhz,t1i kus iat/t temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at lvmv: ,pj:rd7 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece*s52bh k /1 pmpipl q*k8b1oyd of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hmh*b21d/8lpps 5pyk qo *bik1z?    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, r (lv.sfw)t- wy8 q7fybut not at any other frequencies in between. (a) Shorf -.7l(ywqt)fwvy8 sw 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 open :0:g1zizxg v jat both ends. It resonates at two successive harmonics of frequencies z::igxvzj10g 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 emwa )q v2 d58o4x(wcbp*drl)$^{\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 presetrqs1ci c :5o(nt within the audible range for a 2.14-m-long organ pipe1c:r q csito5( at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is opes *ziy2v0 u6qwn to the outside and is closed i60 2sqzwyvu* 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 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 tc (gn6t3 p.lznwg5vaj b-it*t )k9ka9o adjust two strings, one of which is soundikazgwt jn9tlni *(p .t v36)5-gb a9kcng 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mhzqxpzps2 (; 3iddle 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 (brand8iaz hzf21 .mn X) operates at an unknown frequency. If neither whistle can be heard by humansni12 h.z8mazf 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 sounded with :n1dj d b,l.mga 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain yob m,. gn1ddjl:ur reasoning.    Hz

  Two violin strings are tuned to the same frequency, 295 n-5hzqewb5 d4 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frnb-hw5d5 e 5zqequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idue2e d kh12o*u)xrpuc,*9pl hentical flutes each try to play middle C (2)hu2r*e* ,uuoe 2k dc1hx9 plp62 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 f 5szxwt+v/7vp requency 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 beat frequencies are possible when A and C are sounded togett+/w7pzvx v s5her?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A p3 lipdnlq 3x:oj(l8 y+erson stands 3.00 m from one speaker and 3.50 m fro3nl8+ poilqx:( 3l ydjm 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 vibrating at 132 Hz, bubgln ) sdd49f)7d)yz aeal+: ;(fvaf rt a piano tuner hears three beats every 2.0 s when they are played together. (a)e)dva (afd)4n+bfzl fg :9s;dy)ral7 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.3f3 mm7dt1zfm How many beats per second3d17ffm mzm3t will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cq.;npeq h mz9rpl,q(uq47-jjt; o:bv ertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if 9(z4n ;.mjuoth eqjb:q;lq pq,r -7pvyou 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 7o0v /;64 jx9g ytxw( xyunxc9 he,ftsdetect if a fire engine whose siren emits at 1550 Hz moves ,ywg 7oy 0e4ujx(xnx9 6cf9v;xstth/at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz svq y )k)+2 vwm5nzdqcy/0ix ,vource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the dn+wmv xkvyz ,ycq)q 5v)/i02same? 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 frequenarys9 yy)lzi8o3tf/6 h3 mc 1icy horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequh3l3mia6r ty1ociysz89 y/ ) fency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonicnua. dt/itl) d*w 4c)wl 2.nus sound waves at 50.0 kHz and receives them returned from an ob).wt*in l4./ )lwau2ddnu stcject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at szwaa (eoo666 ;; i duszj93gha speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear izj6;ieu 6zdo6g;aos(as w9h 3n the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubatdk jtsg4/ ,axc)/42doxkd f1 was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train xk /s2xf, agdj)o4dt k1tc/4dcar approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flq 2 li/ee7+ qyqmxw2dgwuj 3*:ow speeds. 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 large leg aq: idj2y *2wg+7q/qeeum xlw3rteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect us our48vk:zb-l(t1stou/ j70e om loi2ing 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 frequek h98q(/x1hbe hx8sj 2ulr.b i 2lz-udncy 570 Hz. When the wind velocity is 12 mqj-k9zehhb(2u 2lxh bxdu1/rs il.8 8 /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 landp:8pm/sl+v /jpj5 nui 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 (a) What is i b;8liuum3 2ndl: m+9uo-sre the angle the shock wave makes with the direnl9+ e2sd;iu:u8ui3mrlo-m bction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound i/*nxbn- 8b0r;acn or is only about 35 m/s bx0in;* - obrnc/r8an
(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 thel179r)lvpr z ec-sp4q ocean. Determine the shock wave angle it producp r14-)9 rvqelpczls7 es
(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 1ai,uvm g ; /kt ul;st4j9-gul$/theta$ 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 enr;)s3al(er km above the ground flying faster thsreelna( ;r 3)an 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-Hz8vmb/+ik5 w oz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pboiv k58 zm+w/ulses (in fresh water)?    s

