What is the evidence that sound 9 2(a u7fl 0udjuc7fagtravels as a wave?

What is the evidence that sound is a form of ener 6yk5gzv -3bn wpv6+zox/qt)igy?

Children sometimes play with a homemade “telephon t naoazp1(6f4e” 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). Exn1t pfza 4ao(6plain clearly how the sound wave travels from one cup to the other.

When a sound wave pa*bj z1x/xi/aisses from air into water, do you expect the frequency or wavelength to chb/ *j xax/zi1iange?

What evidence can you give that the speed of sound in airs9 e8h.h-.ckfq6vq ak does not depend significantly o9 ..fehk- h6akvqsq8cn frequency?

The voice of a person who has inhaled helium sound2q.ocd*pm ) nss very high-pitched. Why?

How will the air temperature in a room affect the pitdi zrpi 2i:7)uch of organ pipes?

Explain how a tube might be used as a filter to ikx ,v5idn9i3n/4*x-l kd )flg0dj ao reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.d09li,aj )/lnkf-3* kov dxgi45nxid )

Why are the frets on a guitar (Fig. 12)k 9,gn mmtzc);nk/1vpd*o ai–30) spaced closer together as you move up ak1odg)i; ckpzv),* m9nn/mtthe fingerboard toward the bridge?

A noisy truck approaches you from behn3 h v5mcs.y3oind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hin n.co35smv3yht: See Section 11–15 on diffraction.]

Standing waves can be said to be due thitcy. u59s2v k: m4ldo “interference in space,” whereas beats can be smtd 2y:c.i9hs 5kl4vu aid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the po-a(xu/co1;j ;lpdnr w ints D and C (where destructive and constructive interference occur) move farther apart xpnu l dc(w/-ar1; j;oor closer together?

Traditional methods of protectnlr i3 c,ktu-k,pq1j3ing 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, headphonest1n, lijpc-,kquk 3 r3 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 cg* nez5m:q9y3tas y 58jzrf+a an be thought of as a superpositiz+eqm 59 zgt:s83*jrfan ya5yon of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourg+tj7re7quyb u2+w1j pgere )1, gjg8ce and observer move in the same direction, with ry2pj7,gjjq7g g)gt8+re ee w1+1u ub the same velocity? Explain.

If a wind is blowing, will this alter the fpiip2 t(4n fcl/ev/2nrequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chanlfv2 /4p2einc/ipt( nged?

Figure 12–32 shows various p fde2p29 bq8rliiw,1vositions 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 child hear the highest frequency for the sound of the whistle? Explain your reasonq1ierbv,9f2pdw 8li 2 ing.

  A hiker determines the length of a lake by listening for the echo of her shoutse zs3td/ f:olry9k77 reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aft:l yke/s37 zr sd7f9toer shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship0phqd8ex ; jo4 just below the waterline. He hears the echo of the sound reflected from the ocean floor directj oqh ;px408dely 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ra8 8ktojh13p 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 tuna on a foggy.s 3-)oyz;( ewfluralsy w -,rn-fl;s day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is l-f.nys,y );ow lerzsw(lru;3-f- asheard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whe2s42 2tg ;dk5ndtiamen striking the water below is heard 3.5 s later. How high is t2kdi2m;n tg2s5ead4 t he cliff?    m

