What is the evidence that sound tr nyim kfjm/72u7z856mr-n,z gexbhd: avels as a wave?

What is the evidence that sok2r jqv p vc4+z-vky:7und is a form of energy?

Children sometimes play with a homemade “telephone” by attawcsdd wzg;;az rmle j*;;l036ching 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 fromjw6; ;czdm wdr l;s0elz;g *3a one cup to the other.

When a sound wave passes from air int6p )ldndtoh co3l 69.a;m fwh+o water, do you expect the frequency or wavelength dnhld)6+9awtp . cmo ;3o lf6hto change?

What evidence can you give that the speed of sp;quslf.:dd y: d )r*mound in air does not depend significantly on frequen.d l y:msd rf;)*duq:pcy?

The voice of a person who has inhaled helium sounds very hiqu0ond**dbb lsu9 as uph38 q7z rf16,1vd6b ggh-pitched. Why?

How will the air temperature in a room affect5 bzsq j/*jpww-o5(i6m7sesw 6 6jfcx the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce+/m0ixna1-l7 z4f;r -0q wprtcqhib2tggs)p the amplitude of sounds in various frequency ranges. (An example is a car mufflespgt -4 c27izqqlpn)ihg- /w;rb0m+xrt1 af0 r.)

Why are the frets on a guitar (Fig. 12++u w2x1z4gp 94 tookv7fwnfu–30) spaced closer together as you move up the fingerboard to tgp ouzx4ff+w4o9k2u7+1vn wward the bridge?

A noisy truck approaches you from behind a building. Initially you ix/h z5h .aj nf:;6ceehear it but cannot see it. When izf :;jex 5eiahc/6hn. t emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfer0 tk/ h* 2j;nt k5yrfybn57kngence in space,” whereas beats can be said to be due to “tn bhfk jr7*n05y ny ktkg2;/5interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowervffys o3d06h-ed, would the points D and C (where destructive and constructive interferency-d6f3o h0vsfe occur) move farther apart or closer together?

Traditional methods of prjv118mj5lik04a b vgv otecting the hearing 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. Instead, a device is used which detects the noise, inverts it 1v8ibvm1j 4g jv0a5k lelectronically, 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 wave +ahljp4yw. *r-vtd4 es shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18.ewvltj y4a*. + 4h-dpr 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 direc;hpz byd (8v0t n2a .x:god 12tce*wittion, with the e (.:t h0zc2 gt 8bnyi2;dto*v1pdxawsame velocity? Explain.

If a wind is blowing, will this alter the frequency of 0ocu3ddc1,3 z /:(tszk qojqy the sound heard by a person at rest with respect t: q 10uo 3,kcz y/qjzosd3dc(to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of az-zb 3xp0u 8x lnwwiy(a e)j* y8k:5hl 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 child hear the highest frequency for the sound of the whistle? Explain-j (z 5)k0yzwi ha: unxpy*lxwb l3e88 your reasoning.

