What is the evidence that s:ic)*wnop w/k4 3 dvhvound travels as a wave?

What is the evidence that soundk,u 1,e: nwl p1rv,ptz is a form of energy?

Children sometimes play with3e+;+g w +blagis7kbrw.5ivm a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other+5iibk 7s3 grw ga;wev ++l.bm.

When a sound wave passes from air into n cdmv,- v-p/uwidy baj/8(d(water, do you expect the frequency or wavelength to ch dvn idj p-v/ au8dw-/b(cym(,ange?

What evidence can you give that the speed of sounpd0s+ o biz.(k xwv7x4zkf.5q l,yu1jd in air does not depend significantly on frequency x,o5f 1d .w0zpkyq.z+lsk7j(x4 i ubv?

The voice of a person ;o84jd/g 6v1 bmaehihwho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect thqie qf.(ic; d9a2f hv6e pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ;i h,m 3qzdr*samplitude of sounds in various frequency ranges. (An er si*3dqh;mz ,xample is a car muffler.)

Why are the frets on a guitar /;zmh.w g 1khypx,o9s4ry 0 ct(Fig. 12–30) spaced closer together as you move up the fingerboy 9c 4hh sptz.w;yg1rmk/0, oxard toward the bridge?

A noisy truck approaches you from behint6.wf em:yati el/p+/(qeg3 o d a building. Initially 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. Explain. [Hint: Seogyt a 3+q :m6 ilfp/eet.we/(e Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference(g (i jd-wnt: vj-uqm/ in space,” whereas beats can iqtmdu(- -j:jgvw n /(be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would tg(fobcf 7ajwlap*t ,3 ,sci/82 zhc7q he points D and C (where destructive and constructive interference occur) move farthe7acgwf/ c2*tp3bj zo,fqs7ia (8l,chr apart or closer together?

Traditional methods of protecting the hearing of people who works2afr h:6 3mo,dxz2om/h-e ew in areas with very high noisef22aos-/hz6 mr mod3ee,w h: x 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. Each wave can be thought of as a-+ s fxvbn1b8b superposition of two sounbb fn-b+sv1 x8d 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 sa-h2rx 5*6kw :jk0qr jipzz..e kso;ivme direction, with the :;jk z6j..okw0i r2*5v pki-sxeq rzhsame velocity? Explain.

If a wind is blowing,vh o1sio((gj9 will this alter the frequency of the sound heard by a person at rest with respect to th 1( 9shgjov(ioe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mo5*un stzg dl5m1v(vx3nitor is blowing a whistle in front of the child on the ground. At which pvm*lx55 dn(3 v ugtzs1osition, 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 for7e1xe )xuxawixi(t *yv.7*vm0 xsk u8 the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate*u aevx7sy x(x.iwx*)i8emxu t1vk70 the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hisbtdb.l-njcxm 32- *0hk: mfth ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Asft bmn--hhjb02:t.clk3xd * msume 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 wavelengths in :3,1ttfl hn0 fcm(uux 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 7 m)0e0c mj7rcq ,v+lgmuyca0just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time y+0ec7cm cuqvm ,7lra0m0)gjelapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the iw7 (e *zdyk.btop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is thek . w(i*7ezybd cliff?    m