  A person, with his ear to the ground, sees a huge *km.5fdw f 00 1atr2 ln*d8esbjhfqx2 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 away8ra *.bxj hffktemlsw01n*5f0q 2d2d did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of d ivbn))ktxl.l+of u7gqo ./q)il k,i)istance by the “5-second rule” for estimating the distance from a liqtvf)kob))ogln xi l,7u/ki)l+ i.q .ghtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the 3hdvgj 6dw;74pnz wn;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 ofoh+pz3 yno8. av t5.xn a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslyd. nkm0uyag ydlf:4d: e: -n1c at a certain place, what will be the sound level if only one is exploded? [Hintadnm:u gnyl:-4d:dy ck0 f.e 1: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally 9 oc08v*4ly oxq 9gymjnoisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound* oyc xm98j o09vg4yql 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 dB, whebl4klt71 pp l:r;74 hemb9wqxreas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgrouxl97t p:r4ph7mb 4lelkb qw; 1nd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a personfp n7),+vsb:jdeioj s4l()h) k :dw yb speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over s :f wj k bh)4dybn)v:ps+j ie)(7,olda 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 strikesv)wvzs( 3l- ngvijmdvb2wy3+5 0.gh a 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, while thecdi we hhe):c5/,u v;x more modest amplifier B is rated at 40 W. v:h ,dx)chw;ui/ee5c (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 d.nlulznf(.q dd.dpd; ;q q.6tB when placed 2.8 m in front of a loudspeak6 p;.ftnd. qquz.d(.ldld; n qer on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically pmf) wkzkhz+nkr5-cc6pv +2v 58,tlndetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whl,6pv +8ckfc knmv+r nwzzt 5k2-p h)5ose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by 2:,mm:fopyq+i3+isjd r ;1cjo8qid nwhat factor will the intensity increase? Increase by a factor ifomr81:yd+qq: dm pij+ co ,2n 3s;ijof    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frad erevz; 84 .3od6za.wr s8uwequency of the other. What is the ratid. .ozze raad4werw u3;s88v6o of their intensities?   

  What would be the sound level f;gagbgsifi;*8g( n 8w3d0ps (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air moleculesp8a;gfb gdg*i s3 8(;n wig0sf of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem put5ve.;qt : 6ecf2- )pcivxxas loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 122.- ctv6quvi;p: px)xtf e5ce–6.)    dB

What are the lowest and highest frequencies that an ear9yl: .b4 njkfmyhf,ybi7s *3 2lp bk7g can detect when the sound level is 30 dB? (See Fig. 12–6h3blfny7bk2p *l,k4mg bi .j9: yfy7s.)

  Your auditory system can accommodate a huge range of sound levezl4x3jtrm2 *q ls. What is the ratio of highest to lowest i2z3jtl *4x qmrntensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has +/ /uwgbraxi0bba jb--6fko *a fundamental frequency of 440 Hz. The length of the vibr wb-bgar *ibo a-6+0b//xkju fating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threp7v6ug:bgglwadr3cn i4 +ey(8)sx.sm dxi1 )e audible overtones if the p.g4l :g1rgxi6b e ncdxsyp 7vw)im3u+8sd() aipe 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 frequ7 lss(y y8e vxnn1/ la9a)uht1ency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed t9ya t8x (ynln hs1l)7eu1/svaube?    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 spannie6es31e1k i1r.vyl 7fmyrmf c.+c)zeng the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths ee zc.myfekfrc31)s+ r7im.v l1y6e1 of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540r cs5b)h 2.6.he mkfgv Hz as its third harmonic. What will be 6mf2chgbr)s.h5e. vkits fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string 6a il4ifvf*w7is 0.73 m long and is tuned to play E above middle C (3304lwvf* 7af6ii 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 orgayj* i:dcv5 :- 6)vc1ufhvcfx an pipe that emits middle C (262 Hz) when the temphc a )dyvvv1c: 6fi:j-* u5cfxerature 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 at92ekl io dw1)x 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 12–106 a8wj*o .dh2de*ml ;law7 ttl should the hole be that must be uncovered to *;7m6t8w. a 2ljaetddhollw *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 6e ub hf*p3g4 w74gh)7v; xxymy16 Hz, but not at any other frequencies in between. (a) Show why th vebhhp4g *;m )xw4y37g7uyxfis is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. s-- :yhjirvfvit0* *qh,t9l s a0-micIt resonates at two successive harmonics of frequen*,:mji v ht-yi t-0lif0avcrqs*s -h9 cies 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 szpej 6maxd.x; zy -b/ :8cx(c$^{\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 8 /y)b-qka nutaudible range for a 2.14-m-long organ pipe at 20 n/ay8kq -u) bt$^{\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 outside a1, (r w/i(ltz/oukwqk43ts ft nd 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 your answer to the informati/4,kti/ tfqut3(w(lro wzk1son in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying tolho f/ 6l:h7mi adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ± l hm 6f7ho:l/i   Hz

