What is the evidence that sound travels asl/b. ny b+ rp27)ookue a wave?

What is the evidence that sound stv2+bp;og :d is a form of energy?

Children sometimes play with a homemade “telephone” bor f1m)fs z5 :vsyw3vvvnhv3p1n:3 ( cy attaching a string to the bottoms of two paper cups. Whenvfwm 1 c(n1sv:vv5yho:n33 3v)rzpsf 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 the other.

When a sound wave passes from air into water, do you expect the frequency or t qew /1:p o8hct:)qtcwavelength q 8t:qttw :oecpch/)1to change?

What evidence can you give * dhc/5+hvllza;lp s4 that the speed of sound in air does not depend significantly on fre l 4lhc pz;d/+lvh5s*aquency?

The voice of a person who has inhaled helium sozjj) r6.br; me7f xgs+unds very high-pitched. Why?

How will the air temperature in a ro-oc)g nm6pdi:k: qlg oyn;.+lom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude olg51v llw 3*0fwt)bfof sounds in various frequency ranges. (A*g lw1f fbv53wtl)lo0 n example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togejn(u 3:yhe7fh2hk*oz ther as you move up the finge :*o2 h e3huznkhjyf(7rboard toward the bridge?

A noisy truck approaches you from behind a building. Initr 7a. xdke0 ej+fab)/bmi/h59 r ijf+bially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Expl/f bda+9+bh.ji 0rae mex75ibr)jkf /ain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be5dpucuajr46 z ;uivwxa 4677y said to be due to “interference in space,” whereas beats can be said to be due to “in4;v5 p ua du6a6r7z4ui yxc7jwterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were loweredf+wr **z7csrvgdw3m.z ;n sm5 , would the points D and C (where destructive afw wg3;*5srdc .z zrmmvs+7n* nd constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the he((48tijwd fgsaring of people who 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. Insteg48(si( d jftwad, 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 Fig2on b*ub qn2-;1x4muu h-p onf. 12–31. Each wave can be thought of as a superpositu4-op1bu2-nxnmq*2fou; b h nion of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directioqk7j + f2iz,8-xgodkr e+a/mun, wi /xdeu7gmjkaz8q+k +,i2r-fo th the same velocity? Explain.

If a wind is blowing, will this alter theh *x,muxo (hjz5sq -l( frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changedxhs(zl,m(x-j o 5*hqu?

Figure 12–32 shows various positions of a child in motion on a swing. A monitory wa kro r80sg0m(v1b( is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle?(rv10asbgo8w yrkm( 0 Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout ri c a25chbo0;qeflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the le qo; iac2hc0b5ngth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hearsf1vw2q;3ax/u4f.zxs ahx :d8m; bv h l the echo of the sound reflected from the ocean floor directly below 2.5 s later.lbmx1hfxa4;. / 2 wxvd;aq8szf :3hvu 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengj rau3;zc- 6lavez8k pn.w93 bths 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 b- )m eh4uu4v an,e:dea school of tuna on a foggy day. Without warning, an engine ue:u b h4ev)m-ae4n,d 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. Th)r xgp5b g) 1 b.spmy*w9p6ghne splash it makes when striking the water below is heard 3.5 s later. How h1 rpgm)5wgp.hb6gxp* 9n)ysbigh is the cliff?    m