  A person, with his ear to zxhi8g nw:n82 the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they arew 2nghz:8n ix8 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error mlldn 58r1 q /k. 5hm:w4yvvzmoade over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperat/kl8ynv55 rovmm.: lz14hq w dure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity o-kzs0i*4 tea dwv i46hf a sound 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 whose intensity xjr zvyfm8g8/ax: )w)is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at2mr q/xo .lz/w a certain place, what will be the sound level if only one is exploded? [Hint: Ad2o m rw./xl/qzd intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equalyv jby:c+8*p wk-w;5d yhase 2)t+faely noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if t cjht2y)pas+evdy*kw w;a5+y b-ef: 8he 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 rq66za:cxovpt 84 *zktatio of 58 dB, whereas for a CD player it is 9tk8 :oq64txvzp zac 6*5 dB. What is the 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 sou q0ii gohy62o/nd from a person speaking in normal conversation. Useh yooi/6 g2q0i Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardru2;3v2c+c kuu 5vb 4hird ihv-fm 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 m j)sh m/8csgtemqroe.2n l)91pp7y.W, while the more modest amplifier B is rated at 40 W. (a) Es8s o)p) 2n hl9gserqmc. mjyt7 m1/.eptimate 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 meter registered 130 dB when placed 2.8 ymx8zmmz7m8)os0-x t / hb car8/bj-bm in front of a loudspeaker on bh 8ytb8sxm0-/ 7mjomb8 c rz/-)m zaxthe 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 rhqe srh-2 .x-p8snn:detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sonxrhesh-pn s-r.2q 8: unds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triple6zw t+lqa1fut t8.t/dd, (a) by what factor will the intensity increase? Increase by a factor ttz/d. 6wqalf81tt +uof    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frvtxvd5 bu)h5d03r ( cfequency of the other. What is the ratidu3bh v0dvt r(5cx)f5o of their intensities?   

  What would be the sound level (in dB) of a r,w;6xjq1ug bwp b- t.sound wave in air that corresponds to a displacement tr.b, qwjgu -wp6; b1xamplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as l+8 qb,qt ky,z8og4dldoud as a 100-Hz tone that ztyqgldd8+4q ok8 b ,,has a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when .rqf vf1xcpjr f,/eg r)gp23;n o83nfthe sound level is 30 dB? e,ff.2/8rn j fofgxc3pgqr; 31n v)rp(See Fig. 12–6.)

