What is the evidence that sound travels as+v/5e 4 eblf:sy zm4szzaj-n+ a wave?

What is the evidence that sound is a form of energy?rdqviq9+.j;,za q r :11y sfyj

Children sometimes play with a homemade “telephone” by attaching a string xpjdnhdq3e+ rb2r.cpg7u0lb e7 x6(.d5vcj1to the bottoms of two paper cu 0ppnl. c6v71r7 xr+d2dj eh.q exg5(buc3jdbps. 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.

When a sound wave passes from air intjs; eea wza/ lp g*s..ard ,rzt)aj+(7o water, do you expect the frequency or wavelength to (*g.ae/zl arr d;zja+,ws p7atj .e)s change?

What evidence can you give -2 5xbthgjr-u that the speed of sound in air does not depend significantly on freqg rj- th2x5bu-uency?

The voice of a person who has inhaled helium sounds very high-pitched. Whyi1dnw av.6qi 2t9u ) s w5x*iuo8g2q-q(cvsid?

How will the air temperatug*v7- jgyyb6j gjs(ijn8q 5l(*f ncl+re in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds i;h.9w d48u 52ij a+wlxsou/x j+ zfndan various frequency ranges.jnwso4ldd a8iw+ ujzfa.2+9 5ux; h/x (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together ay k,yq)i js mp6d/r,r/s you move up the fingerboard toward yjkm/,s ,d)qry r/6pithe bridge?

A noisy truck approaches you from behijhqxj+o/kf-x p / jiyr;/:wj 6nd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenl-jjqip6khjxyw;+ :o //f jx/r y “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 z7niwek3a v):j,sh,(h) h i kfi(uj3z “interference in space,” whereas beats can be said to be due to “intwk(hasn37,z vfi izheu3k,:) i (jhj)erference in time.” Explain.

In Fig. 12–16, if the frequency ofwk-;2zo 6f vh4zgj ;rp the speakers were lowered, would the points D and C (w vzzo2;h6 rjp kf-;gw4here destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting dr:)9fx pn1qaxzyw0 *t:wj g.the hearing of people who work in areas with very high noise levels have consisted mainly of effortsgap dnj)wf 0x z:1*q9tw.ry :x 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 ch y bg:+r/ow,3-mocz-huiw,can be thought of as a superposition of two sound waves with slightly different frequencies, asc o-,3izowrcyu/:whm hb,g+ - 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 anthod d 6 :3:dfxaoabrj3 g9;q3d observer move in the same direction, with the same velocith f3r6a3j 9doxg qadb:o3:;dty? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by10yrtv872 rk(yvn 6yign mzj/ a personn6(/7yr ni2y8z0j m1k grtvyv at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child .qjskvr7w44- (jl tpo- omp7cin motion on a swing. A monitor is blowing a whistle in front of the child on .l7-4 4scp7 p wj-qtk(rvjoo mthe ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening foaaq xian7as(0)hgy) rv1g 6f2 r 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 le) ga)q7yi(2nrg6haxvaasf 1 0ngth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the pa,(pgs +p2uj 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? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depthg pj2u,(ppa +s.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths i3tu3 d, )a ddhgv.gr+0l; fdnhn air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of f, - ibbwf9igvy8eyh; 4+xj3ituna on a foggy day. Without warning, an engiyi8 +3,j9b yi;he 4-ixgbfwvfne backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff..iyz u ,l2 b8knr k4ne76k0n1i1ajdto The splash it makes when striking the water below is tn 0114uyirljk.nkbk 2da6ni7ez ,o 8heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr .fe68tq;oy d*hzgdz/, lw fg5ete 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./d8g.5q ,6w l*;geozy h fdfzt1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dista)db5f9flis *amjt+ut7 de4 /nnce by the “5-second rule” for estimating the distanli 97t)5aduns bt4 /j ffd+m*ece from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity () fb.sm3nou pof 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 whosm(f 7 k5zqv3ba)qs3 tle intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sojt0p x de,)*)qm,xkdaund level of 95 dB when fired simultaneously at a certain place, what wil d*)teqpa dm,j,0kx )xl be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certapir/ x*ma5am 5ugh 4c/in distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this p/gc54a h5/m*arxm ip uerson experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is sa.yk*)kh 1 6hfssxx et)id to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the t.e*) k6xsfxskh1 h) ybackground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powertkgw 0rijr49r-/gr8xo ns 8: i output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a08rj:8srtgn-4i i9k/ og rwrx 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 sk a (3lbk4d)axtrikes 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 250 W t 4ub( lkdvkhd8n:m ;+bs43xj, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker cmtks3hudvnb8 x:jl;kb( 4+ d4onnected 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 g.++vcetznsbm-6 j0ic 4a p o7registered 130 dB when placed 2.8 m in front of a loudspeaker on t+ paizj. t6cb+n4-eco s0mvg7 he 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 xso c s2g)k+s1k*r7m,wwng r7psc28 t2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]ssm*rcss p77c2r2nk, x1tgw o k 8g)w+$\approx$   