  A hiker determines the length of a lake by listencg uao/lwyki0kf,n 2.f4 ;,fding for 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 the leng u k ;ci/yfgw,4o,a0kff.dn l2th of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.v -wb5b +tex1hay4 m2h 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? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary+mx- 21abwehyvt 4 5hb significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air +;oamz b s1qnvj uqky )d1ap85)t8wx/ at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a sch(*ol5chd qur:7od z6hool of tuna on a foggy day. Without warning, an engine backfu 5z6lodh*q:oc dh(r 7ire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The sp,og qzq)qp7c xu2zza 3 8my3o)lash it makes when striking the water belo,q3z8uq p7)m2zgoyzoxa 3c ) qw is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pave zzp,s:tnj n:9ment. A moment later two sounds are heard from the impact: one travels in the air and the ot,:zs 9z jnt:pnher in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ovh1u)+it cxq bafkf7i*y+j2yc h 5tw,5er one mile of distance by the “5-second rule” for estimating the distancia,j5 5wytht f)bhc7 kyq ufc+x12i+*e from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a senjv 1jy3 fys,b-+:hround 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 isq xlj.ny m)i21 $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a 0s5ve ;ge;: / jvxyiibz.c8xf sound level of 95 dB when fired simultaneously at a certain p0c .yexi 58v ji f;e;/vzx:sgblace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy j: rhl5py 2dvl48 57cwyn h)gffet engines is experl rch48y hn2lg)w 57v: ydpf5fiencing a sound 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 signaya)r: d(cu-1a .hdolf l-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of hfcad(ay:d1. -) uolrthe signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal cw8 aa kn kl8y5m-nv:l,onversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered o wn -8kl 8m:v5yk,anlan 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 axykugv vf-ieh**im;8m t *x.x+oakt5 1tfm: :n eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest ampzm9b rf 2po(s2lifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at (22s9bzfo mpr 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 frotdg.x* qt10u mnt of a loudspeaker on thtd .txguq*1 0me stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 z 2cmwq2df9-1u phdtbn )dm /7dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–92zuf n)d-p q 1dmbwd/t9m7c2h.]$\approx$   

  If the amplitude of a sounkaiq5ax0b:a6n n ,rs i .:6gcad wave is tripled, (a) by what factor will the intensity increase? Increase by a qanaa i ab.xk n iscrg6:560:,factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaoxy lr4a pk2 p6c-:nx5cement amplitudes, but one has twice the frequen64yla2px-ok xp: cnr5 cy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB):,vp-5n ysv; z h;:r.kx oggpj of a sound wave in air that corresponds to a displacement amplitude of vibrating airo:r,-k.z ;xjh n :gy ppgv5;vs 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-H8nj9u j j03yvxz tone that has a 50-3u8jvx0yjnj 9dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequ,-pjhml,h2xxo0s sn tt74u s :encies that an ear can detect when the sound level is 30 dB? (See Fig. 1n,7sm,hhptj04ux 2t los- :s x2–6.)

  Your auditory system can accommodate a huge ranscoiq :y sy*,5ge of sound levels. What is the ri,ssqcy yo5* :atio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengb41+nw4dx jee h1yf+sth of the vibrating portion is se+ynfe1+h w4 x4dbj132 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. Whatgyo6-pu3p:e9 ptd qtbkoh9 hcs 65)v ( are the fundamental and first three audible overtg oyp op(vc )t35th6heubsk-q9p9: d 6ones 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 b5b1u l ;y/pvp)jp *weblowing across the top of an empty soda bottle that is 18 cm deep,lp*jybwvb;/) 1up p e5 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 ujc)k9 2h;nu fke )+rmspanning the range of human he+)9ukum2erc)f n;j hkaring (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 as its third harmonic. What e6brb -wq5ym) will be its fun -6we 5qb)bmrydamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and isbyr4:-.o;k rd orxw4-s gne ;d tuned to play E above middle C (330 Hzyr4;- d4o.wnbse dxk:r; org -).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe thattxam/38 oz (er emits middle C (262 Hz) when the tempeoxr 8a/ztme (3rature 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 attx+j)g) cmsc1 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 hole pl y fju41sk4w,f6,eqbe that must be uncovered tsyf l4q4jp1u,kfw,6 e o 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 61 b.r.,1jcw* vl2vn*1k3moe yf(i jllo6 Hz, but not at any otjcb.yjew1(.*kr1n oo*3vvimf ll,2l her frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open a;hj4yfoa9q(rq4 qm07 ibj v u1t both ends. It resonates at two successive harmonics of frrj4q7iajmuh;1bo49v fy(q 0 qequencies 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 z gj 33q7yer0f$^{\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 w. u9iy3ssk-z;-sdu zuj 3v rz-k-g3bwithin the audible range for a 2.14-m-long organ pipesz.s-3i yvr uwuzk 3zs9uk -gj;bd3-- 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 outs;lbfiq: g ice .1q nr.lk+hd8*ide and is closed at the other end by the eardrum. Estimate the frequencies (in the audibl gn k1bhf:*dqe .;rq +i.c8llie range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s wheng()mgr9q; h yv trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stry; (g rvm)g9qhing? ±    Hz

