What is the evidence that soc5 7zz0rxc 8rhyug1c twnu8 ady8y(5+und travels as a wave?

What is the evidence that sound is a fn:y)9n 4fl.nd mn9csp5u6 ah rorm of energy?

Children sometimes play with a homemade “teley77 vb z1f+tjubq2 s6uphone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a cfytb uvq17u +z6b7j2shild 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 passes from air into water, do you expect the frequ 1v ;/shccfbh/ dn5dr-xriel .;r3r d0ency or wavelength to chafcrd-d dr.b35;xe/ 0hsi rhnc1r v/l;nge?

What evidence can you giveucq+z2nn 32v p that the speed of sound in air does not depend significan3v 22c uq+znnptly on frequency?

The voice of a person who has inhaled helium sounds very high3ckj i qmzgc.r,we099 :xbi x,-pitched. Why?

How will the air temperature in a room affect the p k5vtpvc2*. l sz(cc2pitch of organ pipes?

Explain how a tube might be used as a filter to 3:unxdey j8llp yesh. h-..9freduce the amplitude of sounds in various frequency ranges. (An example is a car mufflxjynlfe.:- y 3ds9.8.h h pleuer.)

Why are the frets on a guitar (Fig. 12–3hz/0o -mv(u9uu lgwz7 0) spaced closer together as you move up the fingerboard toward -o9l(7 hv/ guz mwu0uzthe bridge?

A noisy truck approaches you from behind a building. Initially you hear it but xe8 l8+w lvap1cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency lpa elx8vw+18 noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bea gyd 6dk;acf)v* z*w4pe* f nld6tx8,vts can be8f6edad x6fg*z k4 ny ,v)dpcl* *t;vw said to be due to “interference in time.” Explain.

In Fig. 12–16, if the+)lut wye3zy chc y588 frequency of the speakers were lowered, would the points D and C (where destructive and constructive int8l3yheu +yy5cc)t w8zerference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wore3sw-1xq 4ad sk in areas with very high noise levels have consisted mainly of efforts to block or reduce noise les sw dae1q34-xvels. 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,xu(/:- bfyco n-h kzo be thought of as a supec xby z/:(of,h-ok-nurposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if c0ocm. ;yhqb 1-; l*mll oz0buz3aoza; qq2.o the source and observer move in the same direction, with the0o;1;huqo*llb.cqb2coza3z ;l moq-z.ym 0a same velocity? Explain.

If a wind is blowing, will this alter the frequency of the so uc(lne2,y5er und heard by a persorl,n5ecu e2y( n at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chilik261ox4wanw d 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 for the sound of the whistle? Explain your61 awn 4iwox2k reasoning.

  A hiker determines the length of a lake by liste(uopm; 5e8u wpning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lwp eomu u;5(8pength of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the w5xalem p 2l3w3z;qdx0(qf bd 9b52zslaterline. He hears the echo of the sound reflected from the oceaabl22 x3xs95 (z0 3qewq ldf;m blzp5dn floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2.o t1o65;7*gf)ytxf d umkrhi0 $^{\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 drift8-1db9a cxivup y6 ex+ qa4 ajw8;)(;j lmrilding just above a school of tuna on a foggy day. Without warning, an engine backfir9exm8 aj via jw6diq;lyd 8 - +urabl(xp)c1;4e 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 tob;exc1j l1f32oodwd+ p of a cliff. The splash it makes when striking the water below is heard 3.5 s latl c+d1d beof ;jxo13w2er. How high is the cliff?    m

  A person, with his ear to the ground, s 4-b34+cer/ mwyu iurlees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact- yb wuirlemc+4r/u 34: 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 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secoc1muo;eic (j6 cm( 2mvnd rule” for estimating the distance from a lightning strike if t(ie2vmjmco;1 c (c u6mhe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitr1,94as i *y/t5b rqjd6pfrpvfi. u v*y of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leae36bn r92j,vbw1t tpvel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired s .9wpo)dgoi -jimultaneously at a certain place, woo)-.jp9 gi dwhat 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 equ8o ux oew d3s) f9 fshawyo::5n0c)ds6ally noisy jet engindneoh:0ydoow fs ) aw8 3s)9:5fuxsc 6es is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas forst ,1vicf:ds k ,tg9az:2m *ec a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgrcge,dma s 2cf 9k1 t:tvs:zi,*ound noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in no*,yd4ijcd .f ormal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouthidcf,d o*yj.4 . $\approx$    $ \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 anicr nfkbv o.c 0t/105n 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:n b*:fhg8v; y9zp rny the more modest 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 connected in turn tn;n8:yfbv9 z* : pyrhgo 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 frontsy85hlja f6 g 79qg3qknh17ggoi e8g- of a lo7 jaq 768 syg-5qkgfneo3 h8hi gg19gludspeaker 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 level of 2.0 dBh;s1nhb)bo6q qd:s/ m. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? m b6hqosdb; 1hsn/ ):q[Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) bons7- z5cvch* y what factor will the intensity increascnszoch 5-7v* e? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice tho7avi z-ds ;k:e frequency of the oth ;i o:zvkda-7ser. What is the ratio of their intensities?   

