What is the evidence that soundj,y*t2zxzb m kx0i8 l-l- .n 16legmkm travels as a wave?

What is the evidence that sound is a form of en dgry k+ 5f6xnne:,m e8f:sxc9ergy?

Children sometimes play with a homemade “telephone” by attaching a string to t tbx.cbli,p5o),r /e+ht 1b yyhe bottoms of two paper cups. When the string is stretched and a child speaks in/e t+li,xrb.o 1 )5pbc ,tyybhto one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequencmfg0cqo iv70 hrnz )/r.1 s5yyy or wavelength to change00nh.s yo5r ri myv1/)cf 7zqg?

What evidence can you give that th-j;uw w9hbhp9e speed of sound in air does not depend significantlh j99b;w-w hupy on frequency?

The voice of a person who has inhaled helium sws-d gsi8gi+ )lr-35clqmc7 tounds very high-pitched. Why?

How will the air temperature in 2y0xi-nnvo5k(v*x6juvvmylg e/ *-ma room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundsyx krzogh )pdjg68( +ythlav qz.g( 1i:55f6y in z5 gd.j)gp1:yhogyfy(6v(x56q 8a thirk+ z l various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spac8gk5g l 9j9sunz94fdq5 j,f jsed closer together as you move up the f9 4g ljn9 d59f8z5gsjkfquj,singerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you he(arh2sa z 6-wyar it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you a(ah w2s6zr-yhear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be sa:lz0ql)omd sk 0 +zn(tid to be due to “interference in space,” whereas beats can be said to be due to “in+:(z)lqzt0l mskdo n 0terference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, i;7h3t/ ,6ucblqn2kia-w qwl would the points D and C (where destructive and constructive interference occur) move farther apart or closer toge; 3lltcu2i7kqqn /w6w bi, a-hther?

Traditional methods of protectin zy*/3aofwy v;g the hearing of people who work in areas with very high noise levels have consisted mainly of eff w3z /yf;yav*oorts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 1,6bn)aqljg//pj 3dg (,o ogg h2–31. Each wave can be thought of as a superposition of two sound waves with sbo,3h gd6 /,oagqg)g(pjnl/ jlightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in4+w+j,or7 ;f judpda b the same direction, wit; j7r 4b,jpufd +dwoa+h the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a p)h 3+( :svrmd dcjb+noerson athm v+j:ndbro3c)s( d+ rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on bz p35e.+vxso, r7im ea swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest 3 o.pzrxb +v5 esim7e,frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listenins.d6u13*or mch-m cimg 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. Esh1.cr6 m icum-som* 3dtimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. wqr usmp q*jg1*(d1qx 9e-i8h He hears the echo of the sound reflected fromq8 eijdp 1*shqqr -xg1w9u m*( the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 209w wziw(n3 ;nx $^{\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 -8 :qrjqt o.ggfoggy day. Without warning, an engine backfire occurs on anojq 8tgr. -:qgother 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 itc7 vmc7p7ssgb 8jz4n8rk: ;xs makes when striking the water below is heard 3;8 nvk c7bpjgms778c:xzr s s4.5 s later. How high is the cliff?    m

  A person, with his ear to the grounlukxg+a jrd61i w(j4)d, 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 are 1.1 s apart. How far away diawgj1)dj6xr i+( k4uld the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-4v1jjtmh8l3 hum8rain.8f (qsecond rule” for estimating the distance from a lightning strike if the htm.iaujqv83 4 nmj8h( 8rfl1temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity os1v qkl xt2.k2g8g/ rwf a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whguf ime x x9 ,o5qy9g:,odj5u;ose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro n.17)2jbqdzgr o gcc5duce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound l) 2qbjo.g nz c5rcd1g7evel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain d;i/ ufit3 :x6oetu4lb istance from an airplane 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 s tt uxi/fb4eiu63:o ;lhut 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, wlv5jl2i8)w 72 u-dtekpbi w5xhereas for a CD player it is 95 dB. b52-ll8)k7xi5pi twuw e2vj dWhat is the ratio of intensities of 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 feu:4 1lq0rsl4 byax09cb s-rnormal conversation. Use Tab1xsb cs 94a0q4y0e:-rl bfrul le 12–2. Assume 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 an84mf:dz , iayd-30l- hws-axe+xcfa l eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B)an07 /ww q; fqby.xpd is rat/;.xp yqn abw d)f7qw0ed 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+sp,uo; 94moa i4oj fe placed 2.8 m in front of a louds4ei ,o9 p;j+4o sofumapeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically de) u(1wz czfhz,tect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectizz hwcu,( )f1zon 11–9.]$\approx$   

