What is the evidence that st;l wu8 xkn h-*dgh-58w3bkl nound travels as a wave?

What is the evidence that s+fps5bk4 . ikround is a form of energy?

Children sometimes play with a homemade .x)em2;ah wyu “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to they.;uxmh2w ea) other.

When a sound wave passes from air into water, do g(2n8l eds1r cyou expect the frequency or wavels18r gnl(2c edength to change?

What evidence can you give that the speed of sound in aq6-cc(t nwlmlo85y6 air does not depend signifi n8q(mlco lw5-66tacycantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Wtg 5lo.b8-n pwhy?

How will the air temperature in a roomk ew0;br. vn8c affect the pitch of organ pipes?

Explain how a tube might be used as a filter to redu17eicwkq.mge5qika vs2 lxo +23h ( .ece the amplitude of sounds in vac5 o.q+x i.71 ls ekev2hqwemg(ia23krious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar ( i:m*nm;cdyw .gpu,u i3l m26cFig. 12–30) spaced closer together as you move up the fingerboard tomci uig3y:mu lc.;2w6dp,n*m ward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it:6ox,k *impc h 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. [Hint: See Section 11–15 on diff mxo p:ci,h6*kraction.]

Standing waves can be said to be due z e vah+ean*)34ri7 mnvxd3v+(j rxu2to “interference in space,” whereas beats can be said to*idv xvav+ 7 xe4 nz2e3(j+mah) rn3ur be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were look v8)8ad(b2 bc /wm) hcwsgc4mcdpuf2j2.p5wered, would the points D and C (where destructive and constructive interference occur) move farther apart or c(k8c5w 2m8)uj /cpab b d2hc)gfsm.o4cvpwd2 loser together?

Traditional methods of protecting the . :neb+nds)rs hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching th+en:.ss n rbd)e ears?

Consider the two waves shown in Fi, j bbjsoy1td60k *nx;jv+)iig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whicbokv sjx j1n0)yjdb6t* ;,i+i h of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in theut s62ppwa9vnt6 0-vr same direction, with the same velv6ps60t aw -nv92 ptruocity? Explain.

If a wind is blowing, will this alter the frequency of th83l*az1zds qpqr 3k5ne sound heard by a person at rest with respect to the source? Is the wavelel1ksdzn8qpr3 z q5* a3ngth or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor5pvg-mov gtq2x;6(g )btojxw2s g53nt2x e-l 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 souwt 5);t2 q5-tgnvgpov -bel2xgx (2j s3x 6mognd of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the e1 pd(w 0t8;gs .wpsyevcwl,x0cho of her shout re gpsve8ls;y. ,0(1txw p w0cdwflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship28nl;24fm qcspm- y89crewrr just below the waterline. He hears the echo of the sound reflected from the ocean floor di fcpl;8mq8w9 ny -2cr2er4mr srectly 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 air akf6.t m4hbij)z /2i mgt 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 ocxp0x): tng,8ly1iz k f tuna on a foggy day. Without warning, an engine backfire 0t l)1nxgy :i czx,k8poccurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it ;pbsm k92r 7dbmakes when striking the water below is heard 3.5 s laters;bdr2 7 9bkpm. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the 39gj6z3w*y/c e tjolhconcrete pavement. A mome / zj6ct* he3jw3y9golnt later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dis ygm:fd/*+nue +z a8i+rn bzf+tance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30if gr n8+u+ dy+*z+afnze:bm/ $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound.1dfg:m 5cigsh) x+v t 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 35r78hvviaw 1p kk hpyy+mw0:a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneou,c9 sc((-p8ksc yl*(wupaq8 tmh: rghsly at a certain place, what wicwqpm-hc8kga:9c ,* h l (s 8t(su(yprll be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airqsg4c-oph* u- vk5j j:plane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensitiesjug-h ps:c* o5kq-vj4, not dB’s.]    dB

