What is the evidence that sound travels as a wave)lcl k o/i)9rfkq:qf/?

What is the evidence that sound is a form of en.l2q; qte(k 1uj,a) jde rp96t(ppy ngergy?

Children sometimes play with a homemade “telephone” by attaching a st:zl2 quk/fbyra 6n; w5ring 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. 12–2n6k 5 rwul2b/az:y f;q9). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fref g8md0u 2t/) ybgj-wbw 6g8fuquency or wavelengtw8f8d6g 0j)-wfu gbmtbu/g2yh to change?

What evidence can you give that the speed of sound in air does not 1pqv5.w3 vic mdepend significantly on fr3.1pmivwc v5qequency?

The voice of a person who hasj3ri /cmre q90 inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgza4ny- r hgtz(ld...gh9 9sd4e*tdx oan pipes?

Explain how a tube might be used as9qe -d,2; iutte5wy kq a filter to reduce the amplitude of sounds in various frequency ranges. (An exatwiq52q e,d ;yt-9e kumple is a car muffler.)

Why are the frets on a guita( i4 pwi xxu:dypwu/,+r (Fig. 12–30) spaced closer together as you move up ti(u,dxi4u:p +/ywp wx he fingerboard toward the bridge?

A noisy truck approaches you from beh t1,0e q,kawyi. b5wubind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenlq,y5,uk.baw web 10 tiy “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 “inte 5kn y3r70ey; qi,gyygrference in space,” whereas beats can be gi5, y ;7 0yyq3regyknsaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers asw(x j:p .h6pnuv5* 7pf lob/o6lh/wwere lowered, would the points D and C (where destructive and conspl7ln/hp p/(hbw6f u6woo5x* ajvs:.tructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people d 5jy,e/(wzu hzmzo03wy7 7zclu m8v/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 electronicallyuzczw ,m//z(z3vy5 7u8dejlmh yow70, 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 . ..c6k(er g- xr2qni)cw wvnbwave can be thought of as a superposition 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? Explaien(wkw ivgn b-2. )..crq6c rxn.
(12-31)
(12-18)

Is there a Doppler shift if the source and observ )c0sngp s51q+ezy6ezm m u9c48w xdt5er move in the same direction, with the same velocity? E) 9ewydm80nmz1g+sq c5 pcutze5s 46x xplain.

If a wind is blowing, will this alter the fr)z xgn :j(6whzequency of the sound heard by a persgj) (hzz:x 6nwon at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of q0v., s: fgr2qelv+via child in motion on a swing. A monitor is blowing a whistle in ,+e vr qf2v. v:q0gislfront 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 reasoning.

  A hiker determines th-nomuo4 y*u cs-c ;p(me length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. Sh-ucono cy-(mp;s um *4e hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the9 1)skcv x zanvr;7m8w echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this poi89xmvz7r1 ns;c w)a vknt? 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 wavelengthsk58 f j8esu*j59xwmqi in 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 fonlh2 ,9zgp)3u fvmf0tggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 1hz mgulnf)23 pvt0,f9 2–33). 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 splash it makes when strikinhm nw(ckm oj*8)0:zz kg the water bel): zomn 8wck0(jm*kh zow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear w klxbv(,6vf 0afy9j: *t3aaqto the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in tha3abf k6,0( :f* ayvx9 qvljwte 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 over one milev2+audn (p*m)va7e d s of distance by the “5-second rule” for estimatiev7 *u )(+mdpsavadn 2ng the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thtnb:vnb7(s8 tc5vew)e 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 soundiij *-lu4sqta/8 oc9n whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously asm 6rm*a2m0ypu w09zat a certain place, what will be the sound level if only one iurmpzma *sm69ya2w 00 s exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dis1qrpl 9ay6zjsie2 k6 9tance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wouayks 6r pe1il9 2zj96qld 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, ww qd6zs:l;zkv5khf l5*;va m ;hereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? ;5 saz h vl5m*;q;f6lvkdzkw:58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outp -9m3poz*onpk. ow :j hlaw1v)ut of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads rough: *nmwol1- 3w. vahojpk) pz9oly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave str2it 2 72dpp hu+rs,uoyikes 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, ww/ib: hf,m 5:c xfu+rmppy(*phile the more modest amplifier B is rated :f,/bypcwmxfuh m i( rp*+p5: at 40 W. (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 dB when placed 2.8 m in front nvbto (e9xv4u/y r/,d of a loudspeaker dt/eu(xvvy,n9b 4r /oon the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What itg60 k17 a,fnak+z ljis the ratio of the ampl,i+fja nkazk017 tl g6itudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is f ;fh*yz8();y zllutw *, uqjgtripled, (a) by what factor will the intensity in;glzwyuuf , zqf 8 lt*;*yhj()crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal disp3,snq +gaby/k lacement amplitudes, but one has twice the frequency of the other. What is the ratio of their iy s3/ k,b+anqgntensities?   