  What would be the sound cvjmf1 mbw21s7te g3j8c2x /dg,v0 pwlevel (in dB) of a sound wave in air that corresponds to a dwm,p8gvxe 73 jbg0mvcjd21s 2fc/t1 w isplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see +7e5,9z*skjwpoo;/e. wjc b 3elzl iem as loud as a 100-Hz tone that has a koze+z7ejei s.ll, /bj9;3 o*5wc wep 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the iypwctyq7dmc;8 vtxs;w43 (q 1:*k iv sound level is 30 dBwvy8dm :;4tciywqpix s;3tkv7q1 *c( ? (See Fig. 12–6.)

  Your auditory system can accohh0ff:vdbc l .m80 q26p+0)lczi ffoammodate a huge range of sound levels. What is the ratio of :08b qdalcc +2)ifzffm0 6 0ofhvphl.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 fundam8n-j2(xve eajental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. U ejv8n -(2ejxander what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audiqj pai1 :t(9hdble overtones if the d1(ih9a jtp:qpipe 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+nwm pr:9h5 zrgl2 zshb.ut)7 you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tub hzbn h59p.7gwumlsr r2zt:)+e?    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 .0s3d7p,cn0vmtxh.rmb mw0d the range of human hearid0nr,7sv0pmmth0c bmx d..3w ng (20 Hz to 20 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 f.z 3pq7ep a3ofrequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originaz73ofpe.p3 a ql length?   Hz

  An unfingered guitar string is 0.73 m l ve4 z.2l3 wg ,q4p*mvuqetg0oong and is tuned to play E above middle C,povg z umgve 4.43*qqle02t w (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 n9*wtn 7zm46f lcgsy2(262 Hz) when thsg69 f7m4nltc2*wzn ye temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 3 jo j2io0v)y-u ,zwye$^{\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 should the holeshf/1ylsbiz5 m7t h,3 be that must be uncovered to play D above middle C at 294 Hz f,szth ym5i73lsb/1h ?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 61u,a4+1 spm-owwkow7 a 6 Hz, but not at any other 4w+ wwa,1pmoo-suak7 frequencies in between. (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 tw 8nv d;ygd+o-adm,uss2sv iqfi1+ /+bo succ 8+d sn/uvb q,+-sdia+y;i1smvgfd o2essive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 cakc7v 6 ztk1 :6v7ett3 he4wo, (jhtq$^{\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 r2i c 9ymzt l4 9(knuxea7g/n,oange for a 2.14-m-long organ pipe,/ie92a4yt z(7no uclmxkn9 g at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is b2. katktc.u/ approximately 2.5 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 the relationship of your answer to the information t. ctuk2.a bk/in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings,vo-,cji 4l 0ne ,v zqkd-5y.ll uxcu92 one of which is sounding 440 Hz. How far off i5- ouve9vl,k 4, lcdn0zlcu.x2 qijy-n frequency is the other string? ±    Hz

  What is the beat frequency if m 63+azv7xj ;d fren4ru i,j,mztc :,pciddle 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 kHz, while another (brand X) operatedv8 bvv7lg .b12aig( gp1k+ges at an unknown frequency. If neither whistle can8dv gvabb7 gg1i.lgv (1+pke2 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 f 5qd(9qn3)y prw++vkb sdtr.iork and 9 beats/s wh5qq3rtnpb r+kid .9 yw(sd)+ ven sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 -3fc re lt9fbxb1-+hmHz. The tension in one string is then ebm b-h 193+rl fxtc-fdecreased by 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 be heard if two ide e ,*j0x1okozqy)sx z(ntical flutes each try to play middle C (262 Hz), but o)zoq 1x y(*o0jkzxse ,ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,y5g14 b 85zd2rp f;iaq8fp dbtb df2k( 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 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 toget5f4d1 d2f;fzp2tybr aqg8b5pkdi (8bher?$f_A$ =    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 ojqskf8z zr/xg*1/ h8y ne speaker and 3.50 8qg1 r8hfskzjx/ zy/* 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 sup4 ksven.*d0vbsl.: nngjr) u6posed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when theydn 6. vvn.nskjbr): slug4*0e are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. H62l kzbn9x+y oow many beats per second willbk nol9x+2z 6y 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 a f yzpped91stgm5 8.--pm) nxogq/bk 4t rest. What frequency do you detect if you move with a spee pdtyg-np1mo9e8.q-g s/fm4 5zb) xpk d of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yo:rj4y 1tnz5xg5mlsj e+0 vi:du detect if a fire engine whose siren emim55 ndtjvji+yes zlr0g:x :41ts 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 moving tow,hlxxbg2;z: y 3ozl3iard you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? A ,g3o2i:bl;hxz3xzl yre 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. When onejkjp cda/p s te+,n-61 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. 1cdtej,k/nsj+p 6p a-What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonicd(h0 sy p l;xz*1se0cm sound waves at 50.0 kHz and receives them returned from an object z0s0x;*dlpc e1m(shy moving directly 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 fliesj:upb.k rl u;8, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wu8l b ju;p.kr:ave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving f9o5pmuz8iqdkk.n mn:x8(+u cl8s*l alat train car at a frequency ofqc88dx u+kuom:k9pimn zs5.l 8a (l*n 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 blixpy+*, mmq*a;*jf ccood-flow speeds. Suppose the device emits sound** ,xpccq;+yaf*jmmi 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 source?   Hz

