What is the evidence thatywfo 4;6gz le, sound travels as a wave?

What is the evidence that sound is a form of enerh(,xa c8m3y4uf 9ah nffa6l-sy.x- wygy?

Children sometimes play with av iw -.:oawkw2oi f w7v6c/2ty homemade “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 otw7wvot i-2: aw6/.2ko w iyfcvher 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 frequency or w0vq, zgb 5z8kh: 9 2p dyxbefgne471ioavelength to chafeb qhyg4 79: zin0ekxg ,51o b2zpvd8nge?

What evidence can you give that the bdjtxve6/ 2 ;wspeed of sound in air does not depend significantly on frequenx 2;de6j v/tbwcy?

The voice of a person who has inhaled helium sounds very high-pitcht5kfnbbl;* vth 5 ug2q*4g) kied. Why?

How will the air temperature in a room affect the pitch00lx y6w u2/(eay fxge :zqb3n of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of so-qv.pi9t7r 6csoe ;launds in various frequency raoas ; .tr9lp7ie6vq -cnges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closf( 8 l3qxe pb;8*grtm1rthpi)er together as you move up the fingerboard toward tt 3* )i;8pfexgrqpm1b(h8tr lhe bridge?

A noisy truck approaches you from behind a bu bej ch)l/z:a gv67-cy vxw-my,b9:t xilding. 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 mb7/)va jcyz:x-9v6tlchg - ex :w,ybthe high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,gmda 6hn52 h tk7lh0t(” whereas beats can be said to be due to “interferenceln5h m7(ah d0t6ghtk2 in time.” Explain.

In Fig. 12–16, if the frequency of the whtezl8+f5 c+speakers were lowered, would the points D and C (where destructive and construct feh 85+lcz+twive interference occur) move farther apart or closer together?

Traditional methods +. j gf80eluqtof protecting the 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 technologutj.q8 fg le+0y, 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. 128 iik +dti; q62xxf4 ,vw4psfh–31. Each wave can be thought of as a superposition of two sound waves with slightly diff2,dv 8wfh+qs x4 pt46i;fki ixerent 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 observekl..)y*y8;qdt vt.gg i.t zn tr move in the same direction, with the same velocity? Explai i;).8*tyvgt.zl qkny. .tt dgn.

If a wind is blowing, will this alter the frequency of the sound hearh++.lgnetp js;3xx/k7 l wf4gho60 x xd by a person at rest with respect to the source? Is the wavelength or velocity c 7 w+ lk n64;xxeh xolts3f/x0gjp+g.hhanged?

Figure 12–32 shows various posit5wo)yu7pni*s6pwaz b-cqo*9 ;tn7 glions of a child in motion on a 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 frequency forc)lonw ao 5y*z*tq7n7; pg 69piswbu- the sound of the whistle? Explain your reasoning.

  A hiker determines the leng91i t2zjds 5htwu3b d.th of a lake by 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. Estimat2sh.t1w t5d d9uz3 jibe the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ec8i)w-:k rtxar ho of the sound reflected from the ocean floor directly below 2.5 s later.x 8trwr-ak:i) 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 q;5 h fxzp,,/pt vm.lmair 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 gdixlq41e5+n;y-h htschool of tuna on a foggy day. Withi-1+elqng4d thh ;yx5 out 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. The5y 5n k j6a)c(0yqlakm splash it makes when striking the water below is heard 3.5 s later. How high is the (5yn6l5akc0 kyq) jamcliff?    m