  Your auditory system can accommodate a90gv6ipyi a*2hrg: bi huge range of sound levels. What is the ratio of highest to lowest intensiti*09y6rh2ibvag gp: i y 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 Hz. The length ofojx* ;mu;dy d1 the vibratingmd 1;x o;ujdy* portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thrl0ri+ az)+- zivww f-lee audible overtones f )lr-l+va+iziw-z0w 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 83*f sot*ddvz from blowing across the top of an empty soda bottle that is 18 cm deepz t* *sd8vfod3, 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 rvd2 0s 8(f spf6/xsblsange of human hearing (20 Hz to 20 kHz), what would be the range of vf26 8l/ss 0sd(psbxfthe lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has gmamchg2s4() a frequency of 540 Hz as its third harmonic. What will be its fundamental freque ma4s)cg2 gmh(ncy 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 tuneda+p.ib7hrbh7gou (rdufq+( : to play E above middle C (330 Hzh(i(.uu gbr a fb +:rd+ohp77q).
(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 pis5ojmd,yeiyx 4 8eu-p i,ccxw7;:cz8 pe that emits middle C (262 Hz) when the temperatur e;e8mxw:xicc,4cjso 5yy iu 8 ,7p-zde 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 20 i91gv ((sas+ gnjiw r2 p4rb7c$^{\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 hole be tpitaq4)2,rlp+mlc vd 1(wfgy8b/ v*vhat must be uncoverglcw)8vpv*y(tvf la2 4/ qi +dr1b,pmed to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at a0jln -u l4 4cwx.vj kk(xdwl(.r:tmi.ny other frequencies in betwe lc x(w:l mnx k.rkt044.-ju.( lwijdven. (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 both ends. It resonates at tcn.n;li sc 95zwo succ n9zl snc;c.i5essive 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 :xksu4ple3-,,8 vg :vygd/mn gj+xvr$^{\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 aw4)e+tl2am 9xdx( rm 3)cx uuwithin the audible range for a 2.14-m-long organ ax34ced 9ut+ (w 2xxaml)um)rpipe 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 open to the outs8e5 *tk9q3bbm pzp faxf9o; 3cide and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. Whacmq ob p ef9*3 btz5x93;fp8akt 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 adjust two strings, ork4e wv3.0lzmhe2i 3yne of which is sounding 440 i y.he3r0 zvkle243 wmHz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (:/h aaum/m qe 0ah9gn*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 opera/fkbo w.7*uc ntes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when pbfnu*cw o 7.k/layed 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 a 350-Hz tuning 95a)dy194n h wwuvhbifork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string?hab n9i4 1hv ywud9w5) Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The wpim/o 0x*9r zg8q my4tension in one string is then decreased by 2.0%. What will be yw m4qz8rxo0 *9p/mig the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be r2usx*4o vpsdg7.e q7heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othersxo2.r 7 usq e*v4dpg7 at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.2oyimpm ;l3drr z /6)c+5l(v.olcy; j(s muqv Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are th;pm(i;l .rc)+ vsvl mc /od(or 2yzq 6jl3y5ume 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. A person 5c uotwti5h:9 rrtw.2stands 3.00 m from one speaker and 3.50ohiw.rtt:u5wc 52 rt9 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating wpn(j 6l16bqx at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, n6qx j6 1lpb(wwhat 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. Hi9(fhv 18gcj wmp a+rj6ur9q) ow many beats per second will be heard? (Assume T = 20 v caj 69)rgw1m f8uq9jrp +(ih$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency o pr-o (x3ysj*mp-vg 5sf1oi4u f a certain fire engine’s siren is 1550 Hz when at rest. What frequenc s*1 xi(-fms 4p3vgpo-ru5joyy 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 sti)tndb2, kkwnygz; 6d0ll. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s bk;y206z , d kng)dwnt
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz y3zj+ .b + 5ve.ply:vyux;o ycsource is moving toward you at 15 m:cj +y3yzp .. lv exu5+;ybyov/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 frequen3c3-w gbj2 laewn:*7/hnu z ehcy horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hearwnezu/ngh*cjh l bwe 32 3a7-:s 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 and ixobebe +dp;2.vd+l8receives them returned from an object moving directly away from it at 25 eb +lp divbeo+ ;2.dx8m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a way (k5yk;k g;)ui/pv2be)h2 1ktyiz xvll at a speed of 5 m/s As it flies, the bat emits an ultrasonic2kgvkyk utix;)1p;y /2bveh5(y) kzi sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fl+w4jlj o/c6wqnz :yrwar.g y bd;80b 5at train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway staty.o bj: 4b0wr+w8rn6 lgd; y/cwz5q ajion. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to 3cuw gy. w ko1edlo+p4k662zy 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 is the expected d.ku +62oo3pykec1w4z 6ylg wbeat 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 frequencyq+* /hmgkei .bfp,rz 16m49 sxxhmb(e $2.25 \times10^{ 6}$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 frequ. 734nls hi2blo)fhn 5dubvg +ency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who 4l hb7 l)2fbv .ni5g sn+duho3are 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 movin 7m1 rllmg4xz3ipo;/ whw(e4vg on land 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)8,b4 i5zdm/e:nop+ z nrxnve/s (a) What is the angle the shock wave makes with the direction of the airplane’5oeriznbn zx4 de:/nv) 8,p+ms 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 h6x 9lcij 5 +nhibs8w/is only aboutlh jbx8hi6/9 s+5 wnci 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 m6zxj7)ufx )/ qpqhzr7z lqt86b c6c-i/s strikes the ocean. Determine the shock wave angle itcu q8t7/)qz r-xp 66xzq6 hlijcf)b7z produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle walgs ws7so8x,0ic 2 6$/theta$ 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 grox3t2 ppk qxu m1c207vpund flying faster than 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. 12–3u3 2tkm qv7cp0p2 x1xp4. 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 th /p3hno3 hiv*gat 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 mn 33g ph/*ihov, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves ared:dzsn8 mwns.infs+ 7g4 /f+x there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It1 p- 6-ry5 so4; ryv*sff/7rbkdtlgjh consists of many plastic pipes of various lengthkyjo s-hr- ftps*gb6yl4 7vf/r5d;r1s, 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 makes a sound close to fjpdsqb)r0+ rd;13z8 r(l qrh4,sm fdthe threshold of human hearing (0 dB). What will be the s4 fz r3)s0,8jhpmbd rlqrd;r sdfq1+( ound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-de* 9uhp;panq+B sound are hea na e;hq+*pup9rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10k7i;vwc wvqt,( n l6*e5 dB. What is the acoustic power out*; e6,k7(w vtivnwqlcput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. T(qt3 xdc8u7zlgp 1 jt)he power output drops by 10 dB at 15 kHz. What is the power output inz cpd 7ltgju8t3x1)q ( watts at 15 kHz?    dB