  If the amplitude of a sound wave is tripledi9o6yf2ll 8bqew. bvj+ zc71n , (a) by what factor will the intensity increase? Increase by a c2qwze7l bfj ib1+8.voyl9 n6 factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one/oqx fcn/ k7w4 has twice the frequency o7 /wcqxn4fk/of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that 5y u:/6lwfey kcorresponds to a displacement amplitue kluf/6w :5yyde of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemi s )wy0g0 jv8o0g7end ail4vh(cdh49 as loud as a 100-Hz tone that has a 50-0ihdgg7 vs( vjni) 8 ehyw940co4a0lddB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest f+ot5i .x)7o/ n dxifqmwen 1h-requencies that an ear can detect when the sound 7qn+dow-5ix i n/1f.hox t )melevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soumik6j+/, 4pg vehak14ywq 9jond levels. What is the ratio oj/ok,p9v14eh a6q y+ m4gki wjf highest 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 f*a. vq7v :gur*axuoi5q9z f 4srequency of 440 Hz. The length of the vibrating portion v9ao u5 agv* iq.xuzq: 7*f4sris 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. Wh ;e/d1) i/pduplshn k id /)f//xzgds*at are the fundamental and first three audible overtones if)ndkss*h/e)d1u xp/gd dz ;l/ i pf/i/ 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 across the top of an eugyb4q*r s8. jmpty soda bottle that is 18 cm deep, if you assumedr84j yqb*.s ug 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 orgatrz 3lx*u ; w*vy./u*u/ b cmwzfn7t9a.0zqip n with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?*3u/vftpzb0lrxn. ut q.* za9; /wc*iym7wz u $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as itsncd2 ,l k(hjou66+1x y+kt ;(phjhn ka third harmonic. What will be its fundamental frequency if it is fingered at a length of on66,;y+jk+(2 c t hh1jlxp kk(a onhnudly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned toy b95whw90tsc play E above middle C (330 09cy hw95tsbwHz).
(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 o 9dddj(wev 21eqk :nbgc;.mw-0dqm 5wf an open organ pipe that emits middle C (262 Hz) when thwwbkedmn0(e d w9 2qdqmc.dvg;:j5 - 1e temperature 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 cdm2mdp,l . ;l2gk.wu at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiercz czeo hi s/(8 y+,lu8 ux;k 2v*xu.pnze7;sce of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 zz z7c82, hupxr;;v.*sk/ls xoc(n yi+ e8u ueHz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at oh nn5cis2up t+9p6-lany other frequencies in between. (a) Show why this is an open or a 5tlcn+9p-pi6hu o2 sn closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open aotb7vc pp9ht + wa-1o3t both ends. It resonates at two successive harmonio ch31a-p+t wt7p9v bocs 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 *vrijbi2-kyx p/ )a99fiq+i j$^{\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-long organ fzg 7wwy;4 x;spi;fzg ws yw4x;7pe 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 outsid (i-t 9:wbtcgsnna;mtw adnqoh( 56)b o 295kke and is closed at the other end by the eardrum. Estimate the frequenci(gs9nbmtt ;a5ct-bn( awin 2o5 o9kkh:wq d6)es (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 buew3whe 4 e2o+eat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in freqwuoh4e+ewe 23 uency is the other string? ±    Hz