  A person, with his ear to the ground, sees a huge stone strike the c6:ac txhdf:t(5o: 1nin:o ouuoncrete 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 aontt xf6h::ou:1co i5nuad( :part. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of / yies 2 l/v yu:.(7yjtzpj/qddistance by the “5-second rule” for estimating the distance from a lightning stri v(pyyed /yti j7/s:j q.u2/lzke if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level oj 85 tctjlumrr/vn;;1f 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 intensity isauir 5(2 milief,3f) r $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when nv hzww.;7/izfired simultaneously at a certain place, what will be the sound le n;hvizw/. wz7vel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance vlx7f(a+fj,c3 s e5xmfrom an airplane with four equally noisy jet engines is experien,3x+l 7x(m c5jefva fscing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of s*cdf qqcmda.qz3a: nq- 4y.(4 /hleq58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of thlan3qd-q .4cm( ys q /4.qf edz:*cqhae 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 speakincq,/ m968 oq pe*hc/h 2mwm+jgqmlde 4g in normal conversation. Use Table 12–2. Assume the se+qmc 6pghqmm j do //e4w,m2q h9lc*8ound 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 arc,x)dmfef hx7 ()a 4qn 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 m szukzsq e-4aoiz1gp-tm7 6f s hr.)+-odest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wout7 shiquzo-arz4g 16 +sm-zspke)f-.ld 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(ogmzbj 1ql2 5 placed 2.8 m in front of a loudspeaker on the 12m5bzjog (lq 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 levf/ 2o. zyhg/rgel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Szrgf./yhg2 o/ ection 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will tsi* m4hfu9 ,t6db2bpnhe intensity inc*4b fu nhp6db i,m2ts9rease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacgxe1;,nt m7:x::(mi3sm pirtxdhl hz* :a +whement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensi; :(mxtgr ,dailpi7mnht :1xwzs mhx3*h:e +:ties?   

  What would be the sounuei5m3wl mgib6/z haz;z ;2 q5d level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air me65l z a 3i/h mw2g5;qmbuz;izolecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must haveiqo)lqu: //hi0z:dto b 1vr 9q what sound level to seem as loud as a 100-Hz tone that has a 50-dB sd vb:/)oqoqlt 1/zih:u0 9rqi ound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whe h vlntry3-):e cw.m1un the sound level is 30 y 3hw te vn:m-.lu1)crdB? (See Fig. 12–6.)