  A cassette player is said to have a signal-tof (i6-imav*dxjjom+8 -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 background noise fofmj8x*i+-id jv( o am6r each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from9o/,o. 4.bj nym-bvkhuzs vi; a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughloz9.ju;/o4mvb y s-kb ihvn., y 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 strikes an earda5r8f cq .th9drum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest n,;e2g6 kqamuamplifier B is rated at 40 W. (a) Estimate the sound level in decibelsn6 g u2ke;,mqa 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 f( .sl vuujrypf)//ype+ c3/ oxront of a loudspeaker on)u+r3 .ofy uv/plpecs(//yxj 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 v2a5:a+ g0yzre qco/k is the ratio of the amplitudes of t2rvo0 gy qk+5z:c /eaawo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a9yl 8vth *kan*4 cm1d.c k:cad sound wave is tripled, (a) by what factor will the intensity increase? Increase by a kc* v9k c4a 1dlthyadc.n:8*mfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves havee: stte .pl;qfubc61+ equal displacement amplitudes, but one has twice the frequency of theqtfel6:csbe up.1t;+ other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wav )wgulaeps.0 b b+4m*g*:rthae in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 gbw)a4p0 *s+rl:atumb* .h eg mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as o,nskfo*ilph 29cc o8y d ,amhcb6fm)g8x) 47a 100-Hz tone that o )a xk*mno4go hf8ih,s6,c 827l) 9dbcpmycfhas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detectw0qy9 2hf-v m(ay85 mabmhk. q when the sound level iab0hw8 hkaqv.-y(5mm f m9yq 2s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate:q/8ez y:jvc j a huge range of sound levels. What is the ratio of highest :jvez8y q:/jc to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz.ne0/m7gzu p32m axe( t The length of the vibrating portion is 32 c0ee( agu t 7zpm2n/3mxm, 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 firsn/ /k cl))u-b sqtkhd)f y+nl6t three audible o dqscu )ynkl n-+tbk6 /h)/f)lvertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acropl 5ox 8sx-87 oibqmz+ss the top of an empty soda bottle that 8+ 7op z8xmob-q lxsi5is 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 humglyiryt(m q;5b7ga+8an hearing (20 Hz to 20 kHz), what would glyrt(y+7mqa b;85 ig be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Whx pik, :oilj .d403ae.z/ bo qgt2(,4vbrtsvaat will be its fundamental frequency if it is fin/o,z 0t24,iqb.is4oe3j.(: dv xakt g lpbr vagered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73;o2 rp:jxyg bon8,l8q2l6 ltt m long and is tuned to play E above middle C6 y8l l2 ,tj otnbpqolr8gx;:2 (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ p j;s0)zrdb y)sipe that emits middle C (262 Hz) when the tempera d sbry0z)js);ture 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 26 bn )xgrwiq/ 5nl7mgkz89id/0 $^{\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 shoupxe27;5 klmln2q uqn5t w( n)w66jluxld the hole be that must be uncovered to play D above middle C at 294 ;6 k5pu(n qnejlt26w w)7 x nql2m5xulHz?    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 H)j4/-odth- g; rwqyyaz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe)w 4jy- ohtqad;g/yr- . ----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 bi)vn 0/g plc m9wgsbb-q(f3o5oth ends. It resonates at two successive ha b) bg0 if9mos/lncq5v(pg-w 3rmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 j9m)bf *zs; tju7rha 8$^{\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 for a 2.14-m- 0 kpro5tz+w dm)z0*vk.htmp5.he,j rlong organ pipezv5r)d, kp*rt+jkh. 0m5mzep. o0ht w 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 i:*fgqvc56x /sud k td-s open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the s v x5u:-cgt/qk6*dfdaudible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s whenb 2u wyk;t.a2p trying to adjust two strings, one of whic .2tap 2k;uywbh is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequencyq++r2i4z znoxoj9dhl 69xj0m 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 wzpkp j 2pzw4y,+8. :e8o qhra23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played sepepzo4, yr:k8 p8jpw+h q wa.2zarately, 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 350pxqtt5 269hhh-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.526hq 9t phxht    Hz

  Two violin strings are tuned to the same fc-u( l(5g /)z pofbsmarequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will b/u pb-sfzc5)g( aolm(e 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 playcb(gj q96/u q;bl93tnpiiis , middle C (262 Hz), but one is at 5.0°C and g b9uq/i9bii3 nc, s(j;q6ltpthe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 1oa74o 8jcbxm 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 c8o1a7bj x4o mfrequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stanzge+yo.u(pmu u)9z*. tc1n ovds 3.00 m from one speaker and 3.50 m fro1) g+9u.ov(*t e .uynuzpmczom 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, :dwbs/u bk* ywwm2p6b9hc8q:but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is w9 b26kmb:bh 8ys:q* /wwucpdvibrating 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 h0u am74 jm- s8tgt:buu/um:s2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T =/m:ujug-am4uubs 7s :tm 80 ht 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firerhdfa:*(o dc04 x 6odo engine’s siren is 1550 Hz when at rest. What frd6d:0 chxfo od4r(o a*equency 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 )y jq3q/ d,,sjhjf*dy you detect if a fire engine whose siren emits at 1550 Hz moves at a speedyqj ,dd jj)fq/ ,sy3h* of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2005:r 2ylzs(xd c0-Hz source is moving toward you at 15 m/s versus you moving toward d2r(5zysxc :l it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency hqt09wcxhmh7r1:g csk kk itr1m0s2/ /orn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency/9kkt1 2ks/rm0 7cqshc imr0:tgxhw1 of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them ret p8uwuj f6a,d/ l.ccn(urned from an object moving direc cdujp6/uf ,c8la(n w.tly 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 emits iy ma7vopt.i 3u3o2x0 an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hem.xp2u37 tiyi ov a3o0ar in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pla+vxriw ji v:/2yed 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 stati2/i:xw jvv+ iron. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter u v;h a2p3k10ohhiflp(ses ultrasound waves 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 154po20hka;vh31hl if p( 0 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 ul+ kho/0lfmb/ ntrasonic 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 winm.i/n;b k+(;cua k zped velocity is 12 m/s from the north, whn (. kubpm;c;a+eizk/at 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 sq95bu zq 5/rti6h)m nwca -t/kpeed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (awod ix0,+d:y: ska:3 ,qhe ybc) What is the angle the shock wave makes wyx :y+ wiso:e:a3d0q, hcbd,kith 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 planet where th0a)rzkq,f2nbl1( e t .qog/v3ztu )i ge speed of sound is only about 35 nr0 go ) fv3a1kbge2u(zl.,/tqz t)qim/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 shock wave anglecfn(e( 8gzl rl ,h72wz itg7c (8hz,l rwel(2fn z 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 - q*w85r ysqhhdt4oa9f1prx;$/theta$ 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 abovey.( 9ciop.z bf 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.yo9zi .pc.(f b 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulse,p 34gcvgy 8n9.axggl s downward from the bottom of the boat, and then detects echoes. If the maxim4 gngy lg89a,v.pg3xcum 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 octadt:r n +ebnll56dw71d ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display caln*9h e*. b:9b h zhq0wv y+pv-kylbl.lled a sewer pipe symphony. It consists of many plastic pipes of various lengths, which arn9 ple y9kbv:0*.hv +zbhb.q*w hl y-le 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 ttsgza m :6xy((o the threshold of human hearing (0 dB). Wz (ma6s: (tyxghat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sounde u5ixa zedtj-80tq 9/ and an 87-dB sound are heard iqtajt uxe e59-08/dzsimultaneously?    dB