  If the amplitude of a sound wave y-tbb. e;euumjn b8kbu:c -70 is tripled, (a) by what factor will the intensityyn:c k b;8ejb-me ut-b7u bu.0 increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement f69,ldemz7f vg 9hge hs:g 50pamplitudes, but one has twice the frequency of the other. What is the ratio of their intensities7mf d 60ghgg zv:ep9esf9 5h,l?   

  What would be the sound level 5 6nr7l4ae 0dh,ylop5( mza f p wrzn/a,:x*vw(in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm atrl56 a(xpr7a*lhmz, 0zwyf,4 w/:vad pen5no 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud aso );*zlclo- b6y6rqk+w7v lcg a 100-Hz tone that has a 50-dB sound level? (Seelyll o-)qvbgorwc; z *c676+k Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the u6*n11:fs s g .lyw8-phzgaresound level is 30 dB? (S*ngp:61es8wy1g.zsurha fl- ee Fig. 12–6.)

  Your auditory system can accommodate a huge range of soa .s9/-p f0fo2i covhxund levels. What is the ratio of highest t cxofi 02hp/ ov-f.s9ao 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 frequenc feuj5gg9hw9fnm c6yt2s94;fe w4p g3 y of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be9wy t gmfc 9sfng;3f 54wu6p42ghe9je placed?    N

  An organ pipe is 112 cm long. What are the fundamentupg+5w j1 nbsb dc7p*l:-zhf7al and first three audible overtonesg+j nwd 1-bfpclh:*sup 7zb 57 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 fr+/juisodq 1 5r0 +uuajequency would you expect from blowing across the top of an empty s+qujs1d u0ari+5j o/uoda 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 pipes spanning the range of u gc aijpsv gbkrl62yuj1h 7qb74q)5 8d1tq/- human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requir /i pqbqy71dgql-)g71kur5 sb6c h28vjat ju4ed? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third wo 9f 0yi;vliwii iq329 j1wt,harmonic. What will be its fundamental frequency if it is fingered at a le,i w9w3qi i0i 21loit;yw9fjv ngth of only 60% of its original length?   Hz

  An unfingered guitar string i5n :p1w2 gut:*i goysh7syhz/s 0.73 m long and is tuned to play E above middle C (330 Hzuss:yh 51ozth: *ygw2png7 /i).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle Cz+hhvv.l;6xwj: q;jhi l ,iavb 4a5d . (262 Hz) when the temperature is 2lxhh .j6+ 4vlia.zq wi;bv,5 vhj;d:a1 $^{\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 +qakr *:1qq 1s*jpyu cat 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 holesz0r ba4h1a ,b.ulh5 s.np1ba be that must be uncovered to play D above middle C at 294 Hzzuh,.lh1s.a4a01bp5 n br asb?    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, buq :cs 5qkr - :att**wpfy5i(fft not at any other frequencies in bct*kfqa:ti(sfp :5 wyr*5qf- etween. (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 op3f;88tnw;g yh1djxctgtb8 l8en at both ends. It resonates at two successive harmonics of frequ1 jc l tw88;8tfggbd;8t nhy3xencies 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 hx*o5 a ,v znjc il1.1,cmxp;v$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audir0(v hr)b9eh yble range for a 2.14-m-long organ pipe at 2 bhh0rrev 9(y)0 $^{\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 vat2hl; tn qu6 d:1ej5to the outside and uaqld6h tn:;t2j51 veis 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 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 snv 288j opn5vn when trying to adjust two strings, one of which is sounding 440 Hz. How far off invv2jn 8no 85np frequency is the other string? ±    Hz

