What is the evidence th pplt ffa/6r3y 63s,yoat sound travels as a wave?

What is the evidence that so 5 ec)7vgnop,3tzsuy,pl6-tcund is a form of energy?

Children sometimes play with a homemaaugreb5/a9bq )s bf-, de “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly hoa9 s,qrabbe ) fb5g/u-w the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do yqar o16z c3),av hx;lcou expect the frequency or wavelenv3c 6)rq az1,lxhaoc;gth to change?

What evidence can you give that the speed of sound in air does not6 t. ja k;l5(5j4pg 9jhtyjqvr depend significantly on frequ j5tj(q;vpr4lj y gt5a6kh .j9ency?

The voice of a person who has inhaled helium sounds very h2s4abi0;h d vcigh-pitched. Why?

How will the air temperature in cxgh bj14w875n) ru)n8ppmaqa room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ampl88tqm/o c3+2k 2rmw+xip fyjx itude of sounds i3m2xy/p jo8k+w8r + xfcqti2mn various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced ctgh -2pd;bai9 loser together as you move up the fingerboard 2i; pbhadgt -9toward the bridge?

A noisy truck approaches you from behind a lx1xu*v( 5sqhbuilding. 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: See Sectiox5 (1 xlqs*hvun 11–15 on diffraction.]

Standing waves can be said to be due to “intera7adwsg. a3 a1ference in space,” whereas beats can beaw1d saa.3 ga7 said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points gtxn9d6kf b6xajo4 j 7l/ha(: D and C (where destructive and constructive interference 4fhxb9lkg(6d jn : ajt7oxa6/ occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work/hux 8afc6;o yc;;ey . slnjfc1ro8s2 in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reachingal68;yc;n cxf;hsor o/ye8fuj2s c1. the ears?

Consider the two waves shown in Fig. 12–31. Each i 7-i.j6hu)k/iekmk kwave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. Iemiki7-ikujkk) h ./6n 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 4 z66cvkaarv gspg(5* in the same direction, with the samevk6(v a*pr a6zgs4cg 5 velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a p1 6:; dl6x p:iwqe wldk*pl-tterson at rest with respect to the source? w- l*d6qil;:ldpkt xp:wte61Is the wavelength or velocity changed?

Figure 12–32 shows various posibk .x p h acf8-9*5bh1ekcgb8yf w4+mitions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the wf- ax5*whbb+ 49cc8k gy1m.f bkpi8ehhistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her ;x3,fd-o ij ynshout reflected by a cliff at the far en-d;fxy, 3j iond 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 zmka3k9+y j+k ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not ja+3mkk 9kzy+vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths a56zs/i),nzr;vpe mm in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tujqo8aj6p,f ogvs0i92 8hba f)na on a foggy day. Without warning, an engine backfiga 6f2h9oja v0, 8f8)jpb sqiore 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 top6 (b4 zz)vuak3gzpd8 w of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How h uzb3zz)k48wadvgp6(igh is the cliff?    m

  A person, with his ear to the ground, sees ath *ms(n*zu;2-ze+m* ( q;2ulw iz nryasqfp1 huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: onehi+mzsspntn r a* zqe;l u(*zy(2;1-fw* uqm2 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 distancej b9ccf s0;yj4c*d3mx by the “5-second rule” fcs b9cj*x;mjy0f34 cdor 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 sound at the pain level of 120 dB?) nf6t26oop2wr kzbhd y(0twt z*uw29    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity is(czqqug-03 dz $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9+ pw 42xm o-ywaug5s6a5 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add iu aaww4m-px2o+5 ys g6ntensities, not dB’s.]    dB

  A person standing a certain distance mjmo8l51 p qy5rhlvb. b97.oefrom an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would thisj9qlbemylorb7. 85ho .5pmv1 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 9)zmtut;49q d6 epjz;; zo tmtfor a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgrouuzm;t6d) 9e;j ozm tp4zt9;qtnd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound f8 bmf;v,kdtj. -hayb-9*uup y rom a person speaking in normal conversation. Use Table 12–2. Assume tkbhtd8- .f by9v,juap *uy;m- he 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 ;t9au8vsfcz d12 5.is icac;s+hi7aa an 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 ratedpjbdqecnf/ah ;)n79( at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a pod/( pje hnqb;ac 9f)n7int 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 txd v0-)c.m: zd i/nbym in front of a loudspeaker on themvz bidn)tcdy0 :x/-. 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 sc+0d 7mqb.7mmicyq1cj 2 0i zmound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose leve q7m2.mdcmccb0+ 71m i z0iqyjls differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of k;6k8fwll 6arv,3 ze/,a h+yd2bxyppa sound wave is tripled, (a) by what factor will the intensity increase? Increase by a ffw ey 2ka y/bpahxlp d,lkr;3+v8z,66actor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eq0lo e60j g(grjual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their l(rg jg060oejintensities?   