  The sound level 12.07m11, k7phj:/ j:btabjn hjmw :vmxo 5 m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radih hbm1mpjx::77ownb5m k:j 1jvjt /,a ates equally in all directions?    W

  A stereo amplifier is rated at u7ul uz,f.e.)s/9llq q5o khdb o2d)i150 W output at 1000 Hz. The power output drops by 10 dB at 15u.sk5 )7el 9 u.2l , qoldhoqud)/fizb kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivff+c hhx, wp(l8 d5: qfr2nr3ve 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 wc ff5,rdphhxr(3+l8: f2 qnvintercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, th, bax-zitwbj.i95e+*b pmxb j/) 3lpqe 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 f 7j8h-pqym ty: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 b0+pqx4ew l-j + updf)aetween fixed points with a fundamental frequency of 440 Hz and a+4wadjeqp+p0)l f- ux mass 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 tube9ke9c2svjfj:v- *s bw 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 wf2: k9j s9jvbe vcs*-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 es+;c5q5nxh m nnd and also 75 cm long. How much tension should be in the string i qh mnnx+;5sc5f 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 u urno/8(n03r5vv shlas 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 wq4o - 5:yhkvdtone in the 500–1000-Hz range coming 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 -oydk5w v4 hq:minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductors9x w1m1 szueb nv6 x8cz)q-;y on the stationary train hears a 3.0-Hz beat frequencnvqzx csxsz61;e w81y9 m- ub)y when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After99ozy zr* 87i8mhax lp it passes you, its frequency is measured as 486 Hz. How fast was the t 9pzh8r9y8o m*l izx7arain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speedm7to *gh3n5lv 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 (frequency hav3 ot* nmh7g5llved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat rww);4 m819+0*pbbk; lxns pdpkd mytfrequency of 11 Hz. The shorter omd lpmsp+x*y40w) ;krt91k nw p;b8bdne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car r,/hui 9h2ow;xose5 bz3-ja fas 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 heari3xs9heo2 uhwaj -5zo/ f b,;rs the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bea.lakde)/ahls9ld--p d7l +bb t frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflectedp h+bl)ds/9l-d 7ba -allek. d 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 isyrnb b-k):70fo0 ktzk flying toward the bat 7 )yktb:kb0 o0nkrf z-at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a e k z:;ws*p. ftouc)u:moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo frzw.sku c ftupe ::;o*)om one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sign6xj42m -ijz-l jyc4xxals from one Alpine village to another. xjl 6xy-i-x 24zj4jmcSince lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can beqb) deixuerz 00g9*b( compromised by the presence of standing waves, which can cause acoustic “dead spots” at tud(req9z) 0ebix* g0bhe 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 “singing rods,” involves a long, sleejvl/ o,*gw1u0uz h /snder 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 emit a clear, loud, ringing sound. For,jszgw0 ulh v*/eo/1 u 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 humanoxgib6pwr69s.0 tlmv6q. cg -wkb; d/ ear at a frequency of about 1000 Hzgsr wg-qo tl db.v6 6; ixbmw6k9c/0.p is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An xg8i+d7grhgpal 8;(hja( m 0oobserver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whh0hr+( ago8(l g ;a7img8jpxd at is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isick j/avjyn +t7 . i4i9(mzat- 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