  A person, with his ear to the as8c* g. j6ueoc,rnu8zzi;9 iground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away didno9u 8c 8,ia uzsecgji.z; *r6 the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ova- 7tr;9zni1 .oxgwa-j piw* yer one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a 1*9ipazy on7 wi-g;wja-.xrt) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level oz* z+veakzcrex .8j+ :f 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 whose intensity ie6(lo u zv,;hqs $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired -l 8y rbvhpfnhvi)-;;y0*tov simultaneously at a certain place, what will be the sound y otv v;-vp-)hyhr0nil*; 8bf level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eqhvb:)rha+ 3ba ually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pebrh +hbv )aa3:rson experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB99mg8y(z a +iky*gs1mj3 r sme, whereas for a CD player it is 95 dB. What is the ratio o j ym a9+rs13i8zgy*ms(9g mkef 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 fr4 p7 cm*(b 6hschlry wxgd+if-s(8lxbpq41h:om a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered i rm( -yb:lh q48lw 7p(p4h1scxgh*bf 6+dx scon 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 eai6or7ci:8d-yga.g dvbl 5xm9elb( 2nrdrum 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 mozws5tl//( /,jr6 bji yj.uo ldre modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wo/ws riot.l lz(u6jyj,5/ djb /uld 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 rega;pd bu9om ;7jistered 130 dB when placed 2.8 m in front of a loud; mab j9u;7dopspeaker 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 di+u.etvk s+ (g v5ueef(fference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Secti+ 5+sef(kueuv. ( vgeton 11–9.]$\approx$   

  If the amplitude of a sound wt 1u41, hz)bs1f bcflwave is tripled, (a) by what factor will the intensity increu bchlbwzts14ff )1,1 ase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one -w)v g;+5dhwhhvyoi ) has twice the frequenc wyhi)d)-h vwo+v;g h5y of the other. What is the ratio of their intensities?   

  What would be the sound level (inr ;;3)qltd- z6 8 hplym2qtbqj dB) of a sound wave in air that corresponds to a displacementq- lqq63p 8yj )t2trml zdhb;; amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone(m(:l tsiu k7e that has a 50-dB sound level? (Seseti(kmul ( 7:e Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detecplm3;2iz wnpcs x 0.i h,dt6 om+9tt1kt when the sound ltwxcmh pn ;t0lzk 1ti .2+ s9mi6p3,doevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range fc(/(e xtm)qs of sound levels. What is the ratio of highest to lowest x mtqf(e(c) s/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 1 0n xw1yj ;naa,3gci+7eoqswfrequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Ua+ wnc10sog;qaey7niw x3, 1jnder what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first nl (go2, ftveh,) hfe5three audible overtv e,hhnf5)oel ,2tf g(ones 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 acrossw-q/8tyqa wc4 the top of an empty soda bottle that is 18 cm deep, if you assumed it was atc4-aqq ww /8y 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 spanningp2mnrz8g.ogsd/n +)icjl m1 ( the range of human zd8o)cg+ s(/njri1gn.l mm2p 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 asoe *8)taa1 ii zfc (9w4j9 otq,dqpt.e its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original leng) e oe1f9 4qowatzdtt,.8i(9qai c*p jth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E3iikzlmz z9 kywv )9x6kog (+0 above middle C (330 ky+i(3ixlmvzk99 o)60 zgwkz 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 o5ha:b o pjl:uuur(*/ xst gif5/m0je9rgan pipe that emits middle C (262 Hz) when the tempe :x moujb*tfrp/ hl:ui0e9gau5s j(5 /rature 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 ad+ rp5 /frbd5eux5y+ hn/,x4thcjx q1t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the holeii2l(hb y6 n 7 gm3)dgk2gt9seu,t vr -s0ol+b be that must be uncovbdy03 sm eusv2gtn -)r+,ih(6o2tigll7b k g9ered 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, ajjv;-rc:4sm folh;a 4 nd 616 Hz, but not at any ot -ovmc;s4f;:j jrla h4her 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 bqtmdz hac /,ogd875s8o e3v7.80 m long is open at both ends. It resonates at two successi8/bod,zqd s3vg e57ac8th o m7ve harmonics 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 ,i p 6lvd3ou6dtgj -+i$^{\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 2.1l rpz uu/9-9qk/a+ak9frln:) wi5o dw4-m-long organ pipe o 9afl / udr+li/u wrnzkpq5:kw-9)9aat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxiu*kp 88hnhmd*g t;1f dmately 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*mtud8 fp;n*k1d8gh h standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to ej;4bf l+vr e:xd0.d eadjust two strings, one of which is soundrdelvbx:d.j4 f+ e; 0eing 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2z ,3nmi w ny:enm4ax0.62 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 opexjuq*)* k.f ezr*y4flrates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If nei4jye *)xf*u *lz.f rqkther 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 sounded wts v,blr;3v9 lucd7 z e+xb,lsj;zz.)0k;yd dith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency +3v;.u)d;9klel x,sblzdc 7,ybs0jv; rdtz z of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the pgr:pv,). t :xqd*sadz6 uh/cj m8(d lsame 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: Recall lj.) p:g*v,ddaqpdsh uz8:6cr/x t( mEq. 11–13.]    Hz

