What is the evidence 8or i,;p mn/fx*:jqwethat sound travels as a wave?

What is the evidencec9zgtf64jsd sn q,mu3 )(ykx: that sound is a form of energy?

Children sometimes play with a homemade “telephonew 1z9z27d gluq” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. q 2dl1z gwuz7912–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, dlh-tf(kf by 8: ; fmfz-wq9.kpo you expect the frequency or wavelengl-;m ffq-pw:(.f 9bf8t hkyz kth to change?

What evidence can you w, vp /--qq0ctv( pvnfgive that the speed of sound in air does not depend significantly o 0(q,vf /-tc-pvnqwp vn frequency?

The voice of a person who has inhaled helium3dcwr8/*ho q:e rj.t rr nub6) sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch )zn) ohu+bp5:i ;ahmr6qa 1 vgof organ pipes?

Explain how a tube might be used as a filter to reduce (oi cid,jir(9 9x, yrn7ocgjd6-qju: the amplitude of sounds in various frequencyo dj 7rqo(y-c,9:di(6nc rixg9ju, ij ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethe/a r bjf5i6h6kbjhf( 9zqf9g3piw/6 t r as you move up the fingerboard toward the bridgeji6 hbqkj rfz 6i6f9f/3g9tw(5a hpb/?

A noisy truck approaches you from behind a building. Initially you hear it buy6q- q:*qdp egt cannot see it. When it emerges :-epq*y gqq6d and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can b,cthcvc*2ru ) mo i4nvi5 0fn;e said to be due to “interference in space,” whereas beats can be said to be due to “interference in time.ri,u vn0t;hif4cov * mc25 c)n” Explain.

In Fig. 12–16, if the cgwu r:.f(0clq)i/vz frequency of the speakers were lowered, would the points D and C (where des/)wv0 (rzguc i:lf.qc tructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in 16-r. j j2s. y cofd nexbmw8(s ik8m9.hj*hmzareas with very high noise levels have conjn8- foswd y 1xhs(hj2..m 8j eb .*r6k9zmmcisisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be*vka5s gy)g ac)2xbh ; thought of as a superposition of two sound waves with slightly different frequencies, as i)*sx cy a 5;)h2vggakbn Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in th j8eakd,p9p7l e same direction, with the same veloci8j ppa7 e9kdl,ty? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a peryvy65a m5io i6k.l i8yson at rest with respect to the source? Is th5o ii6l6yka8miv5 y.ye wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swbmh(lv y8ks4 4ru:-guing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E8y4u-krmuhl b(v:g4 s, 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 listeni9nggywk9*qjc/ t8sx48lbv q+ng 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 sho g9j4t8wv*q x/b9 qgs+nyc8lkuting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his sh8hf+)nvdh0 ), . m -eojdjilwwip 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 seawater is 1560 m/s (Table 12–1) and does not vary significanh-,) 0 dwe. f )ohm+ijjvdwnl8tly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelezgg)sj g9-7(7gvlwt z ngths 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 l p+eb o4uh+j.school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is hear u+ +.hle4objpd (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a 6fhftjd2u e03 cliff. The splash it makes when striking the water below is heard 3.5 s late0fuh3td2jf6 er. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concreky*7 e y yef,lo:74zrhte 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 impact occur? See Table rye*zl7f7yh, :yo k4e12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distae8+vlz . txhw3nce by the “5-second rule” for estimating the distance from a lightning strivhz3 wx t8+.elke if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s+9vnvp xu4ma. ound 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 intensi,xn3 qioxzp9szfv , 86ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers 3q:7+qpbt2 b uh.rskt produce a sound level of 95 dB when fired simultaneously at a ces: utthq b+72.qp b3rkrtain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally 94 )a/whfed gpnoisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experie fw9d4ahg) pe/nce if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a six*v1: aosqp7riw c+6 wp -xh/jgnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise 1i:cxawo6vhsr/j- p*q +7w xpfor each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persofbuyi1 t2 r4zpob9o/c+,ezu4n speaking in normal conversat,+ efz1 yuc rzpb4o9iob 2/4ution. Use Table 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 an eardrum whose areacg43e7 j 4sn sx-ky;yw.i0qbj 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 3:.wtdc0wi, zgb/j. ebipl -o 1w4wn kmodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker con4 wgibw:o- n3wt1l,k.ibj ew 0/czd.pnected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of ant9ndwxq;e x7w (l-y6 i h/vd( loudspeaker on thled-76 ;whwvtq(x i/9yx (nnd e 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/ijna3cuny cfxn+ ( 0) 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? [Hi c)jan0u(i/3y c+xnfnnt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the if5xxv+pam 0- qntensity increase? I- a0fxx+v 5qmpncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displik5kh6/ gec9aawj5ih. i8s c /acement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitie 8i/kc5gck iah 95ah.6 wji/ess?   

