What is the evidence that soup; pzbl9g-( -c2bcxufnd travels as a wave?

What is the evidence that sound is a form of oglz, f+, icln+pt u (j+h( 4(vqruta7energy?

Children sometimes play with a homemade “telephone” by attaching a stri/r(b;l+l 0ue7q rkbsg ng 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 the sound wave travels from one cup to theb(;l l regb+u0 q7sk/r other.

When a sound wave passes from airw+p-d3 evj as7fl;9jbs*)5 qfbp sx w, into water, do you expect the frequency or wavele* js p7fa +efs)q-b 5djwws3vl;xb 9,pngth to change?

What evidence can you give that the speed of sound in air29wktq2erm . n does not depend significantly mke29r.t nw2qon frequency?

The voice of a person w92sof13x 6g mspqiy: gk ju0b;ho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipe xxxy5vp3hjj q0e7 8z*s?

Explain how a tube might be uofo; hekx; u4.sed as a filter to reduce the amplitude of sounds in various frequency ranges. (Ae .;xfoo;kuh4n example is a car muffler.)

Why are the frets on a guitar (F ( mn3 saau (o52joxfzf7:sl)vig. 12–30) spaced closer together as you move upnoo fls3a5z7v saf2 jx:u(m )( the fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it mv eb+hi6u71.xxwg59g bhu6u but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hebx7w9i m61u bh5euhu ggv6+.xar 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,” w+j7y dj915denv bup)hi8q j+ uhereas beats can be said to be due to “interference in timeb d98h157jyed+n+juji pvqu ).” Explain.

In Fig. 12–16, if the frequency of the speaacwn egtvc6 x532wt (* e-ye5gkers were lowered, would the points D and C (where destructive and constructive interfer ytecew2635w ce(v* a5gn-gtxence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peopl yzpl5 7jux.jh7 8:up znt5yee1cm y97e who work in areas with very hi lyn9ju 71z:zyxp 57m.eu5ej 7 pych8tgh noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eacnw2gn*4.c u 4 y llz-bqa0hnb5h wave can be thought of as a superposition of two sound waves withl 4cn.0 2-4 hq*zb5nnwla uygb 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)s,h-30k)jra piiz y k move in the same direction, with the same vel)ai3,j)kky0 iz-r pshocity? Explain.

If a wind is blowing, will this alter the frequency of the sound peqz; z.+d7 -zy6tcjdheard by a person at rest with respect to the source? Is the wavelength or velocity chatejz.z y 7d-+q6pz;c dnged?

Figure 12–32 shows var5b d0w*z-c 29elormo t)ci7dzm*7sxgious positions of a child in motion on a swing. A monitor is blowing a whistle in fre7g- 5bmdsrz co*wmi)t0oc zx72 dl*9ont 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 of her shout 4o;bkw .pm:aw reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length om4 o.bww;:pkaf the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hgumi8 8vhfny24q0ghfe ;9p z, is ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. H8 gve,hyf znm94h 82qf0g;pi uow deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelen:c+s-1kl -*kxp a exwbgths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foghr j ndwr5. 4lx10qzw5gy day. Without warning, an 5z rr5. q4w1hdxl jn0wengine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The sp+:kmo 9i/ai8b*jbgmv po wr0 ;3 fm.vplash it makes when striking the watovv+3b9/f:mjbm;0im8 a.pr*gw oipk er below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grm( t*9co2u zy6:nhm4o, omjvpound, sees a huge stone strike the concrete pavement. A moment later two soundymhucm9jm,* onov:p4 62(zt os are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance f) 9xg61mjf drby the “5-second rule” for estimating the distance from a lightning strike if the temperature ifd grj1f x)m96s (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a so4oyn/ i0h;me k2noya0 und at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whor8s xqwo) 0.rcse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers 7tn* wg(8of (2 7cvmvqaogzg,produce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? tmgf8* 7ggz coovawq2(7v, (n[Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equl* gu(if9 jw k4yzz2t pg./xl(ally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experi9uz*g ( 2flp jgwix. l4/z(yktence 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-noisebzn;lyifh/ wce2q*y 9rd :0e2 ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intene:*cz 90in2 dye/ybr w lq;2fhsities 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 t4gmi y9m 1o;91xbkna person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on thegbo4m 1n 9ati ;9xky1m 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 a .fji2.eiu qt)rfx)s *n 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.a/i,4u;oh kps s:wl0 pj vrk5 modest amplifier B is rated at 40 W. (a) Estimate the sound level in pui s;a/k, 0sl:4rvhowkpj5. 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 registerj(t/aq ryh e/7p x71rped 130 dB when placed 2.8 m in front of a loudspe 1qjt7 //prr(ypax7 ehaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB.06lw)l d wlrqy u)5v1u What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]qy0 wrl1w5dl6ul) ) uv$\approx$   

