What is the evidence t ., *7mj kiipit8,hnmywj)4 zthat sound travels as a wave?

What is the evidence thfeo d8rnnq8+ +at sound is a form of energy?

Children sometimes play with a homemade)g, b(38k4s9c(omg ybz eux xb/ycu6i “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 tsb)cyu /(x(b czubem3xyg8o6igk9,4 o the other.

When a sound wave passes from air into water,26)m p l149w)w-yd,dprij r: f owwtpu do you expect the frequency or wavelen pp r)tw w-m1dd:j26o)9 pyilfur4,ww gth to change?

What evidence can you give thac ()p rjtpv9(wt the speed of sound in air does not depend significantly on frequency?j(t9cw)p(p rv

The voice of a person who has inhaled helium sounds very high-p y,mz l dki2gn-1 8+str,(libaitched. Why?

How will the air temperature in a room affect the piueqe1fwrx4 ah4y93 *ltch of organ pipes?

Explain how a tube might x* 40 lr3 t77cimuo, uky4nfpjbe used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufr cuimft07ujnp3l, 7kx 44yo*fler.)

Why are the frets on a guitar (wyj91zw61msdw+q5(zujob n. Fig. 12–30) spaced closer together as you move up the fingerboaru.dy9z 1b6w1nmz( jw5wqos +jd toward the bridge?

A noisy truck approaches you from bp9 e pod(ftw18yd*hm4 8g l-quehind 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. Explgdpo4yq e 8l8 u-*( ptfwd91mhain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be s d9q4b/)jekp haid to be due to “interference in space,” whereas beats can be said to bebd49 pj)qk he/ due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakxa w:g0q s1sr6ers were lowered, would the points D and C (where destructive and constructivg:r1xqas 0sw6 e interference occur) move farther apart or closer together?

Traditional methods of protecting the hearingfidfaeto4g 8)*id 8z6p(n( pl 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 ca zi8(g)ftpfe*l 6p do(d8i4n ould adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sup , 9bic-4 xuqeweo6s+gerposition of two sound waves with slightly different frewi6-q,csb xe4o ue 9+gquencies, 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 source and observer move in the same directioni;j 7u(-;gm/no necob , with thg(nnb/e ujom c;7; i-oe same velocity? Explain.

If a wind is blowing, will this alter the frequency of the se5 t g/fftg-/i3/fxoj ound heard by a person at rest with respect to the source? Is the wavelength or velocity cg/5xti ge/t-fo/f3f jhanged?

Figure 12–32 shows various positions of a child in motion on a : ne h3 vtt: bp-kj;rwc0(lt(uswing. A monitor is blowing a whistle in front of the child on the ground. At which posw3( tvnepukt b ;:r:0tj-(cl hition, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake b4doszy:u +ihx:r cn3 ,y listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of+hi:zxys3c4 ,orund : the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wsqxe,qg0 +q6j aterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. Ho x qg+0qejs,q6w 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 waveeag3(vz wsd b-ws/t)i; g4p*+ jsl :tnlengths 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 tny6s, bfxce )5una on a foggy 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 heeb 6)x,sfcy 5nard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it ma /( lc.s0lm5a2emmu4dy;lf pbkes when striking the water below is heard 3.5 s later. How high is the cliff? ul/5 af;l(e 4cmbs0.m l2pdym   m