  What would be the sound leshxwzui2o/y m0cmv y() 8fg kx+ )-x2vvel (in dB) of a sound wave in air that corresponds to a dis2)ix8+(2cvyyomkg suxx0 h /m wzv-)fplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 10p/ws+yjw mfk2 xv-89w0-Hz tone that has a 50-dBysm8xpw9w2 +/jf- v wk sound level? (See Fig. 12–6.)    dB

What are the lowest and highen ksqot 4/h q(,a8ukchh 5xg.4st frequencies that an ear can detect when the sound o5qh44t/xag,kqn(uk .h8sh c level is 30 dB? (See Fig. 12–6.)

  Your auditory system can acnfbg1(*licf x r5kbfj p:)v4. commodate a huge range of sound levels. What is the ratio of n( fxc5jbri)vbglpf: f.k* 41highest 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 violincx8ua9wa; w: vb+*8 l5u5qa)v hqbqt79biqne has a fundamental frequency of 440 Hz. The length of the vibrating portion 58u9 ti9)v5hqabq:q wl*+abceqv8 bu nxw7a;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 tu)o1bfk d; ji ,,bn:a18*n kcwak1hu jhree audible overtones if the pipe is kf ubdk oc,u1wh ji, 1jb;n8)akan*1:
(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 blowin1;shbjm.ty l(n( ;drp g across the top of an empty soda bottle that is 18 cm deep, if you assumed it .bmljd (1;( yt ;nrsphwas 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 oriqe6xau pgt bm2p.5h3 uvt-,:k1r,n ngan with open-tube pipes spanning the range of human hearing (20 Hz to 20 ,p,tb ptv6 ki 2 3un1u:anmrg qx5-.ehkHz), 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 thbb23lu8ibq /+mf z 2wgird harmonic. What will be its fundamental frequency if it is fingered at a lengt+3igu8lz2bf/b bq2mw h of only 60% of its original length?   Hz

  An unfingered guitar string skw v1 r2l9r;;sd7ux xis 0.73 m long and is tuned to play E above middle C (330 Hz)1; v 7;xu9lk ssw2rrxd.
(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 C (2695x 5 mqnyob4,q0lk t+w/wcml 2 Hz) when the lc5+w,m 5q qkbxlnt09om 4y/wtemperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20uj1cw f7ldz9 5rlkg/bmi81* x $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of t)q+oo * m3megohe flute in Example 12–10 should the hole be that must be un m+o*oqe3 mg)ocovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 61jcxp ldt/ibs8 s0s ,(,6 Hz, but not at any other frequencies in betw(x8/lip j,,s s s0ctbdeen. (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 opezd44mp ;icmfs7w+p 4naky) ,k n at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 H; mfmpwcd 4ik7psk44z)yan ,+z. 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 mzzu p,so* u99$^{\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 audible range forar0d uv;.yxl+/ q1xn j a 2.14-m-long organ pyv qrjn+.0xd;au1lx /ipe 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 o c:1ki8p ,wwinpen to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12k cpnw:1 i8i,w–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust db1 *8bf5(z w40nybcbr gkc- atwo strings, one of which is sb84-51 bbyccfzgnwkr ( da*b0ounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat fredtv, *iomc7e ,quency 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, while myd2t(9gd.hi *hrk qde :.b)m another (brand X) operates at an unknown frequency. If n2 : m(i*ddeyb.rhqm)g . dthk9either whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s wh( g(t )m4xkxy+h.x5bn efz)dhen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Ex)mn)g xh(x5 +fzb4.(yxtkh de plain your reasoning.    Hz