  Workers around jet aircraftfw; -o txlh)7f+flff50z2yllgop1 + t0kyso6 typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m1l7opst+0llgt lfkh0fy -fxy5fo+62w) z f ;o from a jet airplane engine?    W

  In audio and communications systems, ,l7ho ; r)xqwha24h0ces3g r94knczn 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 frequency rd887 ol,efb bogh06 z1$\frac{1}{2}$ 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 viol3: tc o+wcs2hgb 4dov,in is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length s 2:coohdb4wg3+,vc tof $6.1 \times10^{-4 }$ 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 abyxdqtiryqn5ylvb-)7 o 5dmw,2 -u 8 r-ove 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 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 for -ubdml5qy odw8txq ,-r57 n2-vi yyr)k?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is openz:f 0 :pgk6kpnc c .te(nf)m-f at one end and also 75 cm long. How much tension should be in the st)nmfnf p- kg:(:pceck0 .6 tzfring 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 restxl. 13eir xl* ofyh;;onate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. 4l6-h w u24ubj orsas1;ddu4pdo.u w;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 m farther from one sourc-o p6ujs4;aou w41sld.w ddubr2h u;4 e than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whisiqzek- 6kyh ,5tles. One train is stationary. The conductor on the stationary tykkeh 5z 6i-,qrain hears 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 i sz,wf l.zd-*ks 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movingd.w-*f, klszz (assume constant velocity)?    m/s

  At a race track, you can ep 5e8chfdsx2 asx+ yng.-*6ao stimate 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 a5nso.p x 2yax 6+aecg fd*-sh8 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/po fj1e)s(n d together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other? fned)( 1josp/   m

Two loudspeakers are at opposi9h ssjwe x+-5lte ends of a railroad car as it moves past a stationary ob wsl hj9s-5x+eserver at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the 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 :2sk y6 wl8cdqnormally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travelk:lwq6 s8d2cy 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 towaw(mu r8lbrk x5f s39/iw ,.ocrrd the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of t(kuo cf.w98lm xrs5/ir rwb3,he wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it appr10 mkmcz9h(r moaches 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 ( mh 9czkm10rmis emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sios+:,x3n g ka ctz/6cignals from one Alpine village to another. Since lower frequency sounds are less susceptible to intct /io,k6acnzs gx:+3ensity 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 open tube.

  Room acoustics for stereo listening can be compromised b,9jw+wc-m6pfl9q jbt0 /+fgjic g qd2y the presence of standi f2jl/w+m- 9tf,j09pb wccj 6q+ qdgigng waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing +bbyul0n.2 ql j.s/tlrods,” involves a long, slender aluminum rod hbl+.sn2b/.jyltl u 0q eld 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 vbxuz1 :,j-mc- yexu-xcm/,z the human ear at a frequency of about 10xj, u:/x1xe c,bmv-mz c--u zy00 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 sonic9gr4vb m1ehn;t*f 9ti boom 1.5 min af vhnfe1rtgi;*bt4 9 m9ter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboezdl9l8v::r ic+ y5c9+uifw fat 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