  What is the beat frequency if middle C (262teqa b, :xb:0s 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 23.4s ic+zdt5 zx45 kHz, 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 5zs4xizcd4 + tthe operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork cz4sm:)*nkt f and 9 beatn4sm *ktzc:f )s/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to tc, l5kpav1rq98-qj jb he same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What 8qpbjqc-kl95j,a 1r vwill be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heafg,hcqohjh(gu;,b/ ry fqj d(+;1o5 frd if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.dh5( qojchgj g u;oq f;1fhb +,r(,/yf0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forkq )f2bdn*v4d,6zr k kvchmy2 - 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 poss2nk ,*z4vhqvky2d-bd fcr) 6 mible 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 stands 3.00 m from one speaker andrj 9kp+xs4p u s/ cp/af2 ;cnu/-ikp8c 3.50 m from the otfc8 s/a cu-/pc2 p4 u+k9x;spk/rinpjher.
(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 vibrak. b a84mz /bno8kuhn.ting at 132 Hz, but a piano tuner hears three beats every 2.0 s whennk/zh4.k8a.mb unb o8 they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in ay:6x)eu bsu-blx uqq5uf5k0z4hz0 : rir. How many beats per second will beqfu xesb:z zr06u)0uh lyx- k:q5bu45 heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenaybw:o; d-;+rb f8 nzs/nmum9cy of a certain fire engine’s siren is 1550 Hz when at rest. What-n w; zb :yrus8n9;bm+damof/ 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 a fire en+5 8jrbg;cl /xxwqb,wgine whose siren emits at 1550 Hz moves at a speed of 3 qgxx l;j5bcw,+/w8 rb2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving m9 5dgen/(vnuz(fqmw,*yr/n toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are the(ngq/m95 u/drmf*ny( ev nw,z y 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 sandfhv h (2kcz5(g(euq5. u5ikme 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 q5 c.(uk(dnkh i5zv u2ghe f(5a beat frequency 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 k h athm l g/s8 krm15/;vqem+pg1j)sk.Hz and receives them returned f;lpq+kre/.jsmtgv )ah15/ m mg8k1h s rom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall ac(x7fbe6 pe/et a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency7x/e (ec6fp eb does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played xk 1u+0j lac )ec-dju*yko7j/on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played thed ua*7xjl /0j+eukoc1c k) -jy same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suae //l1p tnpmp.aq y4;ppose the device emits sound at 3.5 MHz, and the speed of sound in human n .pqp 1a;/4/mylpteatissue 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 ultrasonic waves of frequency l q)s( vsyy0o 72m4nmo $2.25 \times10^{ 6}$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 Hzc im/j:5x*cscvf4wq :sd7dv e.t b4:o. When the wind velocity is 12 m/s from the north, what frequency will observers he: iqx4e v4b: vm*o: cctjsw5c.d 7fs/dar who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 2 eg90o/ zqso,c0 $^{\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 theb6):z,eakvs9 :z gc*dgg ;zsy speed of sound is 310 m/s (a) What is the angle6z:*:av c;)gkgy9ezdssbg ,z the 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 atmosphere of a planet where the spee;h93 kknz b14ua2c a1:oeajfad of sound is only aboa 14u 1jhe9kb;aoc3 a:2kzafnut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shockwlwj8 j5/jkg + wave angle it prodwk/g8+jjj5 lw uces
(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 * y ikh2-blzacgakg,rk0e9;1$/theta$ 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 exzxr7qq1wj, -i actly 1.5 km above the ground flying fxr-wj1,zq iq7aster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. 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):t ( (vn*l,zr9gh8r- i.f,sfyrdvreq sbw q0 that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects ecfzrn,9,rhgrqvr0( -)dly:sq *veb t f.8wi(shoes. 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 aude d;c/,+3 vdkfcg8szb ible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sympho bjbeg62xppfxw m7 /67ny. It consists of many plastic pipes of various lengths, which are open o6/g 6pjfmb2x7wpb7ex n 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 sos0a :vf: y) sm9m/i(jfvflku(3* wplrund close to the threshold of human hearing (0 dwyv/3kfm ()a(i ulfm9:sslr*v 0:pfj B). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant x9l 1fk/va n(bsound level when an 82-dB sound and an 87-dB sound are heard s fl(anb91/kvx imultaneously?    dB

