What is the evidence that sound travels as a wave?xrn4l ang(n7h4moc 9he /r .+uqqk5 p9

What is the evidence that sound is a form of 0ox+ eo .yllg/energy?

Children sometimes play with a homemadozc -x asiwoh5:;xo,8e “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 othx; 8so5zoh: o-cw, xiaer.

When a sound wave passes *k0sucju a,3d7i l-azfrom air into water, do you expect the frequency or wavelength to chan -az3du0s ckiu* a,l7jge?

What evidence can you give j*:n6yp jf4c, ux7 a ss*m7ueethat the speed of sound in air does not depend significantly on frequenc4cn7 a fx:p6js*e7e* umuy s,jy?

The voice of a person who hageydj p 3y.az ;hwc qo4cr-c-u5-t5.f s inhaled helium sounds very high-pitched. Why?

How will the air temperaturep g*f(jo;n xqoyjz de,()*vtmj2 t;b 8 in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude+ x j.nrl(0npbxw87bv of sounds in various frequency ranges. (An example is a car bx(.lbn j+v8r n xp0w7muffler.)

Why are the frets on8k5hxez5(1f ni1 )ebgt:xh yu a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward eh5g fx(ek1:b8y 5 t)zxhui1n the bridge?

A noisy truck approaches you from behind a building. Initially ywz2qt ncn vt1 5.)mez1ou hear it but cannot see it. When it emerges and you do see it, its sound is suddm zvw2nnz5c qe1.t t1)enly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,”x4(u2 s lpzg.zlpzi, + whereas beats can be said to be due to “inte,sp.4x i+g p2uzz(llz rference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin4 x r*sv*mb7 cw43(kehg(oj zmts D and C (where *4b74o3( szemxk*mvc(hwr jg destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas (b:ku wh*(d4 -qt tmgswith very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound leveh *tqkbdugw m( :-(4stls reaching the ears?

Consider the two waves shown in Fig. 12–h 06ap*kut b9+e6ppb j31. Each wave can be thought of as a superposition of two sou* pb9btk6p+ 0u6 pahjend 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 0kiimcm *2;z zsfu 33eand observer move in the same direction, with the same velocity?efmicz 2 3*m30 zuiks; Explain.

If a wind is blowing, will th2 y,bc ycu8u/kis alter the frequency of the sound heard by a person at rest with respect to the sour/,yucb 8 y2ukcce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions7hffp3k7v7 av(j5 4x2hpec mi of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the ch mi57a4c7h fpk(72jvxhfp3veild 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 echw + scrzvqmltw wx-;8/;w:;ooo of her shout refl; x- z w:mwlr;8ot;oq/ww+ svcected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the enp;ick7:2 yxd1h;h fncho of the sound reflected from the ocean floor directly below 2.5 s lhip kxndn;f h:;c2 y17ater. 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 wavelengths in tpuflcg. 5c +*-zuux1air 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 abovepz.e w.o u,d1y a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km awa.p zed1wu,.yo y (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 s6nt*i326b q1 k-pwypkt*ee ti kv/ek (plash it makes when striking the w p 6ktt3qi(1 evk2ykn /6p*w k*teb-ieater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear tok9: x ulxogg)n,cg. w; 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 are 1.1 s apart. How far away did the impact occur? See Tg.c9x:ok) lwu xgg; ,nable 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of diz6ueb8 e*-ur zstance by the “5-second rule” for estimating the distance from a lightning strike if the ezr 8eu*- bzu6temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity oqpld rtq;c7,. f 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 levv+m 7 q6 0 vb6p3;yqowcwkgaynz (m/-mel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simu+ t-;v/pv w l/ f6;as d*h9ptnyluz6ugltaneously at a certain place, what will be the sound lpu;/l yu pv/n6 6tw-v l9 g+t;s*azfdhevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an ail00 8vb*r ubunrplane with four equally noisy jet engines is experiencing a lub0u0bv*8n rsound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 px zpar3k+o4e3 /+zzi dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise / 33px+zrp ko4ei+azz for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal c22(ajngxqk l7xa,f41cra ys4p4 * amaonversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphe amp44a n1yq,la s karfaj472x(2 gx*cre 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 s owel4g6vtp;ud g3d (-trikes an 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 26c2d5o rtq2 cw50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expq 2rcodw ct526ect 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 m in front criv ;: ubr5(xof a loudspeaker onc(u;x5:iv rr b 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 so)ytixf +v, t6vjvve 14und level of 2.0 dB. What is the ratio of the amplti vyv4v61,)te xfjv +itudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soun3 a+mun ;zzf/wd wave is tripled, (a) by what factor will the intensity/+azzf 3nuwm; increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dirh+ iqf*0: :+kc8i aok:n vmujsplacement amplitudes, but one has twice the frequency of the other. Whq ahr+n+:8v ck0jmioi* fu: :kat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that co.vnwr/ euf/2) k alxkbo6o7qg vw1 i9a(5jv9lrresponds to a displacement amplitude of vibrating air molecules of 0.13 mm atvoweva9/wk xaj6/b7f q9r52oli(n) vulg1k. 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that urb 1 x:kw:tv a n+i3.l cv2(imvy-5nihas a 50-dB so2a.x : vicbnvir5w3y (+ :1knuviml-tund level? (See Fig. 12–6.)    dB