  A person, with his ear to , epg jffr(q*f5 i.a:tk6efp:k7j;mg 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 the concrete, and they arq.kj rj, fp56ag*m(:f 7p if ;kge:ftee 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent e;;(zy:i v 0ll*e o)pitbo5 oonrror made over one mile of distance by the “5-second rule” for est;o0ov(tbin*l)e:o5il; oz pyimating 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 uxbnlnl4, mwwy ;j y ,uc,rq+ z5x*(5hsound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a so/ie dkr .+7 hp15jzgtjund whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultans mbx *zd4r2n6eously at a certaizd2 nx*rmb46sn place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fou -/v)zfaso6d/dn y/sw r 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? [fdss /o-w)zvd /y6/anHint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratw odn+f9 d7po4y,sl6iij t.t 2io of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities 49+ydp2 ndio 6w ,. j7otsliftof the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conver (vrtpp-fsu 3z:z/ql1sation. Use Table 12–2. Asr1ppl3t:z( s z-q/uvf sume the sound spreads roughly 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 eardrum whose area .3e-txrgwg9a 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 ampl6qe uhwgj(1rs5h( ,h4p7i g kwsnww83ifier B is rated at 40 W. (a) Estimate the sou8hukjhsw (3h 1gqwwpwg(674 , serin 5nd 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 registere p4:y/lw 3013ysp ntmdyrt+ vmd 130 dB when placed 2.8 m in front of a loudspeaker on ltyy3 m vy3r:sn/wm40t pp1d+ 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. Wha-(t f*e-zucd6gml7c ut is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectio e-mug*fcu(dlzc-7 6t n 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fdh8h 7s0 :du(ysxvt( zactor will the intensity increase? Inc(ty:u(d h 0zhdv87 ssxrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemek1 u7ox ivz1d9nt amplitudes, but one has twice the frequency of the other. What is the uxoiv117 zkd9 ratio of their intensities?   

  What would be the sound levey9ntim vsqg4*x06l 3r l (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating a lr4sg9iy306x *vnmqtir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as vfq;)ndzw 96i( hxcq6o-sp7w loud as a 100-Hz tone that has a 50-dB souniq 66cqp d;f9vos )wxn-wz7 h(d level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whe4 d8u a9kswv)k0ct7ti1ply 9vn the sound level t7l9k 0 14vukv dwy9ct8)saipis 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a jrj8sgbi k0n1vghai409i9mx*8m+ vs8.qzm y huge range of sound levels. What is the ratio of higyh0*jmv+k.8v a nijgm 9b9iszi1gr0s8x8 q m4hest 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 dbqe*qx ffgq)4(p-yr *xnz/2 has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm qfn xrqgp/2*yz-x (d*fb q)e4, 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 ares4vd. .x4:7dajyn8h kg94-yhoi lrwz the fundamental and first three audible overton.o :ywdx974aikhns 4lhry-.4 d8g jzves 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 k;+mt tnqjlzy).*)ze 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 tubket. *t+z)q)z;m jlnye?    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 them.ce5xs(et-q;ti 9 gl range of human hearing (20 Hz to 20 kHz), what would be the range of themqigxtt(l9sec -;. 5e 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 h3 as8bgid;dp4 armonic. What will be its fundamental frequency if it is fingerp43gsbdia 8;d ed at a length of only 60% of its original length?   Hz