  The Doppler effect using ultrasonic waves of frequegxl/;fqxj uws9-zl ..ncy $2.25 \times10^{ 6}$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 velocity is 125t/,byr4-kgg;h gq bz m/s from rg tqk zyb/4,- hggb5;the north, 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 lanb 4fq54 /xg1enqxd/d nd if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed o/r ml3 q/tpu1dkahv 8:f sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s m/u:1rm8hkd3 ptav/l q otion?    $^{\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 atmosq *x uibkav*-k 4sp9d1phere of a planet where the speed of sound isk*uxd19- isk bqap4v* 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 shock wavkr2vd t5d4n+m,x uzz 0e angle in24zdxmrv5k 0d tu ,+zt 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 uwr t,id. xs4,$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhemempap w 8xib+4)+;mead 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.+pe)8eax; wmp+ b4 mim0 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 20,00jje6twwtk- s )ek8:q/0-Hz sound pulses downward from the bottom of the boat, and then detects echoes. wqkewt /k68-j :)stejIf the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible raus3;y -t0oau wb :oeb.nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonye )ig9m5c9c ce s+u6 6mlrpy)g. It consists of many plastic pipes of va gmicl sp9 +6)ece my95ucr6)grious 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 fro fs 1i3nr);chk1h6scm m a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level ofc hs);1 fkin13 rshcm6 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-vg:+a.249krib6awloqavbf ( hdd - (fdB sound are heard sik2h.dgf6a:9+v(( bwo-qdvfb liar4 amultaneously?    dB

  The sound level 12.0 m from a loudspeaker,u5h y: s1jfs6w placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming u56s: fj1y shwit radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dro)xmr2i4 - btow ((gumxps by 10 dB at 15 kHz. What is the power output in wat )4(t o2xrmux-(w mibgts at 15 kHz?    dB

  Workers around jet aircraft typically wr x*iprqd.- vu,lfsa aky;w ;c /6x8l,ear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a * 6xyxuq wps ar8;, ,;.lack dl/friv-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 communication9d zpd87bmwo9 2ig;obs 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 violinthh.2qr mav ocdjwn+*3 j t09,jn cy-/ is tuned to a 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 between fixed points withu2vjq i6 /fz g( wklws0)a2omy6-mim1 a fundamental frequency of 440 Hz and a mass p1w/2 qk0m 6l ifvuz)g ms6 yo-wija(2mer 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 opfa 7 /pp5*7;zr9fpkkz ) iskrlen 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 again at 0.395 m. What is the frk9pk r frz*l/ps5pz f7i7a;) kequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that iv: bnub4 *vpa3s 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 t4v *bpa: ubvn3he third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsvq ( izv1vjn1z 77lh(jerved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Th55f: a7:tmol: xfl lthe sound is loudest at points equidistant from the two sources. To 5: f l:lx:a ot5fhmt7ldetermine 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. q-m qrm9gzurq-8e p9.One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving t .p8rmq-99 q rqgeu-mzrain?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Af c (0xa9th6ukfter it passes you, its frequency is measured as hcxk60 f9(ta u486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenintc ras02hksbb0) 3-veg to the difference in pitch of the engine noise 0 vs ase kb20rtbh3c-)between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 h1;2o7 e8qxw-fenm2(ugn wb iHz. The shorter one is 2.40 io n fe2ew 2(qgnm-7w8u;xb h1m long. How long is the other?    m

Two loudspeakers are at opposite ends ofs(x a-3.stdg h6cpfhu06 ei6 m a railroad car as it moves past a stationary o(a6.sfhs 0-6p hteic x6du 3gmbserver at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bn6ovt c8/ebr. eat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a sotr./e b6 cn8vpeed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s w4ne e6omq8 1su )t2rvhh y38.rx 3wbndhile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off3vb8t uqo)ey. m2x184 r 3 6ehwrnnsdh the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches1+a l3peiv vf2 a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away v e 3fvp2a+li1can 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 scx 7pbke 3p-n7knk,d kolodhi 07+7*eignals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popul bdlk70d3k, -px*7kooihenke + 7ncp7ar 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 sterl8z7nv wos5a /qn oy k4j,0/zgeo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a ligv4w/n j5 nkz /yo0,laz8 osq7ving 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, .sl+y 5 hfy (uup13kgju9 yecw.1szej*.o.fgcalled “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 sound. For a 90-cm-.he93 g jyuw foejupu .c(5.+ zsf1syl1yg*. klong 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 + 4jkdd( wf p.*3yucm2d-ytxjat a frequency of about 1000 Hz isjjd(ypfy w-3t ud+mk xd.2c4* $I_0$ = $1 \times10^{12 } W / m^2$ 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 2q-er;8(rk mbh.0. An observer on the ground hears the sonic boom 8h emq(-rbr;k1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is q6w /n.y3 cqzppqb8 f615 $^{\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