  If the amplitude of a sound wa e/qmv0p uuw 90hnv,l35dpzl8ve is tripled, (a) by what factor will the intensity increas / 90,8vl uqne0pupzmvw35ldhe? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have jnzf rxws dk..j48.lw4pu3) aequal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their in.uzsp8.jdwfarjk3 l. 4 x)4w ntensities?   

  What would be the sound level r b4b+e fb /32erhr2q+ g1fidk(in dB) of a sound wave in air that corresponds to a displacemend/b h4rrefb2 31ergq b2fi++ kt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sti)rs6mng(pdy ynb4 8 2bzj7,ound level to seem as loud as a 100-Hz tone that has a 50-dB soundn6gz)p4j( bs ynt 72yr,b mid8 level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can*g xly a7v+9 bq8m3anh detect when the sound level is +g*a hn b83vy xmq97la30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of )jkg23d-79r40pg(yf - gh (iiwhhvu7pdyaef sound levels. What is the ratio ow(hi0ap- 9 e7g h2rfiy4y h-pgguk7fjdd(3v)f highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hunqg ifz0* +u3z. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension munuu+ g0 i*zfq3st the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fil7 (z0 ri9w.gjxw yrg8u:l hub m)b*2urst three audible overtones xlru9bbww2g )8zuh0ry7 : *.j l(uigmif 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 acros w tna0hry,5;tkf .xv*s the top of an empty soda bottle that is fv*xt ,rt5.y;wnh0ka18 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 the range of huza;aba:,59 pqsii o-jman hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?az9ap: ;bqo-j ii,a5s $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wh hv*h. 21ilgkssl ym9dj n8 d +wfjma+52zci;,at will be its fundamental frequenc. m,5hmyg ;d*ss lad2n jjhkizl w2 c+9f81vi+y if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar stuf5*oi5:b2 jgy qkxn- ring is 0.73 m long and is tuned to play E above middle C (330 Hz)gq2bj5uxi-f no:5y *k.
(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 emits hjg1xi1k/tl,( 7ka jj middle C (262 Hz) when/xak,171 l hgk t(jjji the 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 htw nsyt;z;zgv)ox/qj,p 1(t9kl m::o vw7.e20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of e)s k6mo-*u1s:jl- b sc.r fszthe flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 29e b 6l sc :ofmz)-sj*1-sukr.s4 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, but nowua-kk 4;f bd2t at any oth2a;kd4fuwk-b er frequencies in 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 1.80 m long is open at ae4*+psq2 wll both ends. It resonates at two successive harmonics of frequencies 275l pal4e* sw+q2 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 hzwv ozj;/a t n)aij 19425i)bpm1cw avls2 )l$^{\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 28cp:w+ i)hoim f i0he2.14-m-long organ pipe at 20cfo:+m0i 8 hi)hew2i p $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately4h8bs ckthbmx /*2hl2j )euzndr/l 5 i9j4l.g 2.5 cm long. It is open to the outside and is closed at thh bk8jn tdl24u l.g zbilc2x*)h4m //es59rj he 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 2.6u:th b9w(rg;9 rpqp t0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the ot6 p rtq b:p(u9h9grw;ther string? ±    Hz