  An unfingered guitar string isgab9h+pmaip* v5( z a; 0.73 m long and is tuned to play E above middle C (330 Hz).zi9ba(*g; pv 5p+aha m
(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 (262 wmsas/6,9k mg.6u / frd vu(qw vov5f2Hz) when the temperature is qosmw vu2a. 6vf5,(vk 9s/6mgdfu rw/ 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 a-6mj a o3y/rvq/t vix+t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of d t-v)d3jhjo/r ea4g) the flute in Example 12–10 should the hole be that must betd -v 3 /gj)rhjdeoa)4 uncovered 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 H/ryykyg 8-zc,z, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a cl /y8yrcy-zgk,osed 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 e1 n1rv ;az4j zclq19- k*kpxhc33f gxboth ends. It resonates at two successive harmop1gxakzz 3v -q;4j1*lnh 39rcxe c f1knics 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 3-nxpo v ybmi02)i ixl8gkb. *$^{\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 d0hkjdi )/b q8for a 2.14-m-long organ kqdd)i 8 j0h/bpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outs0 g9 ix++wahnzide and is closed at the other end by the eardrum. Estimate the frequencie9w +gaix0h+nz s (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two string+ pxkl ftgmr8x)9 qfn);oyy25 s, one of which is g)) mfq kr29f85ntyy; +plxo xsounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middli7 8e+hj p*x2a uqrx/uylpgj:51v6av e 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 kw8;u:jbld j azirg8//d3 cpx8 Hz, while another (brand X) operates at an unknown frequency. If neither 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 operatixg;:d/83u 8z iw8 ljc/ dbrjapng frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hgu6gvx d1f8, fz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency od gf8, g6uxv1ff the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freq1e;/ jgg(7nuedie*h nuency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when thiuh 1ne*/ggj ee;n7( de two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heardj5bvw 4zkb9x*+px /vzfdfrp-,eg 7 )b) edx+f if two identical flutes each try to play middle C (262 Hz), but one is ajwd) xkb -exep 97+4fbzfr 5z /+)vfg dx,*vbpt 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A kp se*x6c - l9wbr 0vejg,bi69hv21eb, 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 when A and C are sounded togethe1kix02 *s r hbcw-j v g,9lb9e6pb6veer?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker ani(k/as8 vaa 6wd 3.5si68 avka (/aw0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pi ip.i.zyd*pu2 ano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be t yd*pz.u2p.ii he 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 of6gdr9ft)0j j6 q*y gzd wavelengths 2.64 m and 2.76 m in air. How many beats per second wi fz j yj6t6g0d)*dqgr9ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’vbz-h+dgz)jk b 9r p81s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed 8)g p b 9bzk+d1zj-hvrof 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine who84 krp0 n.w,ruzreeq0se siren emits at 1550 Hz moves at a speed of 32ee zr.8 rq0k4r pn0,wu m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift q59/a 3vqhv80d5vkcacs2e2xyov hw n+zcg,; in 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 fra3 a9 yqh5/c0x5,enc gv;vqksw 2c+hv z2dvo8 equencies 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 equip2 :bhrz7r b30eamj u:xped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat f huxm0b b 7rez2a3jr::requency 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 rec8kg. s(ja6z,o m) rgxseives them returned from an object moving directly away from it(s6rmxgj8ga kz. , )so at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a w;a;9 abln u3abdp-kz ,. m3fbwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave? 39fnbdkabm. p -l; wuz;a b3a,   $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wbaet 99 hy+(ah*f3ooct*hf 3yas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same ton oa ayoh +yf3ft*3 9eh9c(th*be while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow e+al:la,d1 g- k2mtp rspeeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken t , g+dll:21emtara-pko 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 ultraso8lyw2ebi6nuouju16ym 9b/ zfs 3j d++ nic 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 emic u5goy473s dw6g( bmhts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the nord4u7osgbc3 6 mh w(g5yth, 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 l)ikk gp cj78jig) p)b2rz,, isand 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 speed ofd9tyidn,dmiq3 1g+ no2hg r -3 sound is 310 m/s (a) What is the angle the shock wave makes with the directionynd32, -t3og9n gdim+d1 i rqh 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 the spv 66 ..go;ndwa6c sfoeeed of sound is only about 35 m/go;6of.6c.n aw dsv e6s
(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.b 76wcjrn;jp g9j) u* ion-r+ylv-bd - Determine the shock wave anglej w-ujbd9p)ivb 6+r nc7yn-o *rg;l-j 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 aixgfw8m.ro,yh 2f 5$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plal 0q 1yxspo2 t,,lo)5kowmcm (dy6 0pg3ecww7ne exactly 1.5 km above 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.xmcy l)c(pep,m3td 01 2ww6y o7q kogs5 low0, 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 souz1fdxe8qg 0n4 z6cta7u qq/+s nd pulses downward from the bottom of the+gac6 1x/q8fq sdze4nutz07q boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rangeyhg /j16e fm1it n9vinuu0,0 r? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consi84f *6ihauch 085kk r)miw + v7afxfcbsts of many plastic pipes of various lengths, which are orxhuim w+f 8a h)k*fv80cfa6 4bk5ci 7pen 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.m6 l+3mgtx q iw3(wai+0 m from a person makes a sound close to the threshold of human hearing (0 dB). Whawwi6q3m+l3 + gxmta i(t will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-6u yf2ho*4 shmpo3ke 7dB sound are heard simultaneoumsh2*7k6h fo3uy e 4opsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whatlp0;7bvqg 46f x tp)c-rmn8i*iz-fa;n3 kbe l is the acoustic power output (W) of the speaker, asazl;)b8;*4ne3imn-b0fclxfv k rg76t p p i-qsuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outputchi5bu -jwhr+r +/o;v at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts-v o ri+5+;u w/hrbjch at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices overdw 0vnht4lomd80p3p 8 wnh2;x 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 whtv83 4;0 0pnwhxp ndm28 dolhuman ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications syp7zyaqc+cx 7:stems, 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 freu;5 b -qicm;pl-4: k z 4yfrl,xh uaq;b-8nnhtquency 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 scgy29foq/k,sqj66ft.1zv g 1o + tq owith a fundamental frequency of 440 Hz and a mass per unit lengc6gfstto 1+yq f6 9sgvk/ oqj2.q, 1ozth 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 olvzsfc17(62 uv p5asq pen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the wa z (afsvu2c1 7spvq6l5ter 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 zv( 6 pa;cbv:9l qv(e. z-yupmthat is open at one end and also 75 cm long. How much tension should be in the string if it is to p;6zb9 mappe(vyz .-q l: vcu(vroduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to ax4y la98ug d),em5de 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 50.)fnf h(g tphu8*jhr70–1000-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 minimal at a point 0.34 m farther from one source than the otheg hhj 7f8n(r. *fhtu)pr. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One trai4+.ef7 1jc q d77p,dw4)oee7l i kykb+nlyksfn is stationary. The conductor on the stationary ilp77ddf.7 eqck7w4nbo),l kykf +1eyej 4s + 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 train whistle as it approaches you is 538 Hz.gj9 an e4ju*cpol8( e2 After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume coe2 gu 8n9lp* c(jo4ajenstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeninf6fn/siv :: lwl o(tl1g to the difference in pitch of tf:lt/(vni 1 o6 lsfwl:he 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?    m/s