  How many beats will be heard if two ident o0xl+t,wtmunpah -n. ;j30ngskm/k) ical flutes each try to play middle C (262 Hz), b.knl3hmu; -n/k ,xmj)+agptsw0 nt0o ut 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 p ubjxlh d57; i5 a*/g(tvg1wjB has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible f5t dlbg( *j5px1v7/jgu iw ah;requencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stan ;cs x. .l-wiwz8ovm-rds 3.00 m from one speaker and 3.50 m from the oth- - lowiscr8x;w vmz..er.
(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, ri c2*mu cpb7e)ko jv;u3-n3wbut a piano tuner hears three beats every 2.0 s when they are playedc-7 ir32 uvupb*n)w;cmj k o3e 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 many beatf jj*;(xz ri:as per second will be heard? (Assume T =z frj: ;ix(ja* 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginegh+m 6v:v.pvr’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed +vrh . :vvpm6gof 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whostvd1ww-:eb3y tap+8; k;osq i e siren emkw:i3t+qop-1 wvstey8;b a; dits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz so dq*wj6:hx (8y4ipt hrurce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? wqd*i8r(j t6h:xh y4pAre 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 frequepm23da1lf z0ig,m .ku ncy horn. When one is at rest and the other is moving toward the first at 15 m/s the driver10. g3f ul m,mkia2dpz at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anduo o 9rbw42d uu.-.btvf(ojn 9 receives them returned from an object moving directly awaut jbo2w-9.vnd.4fu o9orb ( uy 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/stygw kux y06wdv94g(; As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHzgvu;xdy y( 6 4kg0wt9w. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played (ozm3. 1luus f fs dgfy;4ho/)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 wfoo)gm 3/; sh4 1y fs(.fzudluas 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 s:f0 vq ;ti1x7vlsj mv9peeds. 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 expe7mq ;v :li901tvvsf xjcted beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fjf*/ s2 a0vvnorequency $2.25 \times10^{ 6}$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 thez p k2crho.7l:y1k0 2xd444gmcnbaa m wind velocity is 12 m/s from the north, what fmx :r04zpm nc cak 4 dkb724al1hoy2.grequency 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 speed a9wyil(,x lhcy-3n), b uz b7dat 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) a)x at: r1+c4yhsu(ao What is the angle thucaxa:+ (tha )ory1s 4e shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thi7ved+4jqthw/craob6/,) lxy q9bn* mn atmosphere of a planet where the speed of sound is6a*l9+m7c o)rd4/ vbq/wn qy,xjhtb e only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s sdyd/z1bz4,rm;10 djzsy kgl .trikes the ocean. Determine the shock wave angle it prodmj0d,dk1. sd z1ybz;4z rg/lyuces
(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 lu co.7nlvd)7qm. u1 kr3mf;l$/theta$ 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 the 5/,7md lvw5k-shvpa uground flying faster than the speed of sound. By tw7lum5vv /h5 a, -spkdhe 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 t6f7ske(2 larw hat 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 minimuka (fe2w67sr lm time between pulses (in fresh water)?    s

  Approximately how many octaves sd44fj279nmx+tnv sk are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displ4vl2 od4mp 5mhay called a sewer pipe symphony. It consists of many plastic pipes of varp h4 o425mdmvlious 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 m1:mto7/gk(qenvos(d (sjh.n akes a sound close to the threshold of human hearing (0 dB). What will be the sound level oko(tn. (do1shne g7v s:j( /qmf 1000 such mosquitoes?    dB

