What is the evidence that sound travel7ec6q-( dhdoekjs: al) 5pon 5s as a wave?

What is the evidence that sound is a form of energy? ri g1el*hgalq67k)7f

Children sometimes play with a homemade “telephone” by attaching a string too:2agtb ujoc(s :tbmye.,4g i qdb()0 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. 12–29). Explaiy( a :,jb.de:o)stg g(i0 4cqbtu2bmon clearly how the sound wave travels from one cup to the other.

When a sound wave passes from airf cmi(,,gpwa(ct0cw:67 nsb c into water, do you expect the frequency or wavelength ,nc pwfgc:sccm 7,bwi6(ta 0(to change?

What evidence can you give that the speed of sound vdwth r :o28*0za7f) g;k-x-szmtekz in air does not depend significatkv0h;fd m rxz)a- 7*:2 etkszwg8o-zntly on frequency?

The voice of a person who has inhaled helify i,u5c8ecwn2g 5r t9um sounds very high-pitched. Why?

How will the air temperature in a room ,;yy 6mv es,0n 8n/ 0 ,svorxp)akfllkaffect the pitch of organ pipes?

Explain how a tube might be used as a filter to red 7sz(n.kj;m rtuce the amplitude of sounds in various frequency ranges. (An examp .zt7m(kjsnr; le is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yuqa3s ) 8s3goaou move up the fingerboards)g a33uaqo 8s toward the bridge?

A noisy truck approaches you from behind a builnpyy (5ecgg 497u*p l-xxk9h dding. 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 the high-frequency noise. Explain. [Hint: S- 7(*p u5gl49 edxyc 9xykhgpnee Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wd +ab4ob.1i/w fto c13rp u0gbhereas beats can be said to be due to “interference in time.” Explain.4g /1outd. wfb 1iba3+0rcp bo

In Fig. 12–16, if the frequency of the speak0a- f-0g) ygi8bwtus kers were lowered, would the points D and C (where destructive and constructive interference occur) move fau0 st 0-yg)wb8i-kagfrther apart or closer together?

Traditional methods of protecting the heara a3 igid6: uk7wps j(-bqx1e)ing 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 tecx u i6ja():-p k7a1g esbdqi3whnology, 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. ,u6uw/-rpcb m19hul tEach wave can be thought of as a superposition of two sound wumhrp9b6,uu-ct/ l1w aves 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 the sour g -jyeru,((qy-4 9ngopca*xoce and observer move in the same direction, with the same velocita ,-gg pr*junq-oyecoy9 4( x(y? Explain.

If a wind is blowing, will this alter the frequency of thz kb/qy3n p;s-e sound heard by a person at rest with respect to the -;ks3py/ bzqn source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. Ap h)g6pqi 9 zlx: eorcj3ii:+- monitor is blowing a whistle in front of the child on the ground. At which po +li cir:zpq:6oip9-g)j3e xh sition, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening f .pfg ) tj50gc(r.msnjaxk17ror the echo of her shout reflected by a climn1)7.sg0atcg. j k (jr fx5prff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlinec -,nzydvs eos 5sq,:ag)gt7;. 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? Assum ,t;)ozasqgs7yv sge5- cnd,:e 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 i7v:g, cdd jev s )veh9 b95gb:f8oara5n air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna0am plp5+vqu)rhjk(i 8d+9dy 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 backfirp+ d( q+p) uyh8jv05 liakrm9de is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Th yi2ehpj )z7.ie splash it makes when striking the water below is heard 3.5 s later. How high h.pi27z ejyi)is the cliff?    m

  A person, with his ear to the ground, sees a huge stone s,o 6immj:nz o,trike the concrete pavement. A moment later two sounds are heard from the impact: onjmz ,6mi,on :oe 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-hgc3s+rit u/9second rule” tur3i h+g/ c9sfor estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s0k +v+z ,o 6yx64c4x vtpti4cehqzbr6ound 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 intensithk0x8ft 0 7xmyy is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired s5 qje-v*f;yv3yso /koz k/d jzxf.b 1.imultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intey-jvq5 d f bzzo;31yo./kkx.s*e jf/vnsities, not dB’s.]    dB