  What is the beat freque 2nylb +k7im .nz,os5ancy 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 kHz, whil3y,u6tibg(jtz .f.d te another (brand X) operates at an unknown frequency. If neither whistle can be heard by.(.,gttfdb 6iuyj3 zt humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350) cdpx8yz 6b.rsw( 8k*lnt zr0-Hz tuning fork and 9 beats/s whszw. )(pn86bt*l8cy rr z0d xken sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are og0l 1 +g ;/m.hkykx uhqqq4s4icgk59 tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togethe khs4k;qlqhgoxc5qu1+0m 49./g i ykgr? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tryhoh5(io qe 3k1 to play middle C (262 Hz), but one is at 5.0°C and the other 3(k hh e1qoio5at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; mx ).tb id, lbf:j 7hc++yed1bwhen 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 possible when A and C are sounded.ec),t+7bj+: lmh dbd fx1i yb 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 svffa8inc95 pvs2j.e 3tands 3.00 m from one speaker and 3.50 m from th892pjvaf e5vf.cs ni3e 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 ati)wrr7xt,5 */xbbcb1b d2 zld 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played togethb)w bd1c*7t/db2xrixr l z5,b er. (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 beatfrbhm9 .:qr80yf hbg 9s per second wqym.f h0 :rbh98gbr f9ill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency kl;cstxz9/49c( ectk of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed olx ktccz(s 4/ 99ectk;f 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect o5 ; k4nj5,7rfi2fugxos 1kmuif a fire engine whose siren emits at 1550 Hzj5xsgifk721r om;,54f uuonk moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at0mcu h b 9r to ,)4eap4zm-v0zm0ye2fp 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly tm) ,umvf0 hzcpb9m-z a0e40r t poe42yhe 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. Wu:7mbhr0 -tlzlengt2/ nn-.i hen one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assu0ntbi2z n.e: g/ -llmur hnt-7me T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrason (pf2 2zfq ep,w7j )/xzxb9kyqic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s),7p p9 x jfbzxq( qfz/y22wek What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall( sy3l2dvog ,6 xwrlu(6 i1v)wdg pp.q at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 306d2i3u llrgv6dp(vp 1o .y,swq (gx)w.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubw.yow1wr6;nh - dy le1a was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/w.;y 6 n-11lyewwdrhos ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speed +fi )im-id ph5qs9:vds. 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 frequencyq fv5+dhi9pdmi :)i- s if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequ o7eo9 9 f9mor06jrolwency $2.25 \times10^{ 6}$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,,d boyxqxrm3kq241eb m / a-i wind velocity is 12 imq xod1x4 kba2q3,-y b/,m erm/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 moving on land if its speed bv4o6zauv gj)g(ys*aj hi9g r/63s9 uat 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 is 1jp,jmo )uy o8u0x -nzqd(7jk the angle the shock wave mdo,muj7y8-kqx)jnpj zo u01( akes 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 atmospher1 eiav5b 0t8nie of a planet where the speed of sound is only about 35 m/ 8ben1tiv50ias
(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 shah7xkkr--++kd .9dllnn bu y3ock wave anglel3kd nbyxlk+ 79n-d hrkua-.+ it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 2* y-c d78 d,vdslywv4rezk/m$/theta$ 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 ababf ;m3i*b f9eove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determmaeff39 *;bbi ine
(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 20,0091xtp;5c+gvk-ffr4b1wf 4t, ypm vp m0-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which+f1mwm4 x cbft9ypvrv 5pk;g4,t-f p1 it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are thv2u5qr( n brq6ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a diafmo d m/w6ymc;o7)y0splay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on ;/ay0oc 6ow) dmmy mf7both 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 g b)7f .*ndc/yak2 v8az jfzy,the threshold of human hjava.dkny*b,fzg z)f8 y/2 c7earing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and mt:d91v jf2ro an 87-dB sound are heard simultaneouj29 fvrdo1: tmsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the openw.1y24ojv ib o, is 105 dB. What is the acoustic power output (W) of the speaker, by.v wo1joi42 assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 vuqa9d ) s(z, y.9bb(d xlmb3c:ce dw8Hz. The power output drops bye9 z9c,vxqdd:( db8(s 3mcbl) bwua.y 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. A bo0fc2t-jr rldkh /s4rbx2 6jv9d,0jssume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 3 2t9 j xb,of vlrjd06hjrd 4s-/bc2rk00 m from a jet airplane engine?    W