  What is the resultant sound level wh 4* *qlwz;ojhben an 82-dB sound and an 87-dB sound are heard simultljb4zoh q**w;aneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,l;rggn1s8m zc3wxg41va +k 4b*o 7twf is 105 dB. What is the acoustic power output (W) of the speaker, a fk sgg3wz+o 114l 8wm*gtacbr nv;47xssuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops.au d s*d*fxz7 by 10 dB at 15 kHz. What is the *us.dd af*xz 7power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over tr0gq726ybto jy .9p(fq;lfk rheir 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 radiufr(y6tjp2lyq.g b7k; 90qrofs 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 systems, the fnmkz f2f i/36aich:5 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 frequency 1/(4tphv ak/ w3c* vil/azk vn5$\frac{1}{2}$ 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 fixed points with a fundamental eczc6 es, s-/7p7 lniqfrequency of 440 Hz and a mass pec,qe7l7s/-nep 6 c zsir 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 filled we0u qzh9 if3.qkj b:3lith water (Fig. 12–35). Th3.3h9iqf 0q:e zklub je 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 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 xcf(46kjvs lhq b6xd rg+;q 01one end and also 75 cm long. 46x01q6k g v+rlqcxj;fhs b(d How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lou jwcft; m 1urcz6 ul0-v:u;7yop ($\frac{1}{2}\lambda$) 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 c akcxb h4 av+i:id nkb5p2x250oming from two sources. The sound is loudek2xx +0bp ivic b k24daah:5n5st 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 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 statioz hgrrb*vtn0i2 6/l.rv7sl cx9c+ l/wnary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches9+itxr rngvvr/lhc7bsl /0.* wz6cl2. What is the speed of the moving train?   m/s

  The frequency of a steam tra zi mqi)5;sq 708a.pp.egkr vmin whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movi;7 si.85prmz 0kapvegq.q) ming (assume constant velocity)?    m/s

  At a race track, you can estimatn5;1m lw3srw vo0mvq8e the speed of cars just by listening 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 the straightaway. How fast is itom3wvrl;0 81nvwq sm5 going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency4imy5el1u q:ml-6x qv of 11 Hz. The shorter one is 2.40 m long. How long iqie5l4q-m1 l:mxu y6v s the other?    m

Two loudspeakers are at opposite ends of a ry/d1- bmlxv ,ayw42 hnailroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers h d/n,w2l1avhby4- xymave 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 flow in the aorta is normally about 0.32 m/s wpva3c3( dc6 yfhat beat frequency would you expect if 5.50-MHy fv363pd (cacz 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 6.5 m/s while the moth is flying tt zl1 f;0hxjvw4cy5+c oward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave vl+xt zcyh;41cfw5 0jdetected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as itvk(egqqi) w.i4 - .hsh 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 b-)qgs kivq.ih 4.wh(e at so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpi t6tl.mlrnbuv / -l9/zq-d-ud 39bvkane village to another. Since lower frequency sounds are less susceptible to intensity losszlbvd-a 9rnd.v 3uk6-ul b-m t9q//tl, 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 open tube.

  Room acoustics for stereo listening can be compromised by t-z3bv7tu r(yr he 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 frequbr3 z7r y(tu-vencies 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 aluy/no8 3n zir(uminum rod held in the hand near the rod’s midpoint. The rod is stroked with the otheo/yir(3nzn8 ur 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 thresha + khhmlt5.me3zew8yq29yv*-r r d c8old of hearing for the human ear at a frequency of about 1000 Hz iet-hva852h mkm w3r+e9lrd.* qz y8ycs $I_0$ = $1 \times10^{12 } W / m^2$ 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 obse 51qcb yfj,7ot9agy2erver on the ground hears the sonic boom 1.5 min qc1o5ye2fty97 b ,a gjafter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat868wf an(fa m/v0 opev 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