  What would be the sound level (in dB) of a sms0bc9z w qh+,ound wave in air that corresponds to a m zcw +9bs,h0qdisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz 4evcawx;3 2- yyv w1(wac0gpdtone that has a 50-dB sounycwve(w;c0 wyv- 243 gp d1xaad level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies(d) gjxqm+ )tsq4d-tz:qmk3p that an ear can detect when the sound le3d(ds)m )x t qg-zj+qqk m:4ptvel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soub9hdu 2ci6 hs1nd levels. What is the ratio dihhc912 ub6sof 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 viogz (onmgeu5 vi4( 0is7lin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and i5z0(7 i g4os(mn veigut has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three magokz 6.9 q;9y/m nq0eonib ;audible ooaknmei 0/;9bqq o9 .;g6zy nmvertones 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 aanj x,h wamn.o(rr5yj -:hprz/j3*d3cross the top of an empty soda bottle thh3m, a5/ r (hp 3jonraj.dz*nr wy:j-xat is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pidlxv2 8t69 gcwpe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 lwtxd96g8v c2 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hzzwx1p7( s8r ar as its third harmonic. What will be its fundamental freque1arwrp xs7(z8ncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above migeeo04df+: wzddle Cgofe:0dz4w+e (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 middlzh.8yj 6zm/utl/wn 9gx v w8/-f hvrd+e C (262 Hz) when the temperatur//8 -wyv g8mn/zf 6 z.+j hd9hlxvwture is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 l(m cwhyce:+0nl;zm5$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shoulkke3icog +ed 0n) 73y/ ec,pcad the hole be that must be uncov ekca3yo,g/d0 ke3c)e7c pn +iered 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 pielamlll 3*4qtt++ . qz 5cmg*upe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in be5 qu*3*l+lm gt ltela qm.4cz+tween. (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 botx+mx8 +:*(vpbq;r vki mgzw*k h ends. It resonates at two successive harmonics of frequencixv mg q*k xmr(zw8;*+v:kb+p ies 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 dzb(5zerl r1 dq 2b6g+$^{\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 y7b0c/el 9mjd,y6rfv6ebv( swithin the audible range for a 2.14-m-long organ /v, m d6ej7s96verb(y blcf0 ypipe 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 mkhkx6qbc47bjxkhc41 0 s a9 +is open to the outside and is closed at the other end by the eardrum. Estimate the frbka h70k61q sxc4m b +jk94hcxequencies (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 oneih6f-qs, vmh *dbq9/w beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the bw6s-f9hi /*q qhvdm,other string? ±    Hz

  What is the beat frequency if mtmm+q,.m g/;mx l6f f b(zece8iddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 27s1 c78moiqum;vuhdvl 5vn +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 simulta 1ulqs ud8 vohmv+;72cmv75nineously, estimate the operating frequency of brand X.    kHz

  A guitar string producesvp euv)r/:sw /fjy ;kz6chb dx0i:a*( 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the /ph isk e:r)/uwdbj :vz*6cfay; v0x (string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensio g:m b9/9yxyxmjf 7oi6zz9wo /n in one string is then decreased by 2.0%. What will be the beat frequency heard when thebjygxmo9 m/z9/76fi xwozy9: two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flute/etj 0t3wf r0uqhl; h0s each try to play middle C (262u30hqf/ ;jwh00 lrt te Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork / xohj9uqw2q 0B 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 fw u 9/j2q0hxqorequency 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 3wl oqpr6 .,2v,a5gk8cprjiz5.50 m from ,jg icpv z,o8.rl62qkra55wpthe other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz,pdlg-jyc :4: c but a piano tuner hears three beats every 2.0 s when they are - :4ydjlcc :gpplayed 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 air. How e*kg2 )flv7iye (s k-dmany beats per second will be heardy *ek2-)(lfdv7i ek sg? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain f se .i,7cdtt;tire engine’s siren is 1550 Hz when at rest. What freq7.tteict;,ds uency 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 :vq f7mlf3:cq you detect if a fire engine whose siren emits at 1550 Hz moves at a speed7vfcl3: qf:m q of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz,qt be,1 wb ghx),5vnh kk:qc; source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are :qb1whkhx)t ,bqc;,nk5 ,gve 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 equippe5x5z y9erq.ei,g xir1d with the same single frequency horn. When one is at rest and the other is moving r .i5ri xgey z1ex95q,toward the first at 15 m/s the driver at rest 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 sound g0vlmay n*o wcqm7w*/)e pa,2gk71 q xwaves at 50.0 kHz and receives them returned from an object moving directly away from it at 2 ma/ p yn)aowqqk 7g71v *,*lmcexgw025 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wa00z x g2, hm.,ynaajoall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.a 0.gmoy02anaxz h,j ,0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuby51ii( a0)n*np.-1tumbshif 2w 9akei e*lft a was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 1( 21tn 0ai )ew-tplfi msk * 9n5fiih1buy.*ea0 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds.6 4ras9ejmewo08mh5d 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 flowimrs9wad46805j ehome ng in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ult3 6)f+m*p)-zmp zld qxy ef6jerasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits soghn/3y/ pk2 wdund of frequency 570 Hz. When the wind velocity is 12 m/s from the non /pyg2hd3 wk/rth, 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 speed at 20/w+i(yy6wl hhj kar.( $^{\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 thetshr9k qtyc 8gj4v3)emjy50 2 speed of sound is 310 m/s (a) What is the angle the shock wave makes with9 2hg504 y8mj)jqr3ey kv sttc 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 vmoct . 1bq)(t*+5 cjp 9czlcmwhere the speed of sound isjp195qt)*mcz.lcmbt +o c( cv 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. Dencm g-zjsjy .1+4, uuvtermine the shock wave angle i4+1,uvmczuny .jgjs- t 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 ggwq5 shp:l/avz )(f + t1dts*$/theta$ 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 exac41k2jt gz3kze ,9bklztly 1.5 km above the ground flying faster tk,9el kb3 g1z4tjzz2 khan 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 that39j., w kh8uavx +wedk 6 mpi;vq,/yia sends 20,000-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 minimum time bee8uvxyhai w6,k;, ia. p93qk+vw/dmj tween pulses (in fresh water)?    s