What are the lowest and higheevb7uhut mec -. yih ky)n-2wu,;0b:lst frequencies that an ear can detect when the sound level is 30 ueye:lk7 u- t2b)v,ic n h;0-umw.by hdB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels.pnteaa9 (00 5gzb*h6da x,o33lb jzp w What is the ratio of highest to lowesttao pbj *9 (56l3nda0wa03b h gz,xpze 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 Hz l* 2spr3j2 x;ojy0r0h6u3r az(qnlvu. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 gvoxll jsr*any0h30r 3z2r(u 6;u2p qj . Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three :p5qu qse s;* j/ee* id2zubwr12 hgp5audible overtones if the*5sj2e* ezu:wbhp 5ig esr2;uqp/d1q 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 e++gxqu; nwzpx)y, , doxpect from blowing across the top of an empt + px;wd,y,zxqn)o+guy soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pzzngja7tu * n psk5:/)ipes spanning the range of human hearing (:gn / pu)njaz*kz s5t720 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)uf* af watvo.9rxinl/42c )t of 540 Hz as its third harmonic. What will be its fundamental frequency if it 9* f onttia/awfr).v)xcu42 l is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovz uk-z42xwpdz;:s 3g-poee.be middle C 2d4-up xkzzbe- p.oe;3 sgzw:(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pg78) vi/l j//sltbqkpipe that emits middle C (262 Hz) whenvgq )l7/ibk pjs tl/8/ 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 20rfi b6j-(-3idq br(wh $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exambnm9rk (l32r)ecgwer 9ltr :8ple 12–10 should the hole be that must be uncovered to play D above middle C a9(3 2krlel)gentw rm:cr8br9t 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 resonatp. r+33 js9k uzo9zqtje at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show s+tqz k9jj. o up33zr9why 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 er l)z4qsw( c(onds. It resonates at two succe wcqsr4( oz(l)ssive 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 q ;t6w wulhb+38q n7pwh.ayi61klh; j gj4az)$^{\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 therx6:s zd6g6ski3u7p e audible range for a 2.14-m-long organ pus d6p6es3z7ig x6r:kipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal istoa 6gw4 9hbp (r.9dyb approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of y 94o(g9ay. hprwdb 6tbour 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 egrmlfek/q,e4 v7m;9c very 2.0 s when trying to adjust two strings, one of whic7km fm, ;lrvg qe4/ec9h is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Cm6ri u4gp3fl2 (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, z z mlal;iul)*bhl2 (1while 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 occurs when they are played simultaneously, estimate the operating frequency hblai l; uz1)l2z*l m(of brand X.    kHz

