What is the evidence that sound travels u,va6ak1 *m igas a wave?

What is the evidence that sound is a form of energyz2*-repvr ghy) m kx94?

Children sometimes play with a homemade “telephone” by attaching a striq48wf j*q(u9egk8qx)lf u:7oi) kwhh ng to the bottoms of two paper cukfw79:lq8 wk)xje hhg 4 8)i*uquf( qops. 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 the other.

When a sound wave pasnuj5 m-r (lqq1a vcp7;ses from air into water, do you expect the frequency or wavel5q1; cj7a-rl (mnqu pvength to change?

What evidence can you give that the speed off (ek;c xls 5*vje /wt(ic8nf853sius sound in air does not depend significantly on funx 8 sv* jkwfl53sc8 e;(tic/5 e(isfrequency?

The voice of a person who has inhaled helium sounds very hpy1m i0 y8bm/ v1f.sxjigh-pitched. Why?

How will the air temperature ik 5rtpj9e9p0gn a room affect the pitch of organ pipes?

Explain how a tube might be usedc 0s3(/kodmtlh ob/8t as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufdh3//t lob(sock8 t 0mfler.)

Why are the frets on a479hxrd n )atyf6zb2 x guitar (Fig. 12–30) spaced closer together as you move up the n xxr dh)tzf7 y26ab49fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Init)kb0ni0g h2nhz-j qj t,8krc5 ially 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 nobqnhh8z, knj 0c rg2 kij)0t5-ise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said*6w 2reva5oeo9a cf4y to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explainc4e29aow fra*5yeo6v .

In Fig. 12–16, if the frequency of the speakers were lowered, would the points mx zknbwyd i9k7-0 s5a 2qp11eD and C (where destructive and constructive interference occur) move farther azk 2 19 b1a5y0ki7q- mexndwpspart or closer together?

Traditional methods of protecting th3owxcb x g..o1e 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, inverb wg.x c.3xo1ots it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave ;sz3o/rn;4kss a ;x cgcan be thought of as a superposition of two sound waves with slightly different frequencies, ak/4 gn ;o srczs;as;3xs 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 t tfv,atjbaxj4h9-3:source and observer move in the same direction, w:vb-fa4hx j, attj3 9tith the same velocity? Explain.

If a wind is blowing, will this alt56 qgo 6vwe:oker the frequency of the sound heard by a person at rest with reo665qgo:w e kvspect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various poyq4xuy;0 ,: jovpp 7lxsitions of a child in motion on a swing. A monitor is blowing a whis,xypvy:;u0x l pj47qotle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listeningd(uey:60du(z 6r b ,j 11n9pbhkppqjy for the echo of her shout reflected by a cliff at the h1 9bpryp:,z( bedyu1kd60jn( 6pjqu 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 wmn aw c*n.f m94w(gh:side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seaf:a*h.n94 (wwmgwmn cwater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthsjn- x i(p5af1d)qv, wj in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. Wmalo:0*5ju dmit*a d:omluj5m0 hout warning, an engine backfire occurs 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 makes when striking:ydh-n(d qg6;h +bbxb the wan(b hqh6:gbx;y + d-bdter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the 40jb br ,gjwjku4kht 46,xg g9ground, 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 did the imp wgr 0j,j,g4xjhkutb kb649g4act occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secon-d;m+qd/;-xaf swzg ad rule” for eszm -wfasqda-;g/+;d xtimating 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 souyca* kho*.1zr nd 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 whose ikjzgaj8. 9-dontensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soun2qb/) j 5w8,gqq 8bdye08gelz rn.3c kxwnz n:d level of 95 dB when fired simultaneously at a certain place, whwq je3ez8xynl0gdb q w,) rcnqg5b/28.8n zk :at 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 four equally noisy j0-e. k.vy.p yaesbwb(1nni c 5et engines is experiencing a sound l.1bnn iypk5wea(y- c.ev0. bsevel bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a si/ hkizwcx2: (;df2y jkbvt21wgnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratiojz( wvx2ty2b i2/kwh dc ;:1kf 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 speam+s wc/o7 2;q m(ocvsk l,0lhcking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the 7+hsco cv l0/om;,l(qc s k2wmmouth. $\approx$    $ \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 eardrdz: gnwl+w69 :wf+8ex ;ik il6g ffbe(um 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 modestl w/33tc zfkb- amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you woulzb-lw3ktf 3c/d 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 132 n;hl9sb/p za0 dB when placed 2.8 m in front of a loudspeake/sz2p;bhan l9 r 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 detect a difference in sound levelb-/*v.v 3 e0hdexa;rw(r dlvh of 2.0 dB. What is the ratio of the amplitudes of two sounds whalr*3hewd -vrv0bed (;x.vh /ose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a souwt dtx+,ci5 :ez d:onn)a68 ohnd wave is tripled, (a) by what factor will the intensity increase? Increaset6 :no, n)8e5dztdc+:waoxhi by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displace*rt wd) yan/ ;p)koh4fp2 ,olwment amplitudes, but one has twice the frequency of the other. What is the ratio of krhpwfo;d, a p nwo4*))/2ylttheir intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresp rz3mn.wxql.u9o5m( buh . b;u6,nfmmonds to a displacement amplitude of vibrating air molecules of z. xn5mmw bu m .m,9(ru.uhn36qf lo;b0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hicxv- s( +vev,v0 mcq mn34y(cave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sein 3yms - v,(c4 cv+ev0mvxq(ce Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sou:l3xxa f7e;r,dv lx ;ond level is 30 dB? ov;x ldx7 ;l3,rxafe:(See Fig. 12–6.)