  A person standing a certain distance from an airplane w79cq2r x dr-:6tjtqfa ith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.] qqj -trf t7x:26 cd9ar   dB

  A cassette player is said to have a signal-to-noise ratio 08qgnj ec t15ojp-+kg of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sie j50+1c oqkg-jn t8gpgnal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a personfv bl.7y7g b5+bof9o+lgdvq - speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over ao7 bf. d+ vlg- qv7f5l+g9byob 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 eardru.fk(/ */6 ga9o xctpknxi6b0mtgvi 5nm 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 7ok : vh- ypuvd-)(qjlthe 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 hl)(v:j udy-v p-o 7kqturn 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 mvnk05wdqqb m4/h9 dzznty7z pq ((70a in front of a loudsp5dkm4by((0z0nza7z/9 qt nqpq v7h dweaker 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 level0 m)qs/no gn5u of 2.0 dB. What is the ratio of the amplitudes of two soundsg/sn0q on 5u)m whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is s +vhxkg 5ox;fvo-c35t 8udh4tripled, (a) by what factor will the intensity increav 5ghtxf;x scu oo4v+ 3hkd58-se? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equx-c:j8l/f; wif 3aoy 9v 9umlmal displacement amplitudes, but one has twice the frequency of-xcy9 o8j/3 uml;vmiwfa:l9 f the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponwz5fi 1 dn:w opj62kzvy, (il)ds to a displacement amplitude of vibrating air molecules of w,z(i )vy fnlid5 j wpk62:1zo0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wha)-r6/5mnog pxb vqg :ht sound level to seem as loud as a 100-Hz tone that has a 50-dB sound x gbh56mnv-)qrgop:/ level? (See Fig. 12–6.)    dB

What are the lowest and hiyc mg :b1q/p13t:*ag5r al szmghest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. b pg: cg/*y13 :ma mtsqr5azl112–6.)

  Your auditory system can accommodate a huge range of sound levels. What is th:xhm201 r *o dey3jf h:m4yqgse ratio of h::r ysofgm 02e1jh*m4qydhx3 ighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lenvey:anh l8nq29xl7wyuu2+b +gth of the vibrating portio :xvel+a2 + ynhn78 yu9uq2wbln is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first th br 6s(+ol +6wnp*bj,f-tf6nyn ifz ;tree audible ove6w b+;+6nntyfzfil rf jpt -6on*b,(srtones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top o(jfzyw ,gk / f-mw5d9xf an empty soda bottle that is 18 cm deep, if you assumed it wa(dxf j-/ygk wm,5wz9f s 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 pm)2561 owepzmv c3wz xipes spanning the range of human hearing (20 Hz to 20 kHz), wh21 ewo)zzx3pmv5wc6 m at 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 Hz as its third harmonic. Wh9xeldi( f63co at will be 9olied(c36xfits fundamental frequency 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 n0frxd9ph3. i above middle C (330 .n d0ixhpf 3r9Hz).
(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 that82yl6aqee4 oroybc1j 3ija 3. emits middle C (262 Hz) when the temperat6a1lqy3 42ieebraj3oo. 8c yjure 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 2f2+3wc vpo-d7hqfg2 k:l mz(i0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flut1ei, 8 / 8dzn w*wiy2bnl5gtece in Example 12–10 should the hole be that must be uncovered to play D above md1c i8lgnz w2 *iyw5t/ben8e,iddle 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 Hz, 440 Hz,2 7kexd zqh()a and 616 Hz, but not at any othexeh)k( 7z2adqr 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 ual9a2,vc ) ghopen at both ends. It resonates at two successive harmonics of freque2v a )h,gcua9lncies 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 ce0qavv 2ivx2a,25 u f$^{\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 withinr0:)cmiu31 fdgbv9 a arp1 wo/ the audible range for a 2.14-m-long organ fo0g/a 1r urma9dw):pc13ivb pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm6e(hhxra66nr ;u pm1p long. It is open to the outside and is closed at the other end by the eardrum. Estim(m 6rue1aphhrp 6x;6nate the frequencies (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 one2zmhpe - p**zw beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. Howzw-phm *ep*2z far off in frequency is the other string? ±    Hz