  In audio and communications systems, 7;di lomxh8;q s/2qobqz3c da;, bo/vthe 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 fres57j)s ewh fiu sbn0/h6-mcy( quency 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 vdx 7i6,9 jstea fundamental frequency of 440 Hz and a mass per unit lengthd ti,vxes 9j67 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 fzbz3 r8z; wp.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 lez.zzbrw ;8 fp3vel 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 2c9h*p 52ae2th n6 g ebho8.sxh.10 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 to produce resonance (in its fundamtceh5xp.69 28os*eagh2hh bn ental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was ojj)vtr;me:.uge98 q-np wo y*bserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range c.j)lhvafp93 :sz1k3t dbw8l9j :o vhcoming 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 other. What is the frequency of the sljh1t)9c:l d :zwbv s9 8.kopaf3vjh 3ound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the vdsiv stsw q340+/w;2i 6ygcjstationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spe3dvjwy0sgw;vq/4 i6+2ts c si ed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 5380iu 0yj5t.b+(e 5s wmlgz ku)d Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume te+ u)05s.zmugbkjw( iyd50lconstant velocity)?    m/s

  At a race track, you can estima8 zmx)suf*9wr cy8 tn,te the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (n 8r*utsfzc)y 98mx,wfrequency 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 11 H .ick3gsrt )+zz. The shorter one is 2.40 m long.ci.3r+) k tzsg How long is the other?    m

Two loudspeakers are at opposite ends of a rue mv*vr(tw 9;q1wp 4vailroad car 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 v(u;ter qvw 1*pm4v 9wcar, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow 0qtau- k(uy5by5 f(mcgo8b :zz22i iq in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were direc2 g8ikoycmb0ituf5(quqz 25 :y( z-bated along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward g/.wt5s ei ft3the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wha w efg.3st/it5t 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 sound pulses as it approaches a m 55xh*c 9xum dl8:wbcroth. The pulses are approximately 70.0 ms apart, and each is about8c*xw 9l 5dhxbcm: ur5 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was mn gvi;*hpdcq 5u :dyq/wti(; k56v a(once used to send signals from one Alpine village 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 qgmy v /n 6(p;:id(icaw5h;tdv 5*ukqmust 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 sgi( ee jp1lj1gq. al6:tereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing wavegq agieell 6:j.(p11js in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumin7 pn9ff ik+a9zh.w5rw73eu y mum rod held in the hand near the rodwymw+k73furi. fn ep9az h59 7’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequeno oh; m)objnphe3xc.f1w.5m: cy of about 1000 Hz is ph 5o.me1nbmowh:)focx3 j .;$I_0$ = $1 \times10^{12 } W / m^2$ 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 2.0adiorot1t; 67. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What67dt1ao ;irot is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboau* wio *z,rr3 2rfrm5bqn (j(vt 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