  Your auditory system canif /t2, qm89mnyk*lymfh3bl : accommodate a huge range of sound levels. What is the ratio of highest to nkqi 2/,lbf8:3ymftml* hy m 9lowest 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 )j/f/ 0h+ vtvrrn v+nd7pwm-rfundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Undenr/ v +0dn tmjrw-7)hvr/vf+pr what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fir2 ,3-fqqiam gpst three audible overtones if the a,q-fpi 3 2mgqpipe 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 yoh a6 ),0tycmjru expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed,)rmt6hcj 0a y it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the ra8z ck- xghl9zfd l5: z6rl (c5v)*gsatnge of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requirgzcrlthl 5a: zf 5 gzvk-6(cxds) 8l*9ed? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequencgk2/uu a.ww3,onz k0 zq) u*pdy of 540 Hz as its third harmonic. What will be its fwuzw3udzu gn o),q2* /.pkka0undamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar s(lx i g1mt:bmpy2bn(y/35i fttring is 0.73 m long and is tuned to play E above middle Cn l/m: xitp bf(tybg12m5y i3( (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) wh)i/fkb u6 l b)zp/nr9ien the temperature i)biupn/k/i z b69) lfrs 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2/g2por/ xtv8 h0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–xlj+ whnc1 y3010 should the hole be that must be uncowc j1n +0x3lyhvered 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 fw:ft8q)0 w nlHz, 440 Hz, and 616 Hz, but not at any other frequencies in ww8)fl0:tn fqbetween. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two s;fi0n8w; 1w.wduiw/ j pzpp1iuccessive harmonics of frequencies 275 Hz and 330 Hz. What ii w0;zww8uppn/1iwjd;p 1.f 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 z. op;xzo/ias*p9 :3uk5ucnj$^{\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 presen;s1vv cwibau( m 6ik::t within the audible range for a 2.14-m-long organ pipe sa ii16 bvu:ck:;vwm(at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5:9p ;wzl kt1w1/stl qv cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is 9z1tp wlvq/s :l1wk t;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 adjusdrmttc(ube -s-2wiku bw*9k:6 ( s*ctt two strings, one of which is sounding 440 Hz. H wd b-2ub- 6tr((ms9i*suwt *kt:ecckow far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzoj l8h+n n(/p(zmzvn8vwz :2 f) 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 another (brand X) ops 3)r.gb5f w nr3cah,derates 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 operating frequency of rcbsh) grdna,3fw3.5 brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuncmtbx2i* f v5h ss ,p:/imz.l6ing fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is tif.zh :mxpbi/tml 2s v5s*,6c he vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned zsg5yb hpha6 )r3j9a .to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be) 9 haszb3p5ha6. jryg the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will b fve) , zvzgk(nfrnq(+1h+eed (2l *bwe heard if two identical flutes each try to play middle C (262 Hzeq+) ed(vn1 n *+gwvz(ehb(rkfl2 f,z), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forkqzj -/oqpq9xw a-kk65s, A, 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-q6j w-qk/xz9 5 qapok 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 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 and xt )huqr),.3 uyqsb* fm 5.0a gz1iwbf3.50 m from t.*t 1 )yz s.a qfbbm3wirfqhg)u0x5,uhe 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 pd77ymcwkn56rz3: w rto be vibrating at 132 Hz, but a piano tuner hears tck3nwyr7dmrp5 w 7 :6zhree beats every 2.0 s when 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 wavelenl r45 wh yav7d).bqv*kgths 2.64 m and 2.76 m in air. How many beats per second will be heard?d y 7)h5wlka *rv.4vqb (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sir dihdo 0y5gfw +cje 7)i;,mzo1t:4q,p)c fmchen is 1550 Hz when at rest. What frede:1tdfqg5 zo,)7yc,hc io 0mc h;f )mjpi4 w+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 enginroj)2 nfut1zy xc)/6f e whose siren emi6o ry x/f j))ntu21fzcts at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mov -6czhs;rdz ip31l cd(ing toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactl 1p3ihlc6rd;sd( c-zzy the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Wha0 77x( rnj dr 9x1k-dfh69yw)ubdq ,lwfmj6ben one is at rest and the other is moving toward the first at 15 m/s the driver at re7xxw)m9w6-1ffh,adr b 69yjlk d(0qn b7djrust hears a 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 soundwn1*/c b nzj2/ hcwf:j waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequenw j :cnw*hcn/1z/j 2bfcy?    $ \times10^{ 4}$ Hz

  A bat flies toward a /vlf x5jb0c23r1/ mjxgyf;aawall 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 5/ a f1frxlmxg;ayb2jvc03/jthe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba0 s o7pn0ldcr5 was played on a moving flat train car at a frequency of 7p50 cos rd70ln5 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 txhod3v.us3lm;6 dy ,-m tyd6i o measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 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 sourc3dth ;md,y ylo6m3 dxvi -us.6e?   Hz

  The Doppler effect using ultrasonic waves of freq 7g8n/py2rahmuency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind veloc ui9z42wuote(05 6 bhv,w dgmyity is 12 m/s from the north, what frequency will obseb(yt mdo2,9 5w6huwz4vue 0 girvers 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 speedy p+oy.cc;, 9w 6qa cxdf,ew1j 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 4w0yeyhm2i4p/y6gof:y bs v. is 310 m/s (a) What is the anh.4fws6ym4/yb: eyyi ovp 20g gle 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 :jncmxiu -zybt .*c4.the thin atmosphere of a planet where the speed of sound is only ab: x4cnub.yj. c-i*zmtout 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 8506)oyjwyc.x(jkab zl -j5k 3w -.w ryp,0 m/s strikes the ocean. Determine the shock wave angle i.-3y j zjw.bl,jk( y )yrwowa5ckpx-6t 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 k+e+rz4y+znj 2fh :tt$/theta$ 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 exacthifsy fp yjs8er-, 8b7oxxc/- 57k-xa ly 1.5 km above the ground flying fastf/p hf ix-soyxk7 -srje7ac8-x,58 byer 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 that sends 20,000-Hz so gv5+ r:cl kunbq,syu b/)drpu-5f6+pund pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulse y u5+ p)fb l r-dq6un,5kgusrvb/+c:ps (in fresh water)?    s