  What is the beat frequencyhk-uye t,v03 r if middle 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, wxr7hzw f(u,0web a7; sfy6fu( hile 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 simu fy e7ur(7x ab(f ,;fh0wws6zultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundwi85ki,kwp 4p.7k ziq:e rsl6ed with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of iie pksl, 47 q:krzwpi.w68k5the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequnn) qf b1kv(qj.5t xc(7(ovmkency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.] 7x5(vqnm c (fbt1q.jnok()v k   Hz

  How many beats will be hear)d, fpx,*v5 4gcaw l89mnhao ad if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25fd )h9o8wal,c5xa a4v, gnp *m.0 $^{\circ} $ C?    beats/sec

  You have three tuning fo(nyw4 o(y efyy1dmt,pv+ y e,+rks, 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 nw(tee+y,y(fy4+ ypvo1y dm ,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 4r6zqn: mwrk5 one speaker and 3.50 m from the other. n krmz64 5r:qw
(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 vibratix yo8mf+7d 2w4xspxc f .7buj+a*s7pung at 132 Hz, but a piano tuner hears three beaa2x o ys.fuu4c8*xx jp 77+p7wd+mbfsts 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 wavelengths 2.64 m and 2.76 m in air. How many beats 3gn6x* jc 5hjztoz04eper second will be heard? (Asz 5c hjgz634e0x*jtonsume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fwh- g h0)i*/5a- w6 yycs gkc7homyo xtq4h.:vire engine’s siren is 1550 Hz when at rest. What frequency do you d6h/5m-h)hgw h47w*iyy.: 0kvoocxgq-y tcasetect 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 dortibww--i( )p you detect if a fire engine whose siren emits at 1(iipt r)w- -bw550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shif +p fm hymb-lwg eog8(,f194dtt in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactlg-9 fm wtfpyd+ho8(b,14eg mly 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 saml35 a* b qhwnf.y3a. 6ifuyzj)e single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat f3.bwqz) y5njlu aif*.y3 6 fahrequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz an 1p o7s(t.nx9wpt fe0z/ :q+y;mb mcejd receives them returnesbt0t1/o79+pxnz pyw fqme:j(. cm e;d from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emikc+- vjzid );:vm n0d-p,1q2te n kxfpsi y9g.ts an ultrasonic sound wave with frequency 30.0 kHz. Whatcd izqtn,;s:2-xv1-9pnf ikv ej+g0 ).dk ypm frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experime.i3 eogiowo-e x(:9 qvk1/se bnts, a tuba was played on a moving flat train car at a frequency of 7-b1v ek.oisooei3g 9x:qe(w/ 5 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 -s(n d80xuhahblood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 15(dsa 8hxu0-nh 40 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.q az4l44e pea 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 sound of frequency 570 Hz. When the wind o7jme50rzuctj-1 :m x0yo/omvelocity is 12 m/s from the north, what frequency will observers hear who are loca/m tzm0yoem1:0x ocj-r5j7 uoted, 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 spessz/ld.a/c q j/h6nq0ed 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 speei72fj;x r/s(sgd xi7vd of sound is 310 m/s (a) What is the angle the shock wave 7j7df si(/gi; xxr2svmakes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosppg whx;+5l0 e. s.s4(s+znpu p 0kwbkxhere of a planet where the speed of sound is only aboutslkeg+0w (b05n p4p;z+swkxhxu p s .. 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 th -x55-bcfp n3(rmbde6n rqh )7 ly(dvpe shock wave angle it produl h5rb5nmn(6c3q xvp(yd rp-f)b -7deces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle y:u:qlcc*6j cjud )8 r$/theta$ 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 exactg5au)kn n4z+6 skg)r7g7 mdo mly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boo7u )dsn 5gg46)agkm+7nz mr okm, 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 thahu q6s35knf -et 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 between pulses (in fresh water)?- 6uskfeh3qn5    s