  Your auditory system can accommodate a huge q in9:6wax4t2/hu9h:z mw eo nrange of sound levels. What is the rhq2uh9 :n tz4w/o6ema9xwn:i atio of 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 frequency of 440 hs)qrt95gk .7m c;zo sHz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the str9sg. 5 ;ko r)z7mtqhscing be placed?    N

  An organ pipe is 112 cm loq2i *xnt*f,q + wyve9tr c9mg,ng. What are the fundamental and first three audible overtoni +92mwrtny g*q*f9extq,vc, es 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 across wv,gak2 0.dk6u+s 22tv hcrxzthe top of an empty soda bottle that is 18 cm deep, if yovc6uzkrhvw2g kdt0 ,. x+ as22u 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 organt:.i //em crik-j/fv u 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 requi.jiut-r /:cei vmfk// red? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Whae9 bq7b bo8gro , g8.vtg/5vkqt will be its fundamental frequency if it is fingered at7bgbok8vtggq8 e/9r , q .bo5v a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m cd,.flcawhn/ub) 1qc c w r/nd00g4, llong and is tuned to play E above middle C /cl 4gqc)f ,w,c0.acwh1ddun / r0nbl(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 opx0 . hv*w1ctcf an open organ pipe that emits middle C (262 Hz) when the temperaturewtv*p.c c xh10 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 arez/*q))jr( 5e,ldwplh)v net 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in)cg)h b75g*ssmg a2yo Example 12–10 should the hole be thatsg5*7ys2) bcm)hg ga o must be 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 resooq s*anm(9x es*t6ri.nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open*.i stsnq6 omr9 xa(e* or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. l0)xflg7thm:v9w p/v It resonates at two successive harmonics of frequencies 275 / 9)lxtlwmg:v7phfv0 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 hilxa j92k) aj+c7 c lvn(-4dz$^{\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-lonxxxbk03m-dgl6d9 , zu g organ 6 bdxmzku g,3-d0x xl9pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is o*mzzu( g t x497toi6rmpen to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing wamo 7*6(ttgur mzz 94ixves 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 wrdvy;3w ht- 6khen trying to adjust two strings, one of whi6kwhv3 yt- ;drch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (26zd 74n kgbfy0(2 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while an cmb61.eh*woiother (brand X) operates at an unknown frequency. If n* .1mce6obwhieither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork a/(hhovoamk1o, fz8 zf-;;eutnd 9 beats/s when sounded with a 355-Hz tunit;,o 1/evz8f;fh-oo ma z(kuhng fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 2zwdo9(0 4 u(4q gwusuy;e zmg)94 Hz. The tension in one string is then decreased b(g d4w9s0z youge) wz(u;m4 quy 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will bcb2liuceb e a8*h,p74 e heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other a*,eeb lc7c8u b4pa2h it 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C4pa;.s utho,ys i,bl1. 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 arelb 1tp is.4hoay s,u,; 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 stands 3.00 m from oneemn4q;n unm3d-v4zp ; speaker and 3.50n4p v; -q4;e3muzdmn n 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 1ale w,uz-f;8 k32 Hz, but a piano tuner hears three beats every 2.0 s whenefu;,- kwaz8 l 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 2.6tndwcd),.4 kbnke a/(d w*1cf4 m and 2.76 m in air. How many beats per second )e d, tk *4(ndwfab.cw/1dkncwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when aomr:lq+nysw-j * bej* g7r// at rest. What fre: /r+rgqlw *sjba-oj mn 7e/y*quency 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 engine whwl9qlz+/ae f7 ose siren emits at 1550 Hz moves at a speed of 32 q 7+fwll9/zae m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mov+*t:w mqrj9 eb+pi(h aing toward you at 15 m/s versus you moving toward it at 15 m/s Are the ibm9*w :he j+pr (tq+atwo 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 with53l /w4a8kysy9mn vde 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 frequency of 5.5 Hz. What is the frequency the horn5 nv 93yks84m/lweya ds emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHd3) 2rvxjx0gz z and receives them returned from an object moving directl r02v)jgx3xzd y 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 an ultr* zcfk7ai9,dghkn) ; yasonic sound wave with frequ7;yh,*c g) i andk9fzkency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flahf)ea i *ajn5;t train car*hia) aj fn;e5 at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow6br ()*4ze8vu;mfisy/(otxh nb brj ( speeds. Suppose the device emits sound at 3.5 MHz, anb 4s6 m* hx8;)(v eoin(uytbf(jbr/ rzd the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves )np vym9 0+stxof 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 freq35r/gmq avu pb4)6b.uuqz ,ffuency 570 Hz. When the wind velocity is 12 m/s from the northqz5maub6qf g/p,rf3u bv .u )4, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spe8pk ivk4o xi:;ed 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/7do,.l37edylcjimzyx+ .uy vwey51 7 s (a) What is the anglem.xielj y73v+dlwc.z77y oyy1d u5,e 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 wher*jdu (nw64j8p wlgao9e the speed of sound isu4 9njwp8j6g *(old wa only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shzw:r2vn9qy 1wock wave angle it producesy1v :2zw9qwrn
(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 ln t6v9xr:yo 1s:i3/h n4rkz3 pnye8q$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhjwip 432eebq 1ead and see a plane 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. 12–34. Determ4e31bi eqj2 pwine
(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,/edyce 2x 5 yoq)a;9o5ja 5p xh;lji2i000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minip25e/jl;ye 2ojq d caa)oh;xy9x i55 imum time between pulses (in fresh water)?    s