  Two violin strings are tuned to the samn n) gx;ax6- ljcwe7-le frequency, 294 Hz. The tension in one string ix6 nlw cjg7a;)x nl-e-s then decreased 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 ea/l p js8i4 vjlurun)s;bi.z(7 ch try to play middle C (262 Hz), but one i/l (zl .pi unbj 7)vru8is4;sjs at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A,j u+;6sien7pukevp )8 B, and 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 sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible whe6ev;7pniu)8es +ujkpn 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 f ng0jib0 mwc95rom one speaker and 3.50 m from the othergmwcjb9 0n i05.
(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 artcw n5(p :ov(ly /qej0k* q mo,1xt2*kehx0eqe supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequenq eqc:5,2hlv(m/ kxpj*0w (y0e tet* 1koon xqcy 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 ofpc*1 s, i 8i5tvwgjxe3 mgj:p0 wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume m:i0epgj 1g*3 8,xsjw vi5pctT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sireng3nokm pkfl10ehe 4 7, is 1550 Hz when at rest. Wha304eeg khplm,nk 17o ft frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if mcmhl*e u,s+9a fire engine whose siren emits at 1550 Hz move+h9cme,*mls us at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift imkx kw3a5u p6;n frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two f53u mwkpk;xa6requencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is q .;avy4jgo.y )g wb( m9s1.f 1dqmliqat 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 frequvd9myiq4)yq gjgf 1l.(qsoaw.;b. 1mency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 5l-qq) kr9 f1e. kj3rrf0.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sf kr1q.rr q39l)-kjf eound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an u4 h w1qkc2xa(/ghnm7eltrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in tw/ n ehq(g1x2m kcha74he reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exp , r2j-njxvyt;,1xjcoeriments, a tuba 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 heardrj2y njjv otxx c,;,-1 if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measrn+7cy0 +fgifure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and g fyf+0n i7r+cthe speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultravi1-y1v7+s6t tvzpe jsonic 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 velocity ij uvj5e 0svyto/8 6;nbs 12 m/s from the north, what frequency will observers hear who t ;vjn/06u5osjv b ey8are 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 gjr,sab/ *c*e d; f-idmoving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the spe4c++d tfob7i eed of sound is 310 m/s (a) What is the angle th+t 4fbe7o id+ce shock wave 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 atmosn1 c1c+q.l ) vgks(gpxphere of a planet where the speed of sound islcvc)ng1xk(+p 1.gqs only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s stxbrez,l(o :8i7 mh7*o5uxrqorikes the ocean. Determine the shock wave angle i h8( 7 :exix lo*o,7uqrzrmo5bt 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 fw noa+u9 w8-sy*4kra$/theta$ 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 exa3u8u: t oner6jctly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travje68u3:u ontreled 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 2q/vp*c9 a.rag0,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulsqp/cg. 9a rva*es (in fresh water)?    s

  Approximately how many octaves are thez5lzvcwe, 8a.z b77u gre in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sy o)vbjfsh k1r kxw 28udt,9.,bmphony. It consists of many plastic pipes of various lengths, which v,1fu xk9to.b w,b)h8k2rs j dare open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the tt/0dxs4))m3 y gyox ovrz6a/chreshold of human hearing (0 dB). What will be the sound level of 1xo ty0z3o ) 46/rc/)s xmydgva000 such mosquitoes?    dB