  What is the beat frequency if middle C (262 Hz) aouk gim7:k5gyf*l(0z w 8g;uh d( ,qkvnd $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anot+ y/+arzvte g6her (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played szv ry/t++ a6geeparately, 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 producdp1d6 qrm 90ysh0tab/ es 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibration06dsq1 aym 9hpt/b0r dal frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned i(hlm7,b; /j syu.guq q 9-vd/hda*boto the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency lbuogb. j/dhd*ua/yq;q-9 vs,m hi(7 heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play dw,la tj v0o2k*.q/z imiddle C (262 Hz)diazql ok.2vw/t, j*0, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.(q -b8may mygl u1(bu, 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 the possible frequencies of A and C? What beat frequencies are (u(1-b 8,aqyumgmlyb 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 onqix2*igt. 4nye speaker and 3t2 niiy*.g qx4.50 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 areze 4g;g 8qfmf9 supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) fz9e 4gq8m f;gIf 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 mdhsy,0t. k/ad 2 tl6pc in air. How many beats per second will be heard? (Assume Tlha0k6cd t/ds,tp. y2 = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire ewgwz1a)(988ez) c,y xy q bnbfngine’s siren is 1550 Hz when at rest. What frequency do you detect if yo 9w8nwb, ef1xya)yqg8c(b) zzu move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Whbqv5yc: k3gj 6at frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a vqb:53g 6cyjkspeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yoq k(t38fvdgpx +o8k,; /drjou u at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the samxdf8;u38 k vtgk(q/jodp,or + e? 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-u.a3u3 bfihhqfm16tm 8 i4zp frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat freqm i4 33-.muihb8zqfh1 6ua tpfuency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends vjuf1z h6j;r/ 1 hkmz+out ultrasonic sound waves at 50.0 kHz and receives them returned from an object movizrv6jh 1kzj+ ;1mhf/ ung directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, t cvrg 11 1nbt ;+e2i 4pqy2nzi6qn)xnhhe bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear2xq vqgz+n4in2ic)t6e1py b1n1n r; h in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playe9 r8n.,ay2zwgfaw.luf m:b.y d on a moving flat train car at a freq u fl8abynr9zf.,a:2y w..g wmuency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flowohizt 3 0b+gw: speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing io zt: 3+big0hwn large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrew h m xfg ezfb2fd+rpp05 h3je5g 4+i3;.2zqjasonic 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 the wind velxw+n-ks;j nj r*, 0kjc 8k5hodocity is 12 m/s from the north, what frequency will observers heak8,nj5js*-wcjro n + x0k;dkhr 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 itsk wv 4si 0hx xyu4bl)csl*y7+) speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What i30dmpu/ jnjp hz0,0 4valcr- ns the angle the shock wave mac-v3 m,0dzln j0uph 4nrp/aj 0kes 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 thin atmosphere of a plat t j+4u7 1af(yrp7yjuna3ilg)*bv,y net where the speed of sound is only aboij a7y*+y,uty(34 fl n)bgu patr1jv7ut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oceanoobj wz(c3 (qar18p makp;(,z . Determine the shock wave angle it prok (r q1pc;o 8z,azom(j3w(apb duces
(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 v 9mfw: z lx9i6db;w+q$/theta$ 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 0zxk 0 :jt4/f iar.cp7n3cznd ground flying faster than the speed of sound. By the time you hear the sonic boom, the paftnidpjc. 4:zk3/07x rn0c zlane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,0009: ne9xyj 0lr3++)q +mgcr tbzxjq6rd-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 +mztgr9d)x3r0xqjrly c+ 9 bqe:6 j+nminimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the huleu g376fqz* r ql( oz1(5zwtyman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of man,jq3rm , c/ gxq-vq+nuy plastic pipes of various lengths, which argcx-,+/mqnqq u rjv ,3e 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 nv1an3f6(z tqyv19rjro -,f e m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of9oz tr(vffq1r6nej-n va31, y 1000 such mosquitoes?    dB