  Approximately how ma5+,kwgi eqp+a* ko2uqp24 fbzny octaves 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 cg y /g823 k.dyzktes d2r7 *l1u*f0mgb cjk0cgonsists of many plastic pipes of various lengths, wh8k2md/lg b21ck f yguyg.kz07c0ej** g3r dstich 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 mak ,1g6m,fj7buh/-hd0xz j a xzpeh*lb(es a sound close to the threshold of human mjlb6,1 pz0 f hxx(gz/d a7he,h*jb u-hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dv arr6(zniqq gk9c3c)xi gu: -m;8xl8B sound and an 87-dB sound are hearz(kg)mag ;9i i83cu86r:xxvqr n lc-q d simultaneously?    dB

  The sound level 12.0 m x98 10-m6pm d 1ycwfzveam2 xlfrom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates l0mpf-a y19d8xm6m1zve c2wx equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops b 41*o3d ;oxxu; gkx;hegg +ysby 10 dB at 15 kHz. What is the power output in watts atb3 hg1 k 4xu+g;egxy;xd*;o so 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ea9xhc2g;tu ;/omhbxx .rs. 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 unprotected/utbhx;cx hx.;mgo92 ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systu agp5 qep 9/d9z/oso8qz6k;cems, 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 fa0 sfbk n;q9u6vcrvu+mwtl1k 3 -*ks)requency 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 with a fundam .h,3ihnzd 7irdrfs3e9qp f;f, r +j2xental frequency of 440 Hz and a mass per unit length of d eq,shr+3jzxd23;fn,frp r 9hi .7fi $6.1 \times10^{-4 }$ 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 vert q89nf:-w +9 vpjyogljical open tube filled with water (Fig. 12–35). The water level is allowed tp vq89n+ wj- jy9g:lofo drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube h44hj czf d;e6that is open at one end and alsjec ;4f4h d6hzo 75 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 resonate 5ct:f(n:/zyovmg1x,dbj4nb4lf s ;sas 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 7nscqq1c vm )z gf3z.0in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency )c3 msc0nz7.gvzq qf1of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condt k9zalz9;hrt *r0/ ynuctor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of th9rt yk rl0*t;/zza9nhe moving train?   m/s

  The frequency of a steam train whistle as it aps6rm6 .wwnu47f ux *-wgnv q9rproaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume rg 4s6urvqxfw .7 nun- ww*m96constant velocity)?    m/s

  At a race track, you can estimate the speed :gjo yw --6+4xyrawrb 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 th6o :-gwbar yjx 4y-+rwe straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, prqi1v:rj2kd k rx1v(+coduce a beat frequency of 11 Hz. The shorter one is 2.40 m 11jcv rq (x:rkkdiv2+long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sdane/tc8;3awyo5s u9tationary observer 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, 58ays/w 93uednc;at o at C?

  If the velocity of blood flow in the aorta is normallynhly3;w1q) hijx q; v+ about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflectq3 1h yxhivnjw;l;q+ )ed 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 motz 7/vs 35+y jc u1wsc4rhlic1yh is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is hj5/zysl14cc urc iy+1 vws37the 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 puj 3b8 *fkn)dv gzq*mn*ie t15hlses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the dhk tn5fe3biv1 mq z8n)j*g**echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used toy4;yt cnh68*endixu / send signals 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 dc t;u4n yxn6/8y *iheone 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 ste79gge 94qd unjreo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressue4997 jnguqgd re 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 “singing rods,” involves a long, sleru+3w4 r+f 0viwps59(yeucytnder aluminum rod held in the hand near the rod’s midpoint. The rod is stroked y 0 (4furstw3y5+w+c9verp iuwith 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-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 of1(aorteczk 53 ts* s:s about sso 3kz1r*e:t5(ct as1000 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 Ma34i1 osuesdy 9ch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane e9ud3s y4i1os passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15b /2( .zyz ynwhtr3w/f $^{\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