  What is the beat freqyf-xp0gp0gg6 ut -6 pb1fd7;rjwlg8zuency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHzmovf 0, *( fpd/8au iywpu)o9b, while another (brand X) operates at an unknown frequency. If neither wh/fof ub(0wpadvyo)9 ,p*u 8m iistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produ -pgzcap bi2c8 lq),g7wg:wb-ces 4 beats/s when sounded with a 350-Hz tuning fork and 9 bea 8g gw -w2czbgp),lia-qcb:p7ts/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in on ye) -g(/212qrfmurpv z4aj 6)kyoy pye string is then decrymyz )k(4o) y ep-yqgv /2 f6uprj1a2reased by 2.0%. What will be the beat frequency 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 middle1gzrq 4g,s40at0 ibtk C (20ba tksi,q4tz4r01 gg62 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, 14xypfo1ij p8 5dp: szand C. 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 psipzxj:81od 45 yfp1sounded 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 ze7wp ig 49p skii) 5r*5,baffm apart. A person stands 3.00 m from one speaker and 3.50 m,p59se 7kw)4zi f i5bigr *pfa 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 at 132 Hz, but a piano tuneq2 4wzi.yqt r7r hears three beats every t 7r2zwqq.4yi2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats p/,n 6z dbqm wakxzb o0p3g 2;3v/by-u;2ler xber second vxoula d/ brbypq ;ez6bgm0x2/2 3-b,zw3 k;nwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque+:wpff t1 5gzency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a 1fzte+g:f5pwspeed 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 aakf iy5x9 o*j4 fire engine whose siren emits at 1550 yxjf94oa *ki 5Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequll.txo ;9s:t+:a8hni t .upxeency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s xno9ut+px h.::s.;ll t8aet i 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 frequench43wh* wxge i3 m-fdq2y 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 frequend *weg-wf33iq2hm4 xh cy of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ul84i;wfjwl5za ys3q r5 trasonic sound waves at 50.0 kHz and receives them returned f8 fwjar5 wiyqs;3lz54rom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emypl4b+ o96eou(v tvf5 6n bss6its an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in t(ev 6uv6lys5ot o nf4b9s +b6phe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on hjd -r-ulk5d-ic fo6 d.k9q-v a moving flat train car-u5j q-d 6olckirf d.9-hv k-d at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves.;l2 )h9j6uzii bn+lpqcqhp2 to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flol2;uhh+ zjq)pbn 92 ci. lqi6pwing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fl -o5bpaxzn ,+(y3 mlkna, kx/requency $2.25 \times10^{ 6}$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 soun ;mbx(;9; fjryg7 1fyemr/avyd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear w(fy jgaxy9myr;f 7mr 1 /ev;b;ho are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 20y. f6n,lyl /yabwr7) p $^{\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 Mac7(zs*uxu5l(kf 1ty u yivq/ k1h 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock w7z x1fik1k/*u tl5((yvs qyuuave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a pla ej1pzr:x57cynet where the speed of sound is only ab15pexry :z 7cjout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the/* aggx5c g/ga shock wave angle it produ gcx /a/g*gg5aces
(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 ;z;zi l n6ypxd lm4y 1*,qzb9v$/theta$ 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 abovz2z2 mb* ftm-le the ground flying faster than the speed of sound. By the time you hear the son- 2mbl2*fztzm ic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device6my x3t urt7lj x760sot gtg)+ that sends 20,000-Hz sound pulses downward from tht7m63ox ltsguyrjt7x0)+6 tge 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 minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible+wzsp 4hrbg0 p0n 7(s)yex)vy5jsrq. range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a soupa3ox *5o+r ewer pipe symphony. It consists of many plastic pipes of various lengths, which are ope a3ourop5x* o+n 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 the threshold 13dy:v- f*z: mzlbo:e h3knua*nsu(i. 4uawa of human hearing (0 du i* vmwuynn 1-odls ka3*a:4ez( z:3:ubf.haB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant soujy,j2+/m9o saq ;p7d vbm amr*nd level when an 82-dB sound and an 87-dB sound are hea,7rba/y *vq +ojm9d2 s;mpaj mrd simultaneously?    dB