  Approximately how many octaves are there in the human aihcm o*:m n4x6udible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displaykh 0s5+u1frsy called a sewer pipe symphony. It consists of many plastic pip s su0rkh1y+5fes 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 mro y .)47dqiiu from a person makes a sound close to the threshold of human hearing (0 dB). What will be)4io.7 ru qdyi the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82ty(qh*+sh0/c*t jv ld -dB sound and an 87-dB sound are heard simultaneouslsy dlh/cjt(* v0h+t* qy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.z xi 738x.briem7h ,xj What is the acoustic power output (W) of the speh7x xm3 78e,ibjzixr .aker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops b nmu)(i7 zshzg); q wv1k6)cy7e0qgspy 10 dB at v1z60zhp;u( )qnsgswk)77 y g qe m)ci15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. ye 4zl .n5*9ku ypz v51,kbctgAssume 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 distance of 30 m frb9n51e5 t ukl *cvyk,p4g.y zzom a jet airplane engine?    W

  In audio and communications systems, tag:/3 bmaw-j 2h if2ewhe 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 violig.g28 a37 (dn2jnsybul pib y(jp0u v3oa,mf3n is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm .o6uequu/8g /mitd o2 xqh/xx9ql /j3long between fixed points with a fundamental frequency of 440 Hz and l/xx 6tdmu.9j3q x ohq 2go //q/8ueuia 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 tube fille*o79h a0hwuc 6cgrf j7d with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0u7hj*hgo9 c7rfa0 w6 c.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 3hf1p5eho r*q +aur+m2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in1*rm ru++ah h eofp35q its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loqb :j1:.7hbc5qmuljrop ($\frac{1}{2}\lambda$) 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-e(. 5cv8ftv 0etdbiv-gwy5r:o3 wit-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 io3ydw(i-v f 8t0-.5wc :ebgrvtt5ve 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 conduc7)xz 5pj 4r0llj*b qw3a+f qgttor on the stationary train hears a 3.0-Hz +lqba0)g 7xjz5wr jq4*tflp3beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aft6uhsldc,5bgpn:s1+ ; l6o ff xer it passes you, its frequency is measurbcfs,g5p 6udl6;+f1nhl:x o s ed as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speedqev s xmu 8lp,t6:m6 0,c3ub(cwr6dcq of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. :m8ct eq,w 6p6ucb(0qsmcrl u36dx v,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 11 Hz. Thxrkz8sy-4. mngjbu( : e shorter one is 2.40 m lonb4(-k8rys x.:j mgznug. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mbj t9urj(wk(gl(29s z oves 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 bybj t(k(zrw(jgu s99l2 the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beatl8fy yx9 ; wkl;o5)rqd( ;fazgy, (qjk+bb5it frequency would you expect if 5.50-MHz ultras)axfzb;q5q i( jl8glo;+kftydryk w9(;y,b5 ound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed qg/eex x-6,mg e,k)bu6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bex q- ,em ge,)x6bugk/at emits a sound 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 fr0 exm+7j5dx;damyliadm0; *a equency sound pulses as it approaches 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 chirp returns before the next chirp medm5ay;ja0dma xd0l;7+x*i is emitted?    m

The “alpenhorn” (Fig. 12–f3g. 8e +kj1a+ d rsji8w4recv38) 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 F sharp? (See Table 12–3.) Model as an o8 gd f18j +ekir4e.wrs vca+3jpen tube.

  Room acoustics for stereo listening can be9jfqinhd-5g8so m /p8h o/8rm compromised by the presence of standing 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 standirp/hg9n sihoo/ 8dj 8mq mf58-ng waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves vi867/ea/fx: hs 9i-lqs(:xx zhlonna long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the othenqh7/s:v/ xz( -9 hxol6 exf:inil8sar 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 h0vi*ug7 uze *:aqm5vb earing for the human ear at a frequency of aboub*uz evua0mgq5 i :v*7t 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the soq1btkbry+c kq,3e3p2 nic boom 1.5 min after the plane passes directly overh,rebyk2+ q 3qcp b1kt3ead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 ln90-sy ez,y c$^{\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