  What is the resultant sound level when (jymdaw -7mv *wd8j3o an 82-dB sound and an 87-dB sound are hea (d8w3w od yjmvja7-m*rd simultaneously?    dB

  The sound level 12.0 m from a loudspeakeootx gei5 05l4 pv*ugo z;h l,)n.k8zur, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, as5zho) no.v4pl 0z,g ulk8goi uet;5*xsuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 100xfzo1): l g8pe0 Hz. The power output drops by 10 dB at 15 kHzlpxoze:g)f 81. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircrafm 4 )0j(,r2ood u8 cwf-xvjzzzmm/f 0ut typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 3mr x,mm uzj)o2z 48w-zjf0v( 0uo/cfd0 m from a jet airplane engine?    W

  In audio and communicatidywp,4g f (re3+d3 tt6j njin(ons 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 fbrrg(g-g)(k o q4lb;r requency 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 ao 6lvvj 8ath-( fundamental frequency of 440 Hz and a mavao6lh- vt8j( ss per 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 fille -y4la loaozso;- 16atk-pyj: d with water (Figyoz6 -lt4aojsk-la o -: 1y;pa. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one hs9k2tu*z w(c-vdjb) end and also 75 cm long. How much tension should be in the string if it is to produce r k( js-v h2tz9*)ubdwcesonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obseq9*dl-h s.pv h1 .(2xchtje hprved 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 500–1slz0j r-d 0 +rk2dnw-v000-Hz range coming from two sources. The sound is loudest at points equidistant from thkdl r v-+2zjwn dr-s00e 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 sound?   Hz

  Two trains emit 424-Hz whj4aod5gr yz*7-ooj u 5)ab7dj istles. One train is stationary. The conductor on the statia7o rz7yaoj* 5-j5dj bg ou4)donary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam tr v r3-2cmysc6lp kch 1xw94v3iain whistle as it approaches you is 538 Hz. After it paschsci r32km 16-x4 p9vcyvw l3ses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by liste- l7boja;n;2l 8nlcz ining 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 (frequency halved) as it goes by on the straightaway. How fast is it going? ;7 n8 zlijl;- ocbl2na   m/s

  Two open organ pipes, sounding together, produce a beat*u-yf3gnkdiuicolvb (5sp(s2 8i5c6 frequency of 11 Hz. The shorter one is 2.40 m long. How long is thei6* vi- ly p(5(d82iuuscn 3f 5kocgbs other?    m

Two loudspeakers are at opposite ends of a railroad car as it m uon9(- y2zw dk,ss0ohoves 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 passed him, a9yzd2sku,w-oo sh( 0 nt C?

  If the velocity of blood flow u8cq-mm9 8rrjin 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 from t q9umcrj m8-r8he 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 ajwq1 5 )anhsaoj;a+j abonz5m9r(u/: moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wno/aa5m;r915+uhnbawa (zjosj : )j qave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency s 3f7lr;k p cmt36u6bwuound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abo;7k6cmru36bu ptlw3 fut 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 once used to send signals from one Alpinec 5unq sb- om4b .mobdg:/g-(r village to another. Since lower frequency sounds are less susceptible to i r-gcdb /sq:guo.bo(m-b 54 mnntensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised b 9eql:bze8,e gy 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, a8: bze eeq,9glnd 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 7 :pnxy8wrmr1qo s;)p “singing rods,” involves a long, slender aluminum rod held 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 emm18);p :q rpony rxw7sit 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 frequency s4aqq4o3yy1 +eb( szjof about 1000e(a q+o 4s jy3qsyb14z 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 pru47hco2i)imocv6 6 Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? io74 hrvupc266i om)c   $ \times10^{4 }$ m

  The wake of a speedboat isvd wg x0q3v)s j7z:yg+ 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