  What is the beat freq4y asiik/di9l8oob *5uency 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 kHzjf d.)t o.un kpzpz-r6,kb.x, , while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz ) .pf,-zj pu6t.rzkod .,knxboccurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuy8i wwowp ;xr9owzoln y +i11qp3+/w /ning fork and 9 beats/s when soun/1l19xpwo wrw wi+i po;nw8/ zo+y3qyded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to t t:jqg/ br9y5zx)j4 r2d d:mbthe 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 arej:gtbt 2r4 bxjm/95yrqd :)dz played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical f-;k )77pzea w- exmn0j xyeci+lutes each try to play middle C (262 Hz), but one is at 5.0°C and the other 7ayxee - + kcewn;xi7j)pm z-0at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; -y1rozij d)ms*/+ hi:hdcz-r when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, t +io/zscd z-* jym:rr)1- hihdhe beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart i9fw32qnv s,3t zq;2/tgp 8ph0 qgeby. A person stands 3.00 m from one speaker and 3.50 m from tfq30 2w ,;8q/ni 9 p2gtheqzgspbt yv3he 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 atofbs+ gn /tk6f d,hrw- *dg2 xy5,ml*t 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is gn5ol/ 6dth st*gb-, y2mr,w *dxkff+ 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 inw ,lrvh:dwz)7 yfj2byu.7sh ) air. How many beats per second will be heard? :2)hj.w,dw )7 sf 7hzrulybvy(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency o1d.s2owee*xb me h3 c od3xo86f a certain fire engine’s siren is 1550 Hz when at rest.m1o *d863e ex 2whdo oesxcb3. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect ifu4xuugba :ss4o wan-*:m 3p/g3jci4i a fire engine whose siren emits at 1550 Hz moves at a *aisi4 g3o4ug xum:4p wu:n3c-jb s/aspeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-8uby nlny* /sf5,ab:r Hz source is moving toward you at 15 m: snau fl r,b5*b/n8yy/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one i ;3g r-iexf xef1kj2s.s 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 frequency sk-2x xgejfr.;fe i 31the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz /,.vw6w, * *dzh4vv *kuot:ft;gfdws ;c svnv and receives them returned from an obj,w* ;ow :cz*d,dhvn6k uv;vwv 4t/g t*svs .ffect moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it/,gsgg g hdh im3fy(/( flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequgmgsg/hf3 g (,dh/i y(ency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a0-ro d hwn(6yk moving flat train car at a frequency of 75 Hz, and (6nork0-y dwha second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasosr+(l(l)h nrx+dtl 2 mund waves to measure blood-flow 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 2h( r )t(rxdmsln+ ll+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 ofoy9:f fsw +y*s frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When gotbq*wk/dw 22u5 sc5the wind velocity is 12 m/s from the north, what frequency willw w qc52bd/ku2tgs* o5 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 speed at 1 semiktjxgwd0 i )e-q+4()yy20 $^{\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 a um4;(+im nv74ozfg ,fvlgxc6t Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with t ,;v6c4vzm(n+lx omuff i4 7gghe direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet6o9pl+fi+ :+ qfkdv0.hsxblt k x;4e o where the speed of sound is only abx0p kkoid;o:vx+ 964 lfbe h+qt+ sf.lout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave angine,ft4sl( n ,ij,4hs le it produ4, ein 4s hj(fti,lns,ces
(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 g0gumt3zzc0 sb lb49*$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ove,v.ou)ae gyl2+ y7dzdrhead and see a plane exactly 1.5 km above the ground flying faster than the speed o.yod l+a ze,dyvu2)g7f 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 device5e-kv,t,a(pr l5glk abnf6s . that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the mil. 5gake ,bp tl(kfs-r,nv65animum time between pulses (in fresh water)?    s

  Approximately how many oct *zhi.x7 j)cwh3kzi, yaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipewnxw 53+xh/*2x srep f symphony. It consists of many plastic pipes of various lengths, whixr wx e*/+fpx2nsh w53ch are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close tfd *a( pt9zniq7ehd s/)qs 1u-o the threshold of human hearing (0 dB). What will be the usq- /fh)i9td(za s*nd p eq17sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an ,lip ,kzd:;w c 2hxco1pj(s/i87-dB sound are heard sd,c/ociwk s:1l 2 p,phzix (;jimultaneously?    dB