  Approximately how many octavs/.(i4ivy8l x bf1tlhes are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It con.vidyx uvb;*)sists of many plastic pipes of va.)* ;bi uyvdvxrious 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 the threshold of h/d2 d z2b;y7(z5wv vkcxytsh i-/4uz buman hearing (0 dB). What will be 2 ydu s7/vz 2zwh;5btixybzc4-kv /(dthe sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 8yfrg+6o ge-xsh2*y i: 7-dB sound are heard simultaneou2- gfy*sgr eh xiyo+6:sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB..s zyj bp 8cr8+ci/mt, What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions? 8 c+zbrcp.ijs t, 8my/   W

  A stereo amplifier is rated hb;m(z afhwt. 738tpe at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. hhta73fpb; wz8( m.teWhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft tyhima 8 so45,pxtw.x8x pically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the av.584ah8ix,pw s xoxtm erage 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 systems, th jh+z; t2:sacv(k,su ee 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 aj;)z xgq7m irq7q02x :wf7emn frequency 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 bet iamgrax)34b54f y +0wjvyf1hween fixed points with a fundamental frequency o0b wji1yv34ama f5y )hxf+r4gf 440 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 vertical open tube filled with watei. .8p0kq cmgvfug.e5r (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 open.ggqpf vce 08i5 .mk.uing 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 ne8.7yby.)clyl n kf ca;ar 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 r;yc7.alnk f)bcyyl.8 esonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loue5cruc op7.2 op ($\frac{1}{2}\lambda$) 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 t3tz*2pzccu q;6)5kc n 2msijiwo sources. The sound is loudest at points equidistant from the two sources. To dete5;)* 2miju ptcz s23k6cznqicrmine 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 vqixy3 s6.ve* stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other qvxi se v.y6*3train approaches. What is the speed of the moving train?   m/s

  The frequency of a st (;txsym,(jj60 k9fq sy(qdwbeam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured wxj6q (y;s dmf (qk tbs0y,9(jas 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the dx72i r b(scw1speed 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 goes by on the straightaway. How fast is it r27 cwdbs( ix1going?    m/s

  Two open organ pipes, sounding together, producew1611qpm,0x0vzc ekv ywn -qx zxu24 j a beat frequency of 11 Hz. The shorter one is 2.40 m pxnjz1 w1e4z 1kx qy0vvqx2w-u60c,m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rail12p ,th ;cckg icrm77vroad car as it moves past a stationary observer at 10 m/s as s7 ic2 ,tc chk1gpm7v;rhown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aup:fl, (-ybyv orta is normally about 0.32 m/s what beat frequency would yo (- b,fl:uypyvu 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 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 toward mkzzy5 4,y -jc qzudv+0n 0uo1the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency ouzk- u10qzvyy j5+4cnd, o m0zf the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency s yet ;d8zxsx5y- u-;qcound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms loc xy uz -yq8tse5d-x;;ng. 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 from one Alpine -6;brj,dxn( ohmoz1hvillage 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 h j rxd1o6;,bhz-mn o(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 theha u8z7+y(v7 9yyt b-m lke7nadjd /n4 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 l( 98 td+d7jbz-aka 7/nyy7 uy4evhmn frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invqhjmax-f:c:mz*9nc)v) co d ;olves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hac-d ):n;z*acj9cm fq :o)xmvhnd. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of cx4;yimce 80y-csg-e about 1000 Hz ;-ges8y cei4myc c- 0xis $I_0$ = $1 \times10^{12 } W / m^2$ 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 theetgsu3 ; (hq1 op;wp(n)qzw+ d sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s al +);q e3pn(qzwo g pt(1uhsd;wtitude?    $ \times10^{4 }$ m

  The wake of a speedboat t0)( uuqojr.v 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