  Approximately how many ocrtl6ruiow dh /e6*t59taves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cal)iu 4hi:u 41hiu40ahj wi )onlled a sewer pipe symphony. It consists of many plastic pipes of vw)a i4u4l40i n ou1uihih:)hjarious lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to thy 89;fjseqw* 38ql ;0ng yrgr8 hszjy0e threshold of human hearing (0 dB). Wr; shng0 y9q8 3y*qg0fjy;e wz8j8rlshat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and anei8ngo at o+e:.bi1 6ae.;2g akvyfp8 87-dB sound are heard simultaneofa+eaia bg8;gkn6 te.oy 2: vp8.ieo1usly?    dB

  The sound level 12.0 m from a loudspeaker,a0.p:br qlhlgy1 0+lj placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuhjl0p a0 gqb r.l+:yl1ming it radiates equally in all directions?    W

  A stereo amplifier isn + hpj.ro pg*hp670qm rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in +q*npp7.0 hrh m6pgo jwatts at 15 kHz?    dB

  Workers around jet aircraft typ )cqp//mv t3pm,v1vgt ml79n nm (+lubically wear protective devices over their ears. Assume that the sound level of a jet airplane engingv 1v+qm c37lmlntv,pt/ ( m9m)n/bupe, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications .;x w5fuecdpbpvr*e w9(w+ s1 systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a freque,yziou*ayw 89q5 9xnc ncy 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 fix)pn)5r 0b ) wdajla am:,vn4lned points with a fundamental frequency of 440 Hz and a mass per unit length )n:nam, aav5w4)0pr jd n)ll bof $6.1 \times10^{-4 }$ 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 vibr 7h)o jlnomp .xn3e:8mation above a vertical open 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 water level is 0.125 m and am.7ho8pone l3 )m n:xjgain at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar st6 ;),til/ hhj4fq)frnm9 mkd wring of mass 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 fundamental mode) with the third harmon)9wlm qmh )dfi t;h64/nfk ,jric in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resr9 w*p6o) c jrt5qck6honate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range com d5u.f2ij-t 4,oz2;qryc lnmsbx q:w6 ing from two sources. The sound is loudes s,wl.fmqi q rj2zyd:tn;5o6x2 -4buct at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz wh i5qjt5gkqf+5istles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when theqt+5q j5f kgi5 other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it app 3v,e ,tjyu2niroaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the i,nvy32ju,te train moving (assume constant velocity)?    m/s

  At a race track, you can eso45-l*zq bhgpt +b 0dntimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it gb50ob-p zq4+*t ngh ldoes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounqdb yi8;( x/ gn))npw n5ejpjfxc.tw,,j2qq , ding together, produce a beat frequency of 11 Hz. The shorter one .( gq 8jcjj5nnb/,f)w qe 2pi ,qxp;xn)dyt w,is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as iu 2/kl- djmk0x wj 1l5;sjhol3t 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 thewskhd l jo2lj/m 51xukl;j03- 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 blu86eg) hmeur.g dj. )kood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves wed6 e g ugu).rk)hme.8jre directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whilq +x da*j;e,m2.iqqype the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is thdj2,ax;m+*qp yiqe q .e 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 ityyw)ni3 0(ce buyh re rlmax oor7 34g;*lr94+ approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How xirer) 4mo3ryeo ba+ h;rug74yy ln93l c(0w*far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from ongor.) orhsa +9 5uyprb*iul: 7e 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 a):5ru7 o+ s*ay9 bou.lrrpih glpenhorn 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 canz8ut+yyug76rm55 v0e0 i4 b cyx2 yjnc 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 r+ yuymyytn5zj6ic54 080u g72v x ecbfor the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called 4)w slen9/hn3:fft fm0vm hr 3“singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sounl/4tf e3nf0f) 3vmh9whsrm:nd. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency ofr5lvs*z jgd9/ax k6:a about 1000 Hz is *aldr596 s:j/kvz gax $I_0$ = $1 \times10^{12 } W / m^2$ 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 the sonizflb56nlbw- e e. 9/usc boom 1.5 min after the plane pw fzl/-b.l5be9e6 usnasses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 .6b)q1fxlqf cdq n9g0 l28cx7pu 0s ln$^{\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