  A guitar string produces 4 beb/ gu0 n,0nohiats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is thehb ,nnuo00 ig/ vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to b21aeisc hsvr q-pj/(e1d.l7the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will jq12.(slde-abrs/ ehi 7v pc1be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if tw6 bjw ci0wejs7s92u+r o identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the otheiss60bw+ u9w27jcr ejr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of )z p- ut z0 jc.oee7gtgb(xk-:441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. Whenee:pgxou tg)bj (k 0-cz7.z-t B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker af x8f7 aeh8 8saxj v,wtsz;1*rnd 3.50 m from the othe waxz ,v1a rj7hf f*8;xs88ster.
(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, but a piano tunerx5nqf9 * kzv,b hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of tkv5q*b, x9 fznhe 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 2.6h:kex*d)lize7 sj r)*bfw8(cg5i : sp 4 m and 2.76 m in air. How many beats per second will be heard?:)hwidf)br:(zc5* l x s *8 epg7kjise (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at r,. /cbc2sl k.:2aena9 am;ak2ralc wrest. What frequency do you2el ;9c. ,s:bcaak2wm2 k lrac.a na/r 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 if a fire engxdc)*5 a 8oovsine whose siren emits at 1550 Hz msavo x8 *5cd)ooves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequ+ t k4ulawb63uub:aer9 8,oksency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toa ua8r 4bet:k9blsk,6o3u +uwward 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 id5r9qkus i6/2x bdc e(s at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat freqerdxd 2q6cb9i5kus( /uency 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 kz(*2pdx8 nfnbs)+ ouodim: u3t5lo6 f Hz and receives them returned from an object moving directly away from i2dld8o(:o) f3* bpfn imuznt uxs6o+5t 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 flies, the bat emits an baw1p z;g2 shlenfhh-;+6k rv72o3houltrasonic sound wave with frequency 30.0 kHz. What frequencw fbk hr;zl2n3ohvh2a+67- 1 hgpeo;s y does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on 7hc0mdht, da: a moving flat train car at a frequency of 75 hc0d 7m hdt,:aHz, and a 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 ultrasound waves to measure blood-flow speu gg3 xqdv4)(7leiaqa7 ;gpk w5b :c0oeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in la ia5v c)q0oal;g wxb 3g7ugpqkd 4(:e7rge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonr /7btsjt0x7)inq w+9p3t3l+ vj0bo1 w eic avic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When t9fzw /aj( dbf9he wind velocity is 12 jb 9dfa9 /wzf(m/s from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object movi72u g496k glic kpa+v 17oudykd0lwyr ,;2jkdng 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 wheree fh 5agj 9u3p/o8k-ge the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion? 9gepe8a h5gjof /3k u-   $^{\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 w;zz di2zj 2ny,hxj-;nhere the speed of sound is onlyz2j; 2xnz;d,z j- iynh 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 mpr51av a (1bit/s strikes the ocean. Determine the shock wave angle it prvira (pt b51a1oduces
(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 enoep7wyfc)+tig . n 6uq-/y -$/theta$ 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 thejax q ,pods oa;6f-ha y. 26,c,hwn4gr ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance4;as2j cw d,h6f,px. yr-ga6,nho aqo of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000o6r; z0 7tfjxw-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 iswjzf7;6x 0ort the minimum time between pulses (in fresh water)?    s

  Approximately how many om mef+-c1feuk rs10 t6ctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe syjbxrw 2g10 +yzmphony. It consists of many plasticjbyg01 zrwx2+ pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to th ,rdq2)xb tbr2dr2y7ie threshold of human hearing (0xbrd2y,d r2 )i72trbq dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-d9to0qr: )e liln.f-arB sound and an 87-dB sound are heard simultaneou) ra:t0rifl l9n.-qoe sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in b*ox42sc-medthe open, is 105 dB. What is the acoustic power output (W) os*b4 mxcedo-2 f the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at nox:1oqzd+1r 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the o :dozr+1xq1npower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear proteao m;n p65epq7ctive devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and p;a ep7mn65 oqthat 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 systems, th )4qh8vyjlud4.rm-ll e 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 frequencyx7nz.e; 47xp+0 dkqsfzre a/h 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed tzbjp.gl1smn8/ - . qepoints with a fundamental frequency of 440 Hz and a mass per unit length of pb t..j/ nq1sm8l e-gz$6.1 \times10^{-4 }$ 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 withk 6iuz,4 cor0y 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 witic06rky z4o ,uh 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 nea soi19km x.8hfr a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fo. ifsx8h1 m9kundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as mrrz .)2co t4none 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 f rpi8f78uy5lq rom two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the soulfp58ry7uq 8ind 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 stationary. Theg5m;) )sgr 4mbh za aeuxg:k+8 conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approacheg)4m s +agzkugr )x 5a;bmh8:es. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you istqrt 5v y,;z rq9e8ec+ 538 Hz. After it passes you, its frequency is measured as 4q;e ry,8+zq 9t5vce tr86 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 gw2z r0rnmd- +listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops +dz0-2 m wgnrrby a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat freque -)m h)pqtj.twncy of 11 Hz. The shorter one is 2.40 m lon.) mt w)t-jqhpg. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as:fm8-km1h t a oo7*aff it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c8*-fmao o kf17mft:ah ) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta isbjx6n2xt3 h)o normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed ajo2bxnx6 )t3hlong 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 kn g8mmhd5-exty1j (:.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detectedx5 :j1(-yndg8 mktehm by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it8o0ib wuj3 3nt 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 detect383b uwn ioj0ted by the bat 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 Alpine vill7qy9p 1vi ;fyn mn32ynage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is closnypny7fqi mn9 ;31v 2ye to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of za(v v h(78kn/e(jnqzstanding 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 nn(7a((qv h evz/zk8j in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calle: q*t7rwzt+t id “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the t t:r7wtq+ iz*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 hu 6y-wbz,jioci:hqv713(qv+eq ikz2eog gx 8 ,man ear at a frequency of about 1000 Hz isi6h 2,3 vy+(i 1webkvzjq ie8qoo:q 7g g,cxz- $I_0$ = $1 \times10^{12 } W / m^2$ 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*-+oe*d16szmokvj ol hears the sonic boom 1.5 min after the plane passes de1o6oko lj msz-d*+*virectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo-epp 921aqvy/;k fyyrat 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