  Approximately how many octaves are there in ybok, ;q:w pz(nx9r8athe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called8)j* mfuv nw3a a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are ou 8*3wafmj) vnpen 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(tz*o a /ziwg;ko:ur7 makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 10 u :r(;atgwz7k i/o*zo00 such mosquitoes?    dB

  What is the resultant sound level whe)6f.axuc w3ae bqe8 w5n an 82-dB sound and an 87-dB sound are heard simultaneouscuf6bwaw3 q. )85 xeaely?    dB

  The sound level 12.0 m from a loudspeaker, placed in th vkx uh:j3su1 gd9d:r1e open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it rjv9d1d :kx1 :s ruh3guadiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ouz.1if th a yid,qc59q,tput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outputcdqzh1i9q , y,tfia.5 in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ea9:m)egig3 qdyr .,p bars. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotectr)pg,a.egq3:y im 9dbed ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systeskwjav7-s8kk g0c 4z4 ms, 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 frequency awr* ny19fsox15wg) i1$\frac{1}{2}$ 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 betwee;y*j r hk93iq-e4 pwnjn fixed points with a fundamental frequency of 4-ejjn3qkr y; iwp*9h440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a verticalrx b.dmw66tpv (5 nui* 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 resonat ( urbtn65x.mwvip6d* e with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at ovyj3 ejmz: 6m(ne end and also 75j e6j m(mv:3zy cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to re:oft94ii bt9 b+;/ w kprljft.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 tone in the 500–1000-Hz range coming from twos *fg wob9-met8 /e,fz sources. The sound is loudest at points stfzm o,bge e- /98f*wequidistant 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 whistles. One train is stationary. The condurherf85lrtqm4 2f,. kctor on the stationary train hears a 3.0-Hz beat frequency when the other train ap.lr t, mr5 qk84hfre2fproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistl*4;gtaqt 9y,bwsq f*ak1n6z pe as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the tr,fqtab6*ga t*kp qwn1;4s9yz ain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to theyec1,4 x)xfndyl h2c0 difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straigh, nh lyc2y1c4xx0ed )ftaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frff7 tib, 0bz/cd;bi2 : u2cil*3tzvdmt)ccj,equency of 11 Hz. The shorter one is 2.40 m long. How long is the od ,/fc0,c fbdibv37c*t tzb 2uiji): clm2;tz ther?    m

Two loudspeakers are at opp .660utmfftk bopd0sk.f8ki+ osite 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 frequk0.kktpfb d6 6tmoi.f+8f0usencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is ;vs aoe4j:;pah:bk0w normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that :keaha v0s:;o4wp bj;the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying tzf-s7wnino-0mo pb./ y wb74koward the bat at p7w-7yo 0ibk/on 4sf. zmbn w-speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth.z jvs kci1ng0j15fu9(zmg:6 n The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far awayijv:ng6m1us zn1 gj5fcz 0(k9 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 7u 1*tsb*i yj6ngfua+69e ckcfrom 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 9k* ciejg s+ub 67yunc1ft6a*way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence o*mnc y vz/sr-8dnl9 xhyi2,t yo e/(s7f standing waves, which can cause acoustic “dead spots” at the locations of the pressuret,8*z92yn o(rxcs7-hy/ /ynsv m ld ie nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singi , 07fussto0ting 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, ringt7 t0 ,ofs0isuing 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 hum z8p0e*pu 7muju 8s4naan ear at a frequency of abounup8u ema7pju4 8z0*s t 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 theq* j)2y9w xuie ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s 2)i*j9u ewyqx altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15c(:gew22z md 9r w2c0l 5lhbcl $^{\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