  What is the resultan4tj e+rr ubvs/d2b /3pt sound level when an 82-dB sound and an 87-dB sound are heard 2/3rv/rsbpt 4je db +usimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.g1/2 7gzhmc9/kzu xx3lv2f fl What is theg9lv7/ /fxzfml2 x1h3 gcku2z acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outp40p.*mzp oi(y s-btkyut drops by 10 dB at 15 kHz. What is the imppb*0yoykz-. 4(ts power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earss-rl e4 w96hxap8mu0u. 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 ofea0xp4-mhu sl8uwr 69 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 communi teb: .9lvh1rdxueb/: cations systems, 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 frequenu*b,l my1e;w blkwr hj:t*l)(jo n/ h-cy 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 points with a fujc* f-64iuq oye6u;u wb (vjt.ndamental frequency of 440 Hz and a mass pebj.cv* ;uquyw6ju(6i-fo et 4 r 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 filleum2 3z-1obi/v,q) oly akp2sod 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 frequenlbqom ),p ouok22z y /s1a-i3vcy of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10l .fodjyt4dq: 4t c1m, g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is tt4lc.m4, q fy1 ddtjo:o 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 loop (a .sq8xi 29ubx.d )t/6j oc5xl4vcsd i$\frac{1}{2}\lambda$) 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:xf xt cd67jf* from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the ot * ftj7c:xf6xdher. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whis +ko1ylg or1q luo9nmbz67/3, w1 ojaptles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tooq+1bo wkunj ,zg31 lyl pma17o/r9 6rain?   m/s

  The frequency of a steam train whistle as it approaches you 0r - mpwg;p joir3bob6lu wcr4sb)7)-is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How far-)w3rmi bc opjp7 ;- g 4rlsou6)0wbbst was the train moving (assume constant velocity)?    m/s

  At a race track, you ca jrb-v hrsus3m58f.x/n estimate the speed of cars just by listening to the difference in pitch of the 5r mbx.8-jfuvsr3/hsengine 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 it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 1kgdr- tym6r( p9ay 18x1 Hz. The shorter one is 2.40 m long. How long is the othy6gk r1y8 a9rp(-txm der?    m

Two loudspeakers are at opposite ends of a railroad card0al6k -m fq)t7acxk5 as 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 akmkl 50qa-x7c)tfd6 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 bv 7wy)9j+xwjm/ mi9cbp dmv 97lood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected fxcwm/j9bm9)j+ 9vyvm7 wi7 pdrom 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 atk7erm +h(kyr5ap g r4p 8.nt;i speed 6.5 m/s while the moth is flying toward the bat at spe.4krp5;+t8 iayg m(e7 khrnr ped 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series p8dgvyi oyp3zxc at(3b 0 .bk7hj/)d1of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms7y)thozbi yvpca.b d d313/j0 px(k8g long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Figaq wbbwn,068lq r m+/f. 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns wemwbqf8b qwn60/ r,a+lre 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 c o 5v f6 2qobcc(epneva7s1z26an be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pzs6afb65(ne1 qv pcve7co o22 ressure 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 “singi4+ilaptk2j;9w qc) w +luoj s:ng rods,” involves a long, slender aluminum rod hel2j qw)p ;co9 4wails+ukj+lt:d 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 threshapdqb lyh (v1 n(;s5p-old of hearing for the human ear at a frequency of abo1dq5lby sv-np(( h;aput 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the s, oioea7tqd9-onic boom 1.5 min after the plane passes directly overhead. Wha-doqe 7oiat, 9t is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo gn369oud5jpwat 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