  The sound level 12.0 m from a 42l2r(hsdkah5( uafg loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates eqhl sh2k (5f(a4g2ad urually in all directions?    W

  A stereo amplifier is rated at 150 W output vce :ghn1 q-n2ep1x8dat 1000 Hz. The power output drops by 10 dB at 15 kHz. What x 1ndnep2 -hgevcq81: is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices oc:l , 65+g/lsjg-nzhot4 uaw(-4mgi)pjybpm ver their ears. Assume that the sound level of a jet airplane yp+l a:-nm6j z(iw4tu c/5mg, ) g4l-hgbsojp engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, c/y1-c ff9ef m$\beta$ 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 frequenx cwz+ zlllg.;;)oy )ncy 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 fuy cb ;o,u+u8s 2to*y 9ebrci* q2w,nzsndamental frequency of 440 Hz and a mass per unit length uurbw b*ecsoc +n2* y,9oiz8 yq,t;2sof $6.1 \times10^{-4 }$ 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 r pn+,kh*n k/evibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level isekn,h p +/rk*n 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at onyc(uhsz 382nmcj8 n, re end and also 75 cm long. How mu 8njyhu(2crcm83 ,zsn ch tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ful/ufaih y2e)o.zh7 2j;i s)xinl 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 sourcstxo-zfr )gyj/m9/ g+ es. 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 mmr/gx)jyt/9fsg - z+o 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. The 8 bk;,6l kl:cf zuci;uconductor on the stationary train hears a 3.0-Hz beat frequency wc 6lbzcikuf8,u:l ;k; hen the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistii.67c jh.8r ncp *.u yj1krukle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume consta8 kji.rpku1*j 7y6nc. .r huicnt velocity)?    m/s

  At a race track, you cah:)hj j/ ruia2qql+* zn estimate 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 h rjzi:)qlh 2/*qja+u 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,j 4sc2xkvf9 nyy js:j3a 66sv9 sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Hoyfjk av429vj369ss js6x yc: nw long is the other?    m

Two loudspeakers are at opposite ends of a railroad cu 27+ pg /gz:d0ihnjvu0n* mpi o,0yzfar 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 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 panu ogfzhp,0ivd7ig2p0 j m/yu z+ 0n*:ssed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 lbtpj sj x.) no(c-u5)m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected (osux pc)5-nj)jl.btfrom the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whib,2c e*wpp2pile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave o *cpp2 2i,wepbf 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency tct 2iq2f/w9 asound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms longw2q c9a2/tfti . 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” (Fig. 12–38) was once used to send signals from one Alp m yva)7yri(m2ine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to creamyray 7(m 2)vite deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stannhb- jvu;2vn0ding waves, which can cause acoust-2 nnj0vvh ;ubic “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 “singing2gmsd9eg;jz1ckijaih (x q(/)+d py n3vc+4f rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the otherg n(ixpf)jm+3gs2( da y9 cjzvi/4ch d;q+1ke 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 humae k232.z prns0e 9xtwun ear at a frequency of about 1w pxr3n90e.t2 2skuez000 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.aa8zbcu*7o;a+i:m egynf4) o h (li -g An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plaazc;4 g fag(yao:o- mb+)8*7hunieli ne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is ) ls :c0dr,1rb wwkj;h15 $^{\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