  The sound level 12.0 m froe mn;ek*ag86vlq8t 8e+x+f atm a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dire8et+ akv +;q6a mg8l efn8tex*ctions?    W

  A stereo amplifier is rated at 150 W output at 1000 j;*rgl cswiq(w-w v59e0 9 zzauh7 k,mHz. The power output drops by 10 dB at 15 kHz. r-vc jz(0i7 ,;az w9hm 5seq*uw9 lgwkWhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices o+ k w:5*jlf csiko4+auver 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 o+:jakfwl* u 5+ks4ci 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 sye;kbsp(8er/5hivt2 s 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 freik8kxb mq7zj,,pm 1fctt 1 o(hb/4w )equency 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 vi bax+a6 tfbt3;olin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit le +fta6;3 bbxatngth 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 inr,wn-v7u/k m zto vibration above a vertical open tube filled with water (Fig. /k, v-m7unwz r12–35). 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 ma36 9to(yderk8cv( jftss 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its f3(69 ctkv f(jyoer8tdundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to ree8+qwm.fevz) bd3 +rd sonate 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 t+sl9/jaeb+ t-sg/f tzone 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 minimal at a point 0.34 m farther from one source than the other. What is /tte-9b+ls/a+ gjf zsthe frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One tra:gmlj k nie tgcw2 ;p-0w2w3t,in is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train ak-wmni;3gw0 c2:,jtlw gpe2 t pproaches. What is the speed of the moving train?   m/s

  The frequency of a steam traq whf/l(p iv((in whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. Hpi(qlwh(/vf( ow fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estiu)-nkou;az 2+eft 8v emate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car dro+k; ozneut v-8eau)2 fps by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat freq++svpt.; qew2e cgur 7x1rk :rkz4,kxuency of 11 Hz. The shorter one is 2.40 m long. How lt e+r+.7zxkcugp;r: evw 4kkrs21 x,qong is the other?    m

Two loudspeakers are at opposite ends of a raieco f*k0stk1 wkenko */oal;si3 g,21 lroad 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 a 0 1*2nkt1/geosfk s;l3e *oki ,okcwHz, 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, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bwb) y; gmu*od9eat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed9 od g)y;m*wub of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a motk5r4fwilk 2-jl(ydt 6h at speed 6.5 m/s while the moth is flying toward the bat at speed 5 k45f-wyt 26 kr(idlljm/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 xzyevi21j ftb1/e*.j it approaches a moth. The pulses are approximately 70.0 ms apart, and each ije jb2t1/1ie z*f yvx.s about 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 kzd,, abif+c yvmmbxd:4,0f7from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn 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 sh,zmvm+fx4db ,y dkcia:f7b 0, arp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo list/ff+r2wcur1nl j8 4hv /gm *wyening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the presvcn fj/h wf1*84+grm/ rluy2 wsure 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(b vb wpjt1z;/, called “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 /pbvwjz ;t (1b“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 oia;7n b vk3fj8w q7,b-s33 ufvmwp*yrfg9i p/f hearing for the human ear at a frequency of about 7ipnrk9 3s-,b 3jvvfmui f8q*g b7 3a;fyww /p1000 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 v5b); hhv*hd1g kv6 svhears the sonic boom 1.5 min after the plane passes directly overhead. What is the hv5b 1)ghv*vd6ks vh;plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbol+ 4ggygqvl.2u 9 vq)ws e,g1i3cat0gat 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