  The sound level 12.070qonv0* ,qvo)hz +i9xb bw es m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiateqbx 9 e7)0 0vvwqozsi+,h onb*s equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power6 sa1u nwz;f7i output drops by 10 dB at 15 kHz. What is th7u naizf6 ;sw1e power output in watts at 15 kHz?    dB

  Workers around jet ai vsl)pr/ z;- tf47 k, k/c)gt.jp*jcr gbpe)mvrcraft typically wear protective devices over their ears. Assume trpeks t- p/ ckgjj;,f/vg.vl)*)rb4mz c7)pthat 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 from a jet airplane engine?    W

  In audio and communications systemb /gk2vke2y-xs, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frl0 kbuv+*bf+ yequency 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 ) yz5+7/hwce;,m 8 g(z refr7 z zlyomunas:g/is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per un;z+hzwe/uy 7zlfs :)(yzcgomm 5 e g8 nr7r,/ait 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 vib yhg+g9 r stq v;nf+hfm-n/hv/q1(s t*ration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork wheg; +h vsngyq (h rs1tt9/mnhv-*f/+fq n 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 eeng9c dfjv -t axl4 )7f9om56tube 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 (in its fundamental mode) with the third harmonic in thegv49-emd 7fn5xto6 l fcj9 e)a tube?    $ \times10^{ 2}$ N

A highway overpass was obg -zk sqki0b;l *i+ma+served 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 range coh6n(u3jzu z*-kyf 1tbsy6 zq(ming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is,tu 3zsh1q- (y* z ku6njfyb6(z 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 statio5jeloq:8h,s d* qs9/ zq k cak1ti acg4rn73b5nary. The conductor on the stationary train hedtesa1k nj5sq5ib3rq o,qc:lg 8a9/cz* 4k 7hars a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After ikjtl4 ;8 ygkbu p(m7nj3q, ,z89fxqwrt passes you, its frequen8 ,wz jltk 4q8yg(brjuf 3np,;qx7m9kcy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by list.; kvwkcr. j 02 :6kpi0d/4xnovfdedqening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on th.6 vpow x4vkdcqdr/f20i: ekn 0j .k;de straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, pro rk h2d9zzsjtqf g+5:/duce a beat frequency of 11 Hz. The shorter one is 2.40 m lo +zzdsf/ jt2:kg9h5q rng. How long is the other?    m

Two loudspeakers are at opposite ends of a railroa+ ninx 9ppm))od car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speake)+p9nio) n pmxrs have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood fl rm/t4kawm w:5qd(x.jow in the aorta is normally about 0.32 m/s what beat frequencyk(:jt/w5m 4da w.r mxq would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6pt7ae((5am t)*o0.dw ahrec h.5 m/s while the moth is flying toward the bat at speed 5 m/s The bama(0 w heot(5thec.a) d*7rap t 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 frd ve vl9f0y+3zequency 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 f v03l9zedvy +detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 1j ct4* a57uj ,v8cfsgp2–38) 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 alpe , c4j ajt75pvf*cusg8nhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for st2. maa-gah 449wjiief :o8pswereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the loca s-wgi4h mi .fae2o9ap:4 8wjations 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 long, slender alum)meh o*(3yt lw95y6l;ho0nit)s v wy finueohm i)9ynllts)f36 y5voy;*ht0w(wm 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-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency hf,f19-m vcg* zk5:l,jgpqtrl9f crttl; m7 -of about 1t rpctl9 fqm;m rc,ll,t957 v- hfg *:zk1jf-g000 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 obsu:c, 7jy adu2kf,ee *5rw(og gerver on the ground hears the sonic boom 1.5 min after :,ju *e(daw, c oge25k yfrgu7the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa0nnq 3*eq(o)o9 wfwxjt 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