  Two open organ pipes, so+subyn83; mq;7ueb vsunding together, produce a beat frequency of 11 Hz. The shoryu+ e7bqms3svbu ;;8nter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at 1k3czsn;2 dk iopposite ends of a railroad 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 the1z3k cn;k2 sdi position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0. pm ieh.z+uc.,32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? A.ipue +zh, mc.ssume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth24es o+nzcf-*ig)m: ueox0ou 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 wave detected by the bat after tha o i fc2xgm-een0)*u +uo:oz4st wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses abxtzldrv4u:q 2 w2 zcz7 3)pfw7e(zr1s it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detectedw :zw d tz(qpe72v4lzzrf r1u)xb273c 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 .ruev)4k- -te zmxwi a.vvn49Alpine 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 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 wh.-)v.44umkv zwe av-ir enxt9ich overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening ca2j).s 7,mbxyccfg ug4a 0pc/b n 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 waves im bycc4a2x bp/gj,gcs uf0)7.n this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alg7oa.kktc k(-q*9cvx g/yk4tuminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other -4gvxk7/( kt*o.qkc y 9ktgcahand. 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 frefkhmilel8))4dzx)g/:os md. quency of abl/d 4 8skzf)lhe))mi.m ox:d gout 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears t4ql.q9ei,me d15t z)npe2mxm he sonic boom 1.5 min after the plane p ,l4me5pxqi9m t).ez2e qdnm1asses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa2ss+ :qaz. gwgt 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