  What would be the sound level (in dB) of a sound wave in air that correttov-- a -aru/mr6 8c dz/cp.asponds to a displacement amplidr -a8-poa c/z/-tr m6autcv.tude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level:sv 9.zgu.f *+xn-osldzq sb( to seem as loud as a 100-Hz tone that has a 50-dB sound level? (S z*xoqs-(fus: gdz..nlb+v9 s ee Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear c207s1b v szos(s vwxg7an detect when the sound levv(s71xzsgo 7b0 v2sws el is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huw4pl 0runs; 2ai13 62ibkbogh ge range of sound levels. What is the rwpb s02 rin1ab 3gi;2kh64uolatio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequens:wf9;l4 th s,ok dtxhj-:d,bcy of 440 Hz. The length of the vibrating portion is 32 cm, and i b-dojhs,w4l:s tt;h x :kf9,dt 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 threewk7 n b(58pp oqr9scv* audible overtones if the 78 9bvwsopqn*pcr(5kpipe 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 k cghkvs de(q;t0+w(6d 36ymxtop of an empty soda bottle that is 18 cm deep, if you assumed it was ak e6ys3 h0;q dvk+gx wmdc(6(t closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning thnf aj-rq n4lml y0; foio i;3k,78.xbse range of human hearing (20 Hz to 20 kHz), wj , rfq yxb4knimf o7o30;sl8;.n-lia hat 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 freqmpl uz( ubcn)-v6 v(k+uency of 540 Hz as its third harmonic. What will be it+l (bk(vuu6z)mn v-cps 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 n2e7ebvq 2b ;vtku2t3 above middle C (330 q; tvke7ut2vbb2 n32e 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 tds7l 5sjgocn hg q+w(0/rnqay0c-1:fy+ sk( that emits middle C (262 Hz) when the temperature is w kgl(cry (sn+s1d afqq 70sj h+gcot:05/- yn21 $^{\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 axoty;6kz +s+bncx(q0ifev (cfs .7 /vt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutebyf tq:a/ n+l+xao2s0 in Example 12–10 should the hole be that must be unc+2f :b+ yna0l/oast qxovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 65l mxfl z9bgl/y4/hb 85t6nfn16 Hz, but not at any other frequencies in between. (a) S9l/m 6nb lbngxy5th4f5 f/zl8how 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 atvjbe2 ,zea4 acrhk),b754lsib j*.ys two successive harmonics of frequ*j,iev4y54s2ehbbbj l ),sk z 7car.aencies 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 byopn1i :1w-n$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.f)m0tv8 ckaj,14-m-long organ pipeavtf, 0 cjk)8m at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximate9 andovd*s, r/ly 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 donvd*/ r,sa9in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings1udm+ bx1vv fv2 9:eg8dux5ss, one of which is sounding 440 Hz. How far off in frequem18dgf91v5 v s vedbu xsu+x2:ncy is the other string? ±    Hz

  What is the beat freq+c2eqozg ,c m;uency 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, while another (brand X) operatefdk 2*dfeesek k5bbop 5,t/06s at an unknown frequency. If neither whistle can be heard by humans when*p bebts 5ekfk20fd5d oke,6/ 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 som 0 xz8 )eenm;jg*wy0cunded 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 stri) we80mcxe*jgnm;0 yzng? Explain your reasoning.    Hz

  Two violin strings are tuned to the same freq ,rt48z ,va *lgx5zmy(l t ts6h*lqi5muency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings arzxlgri,6*t5t l qa yzht,sm 4( 8*v5lme played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to plazow8dyx9v xi(1)c ya+ y middle C (262 Hz), butaw9i)yx c 1(voy+x d8z 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 B has a frequency of 44vv2 fqp .59znfqf-y1i )/qbf f1 Hz; when A and B are sounded together, a beat frequency of 3 Hz is hear) /f2fpqvbfqqn5-i zf y9f1. vd. 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 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 )xhnk u.zn084r +thyg 3 +ru8zkyh4n.t)0g hxn .50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pikv 0xbhm1*gb6 ano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mus 1hxbbvk6gm0* t 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 e s;n6 3vezs7 twv3ubc gx64+n2.64 m and 2.76 m in air. How many beats per second will b3e4v 3v6+utz76gc xb;enswsne heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire6 77 +las/ axsjuefn/u engine’s siren is 1550 Hz when at rest. What frequency do you detect if you msf6a/j u/ 7xsnul7ea +ove with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detecc, 7as iap x4 qwgx1n((fjk+8et if a fire engine whose siren emits at 1550 Hz a78p 1aq((cxx ne,i4gjw+fk smoves 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 sounrmg )e l,bvu 2)rek+bexp, :(rce is moving toward you at 15 m/s ver) ruee bkb:2x (),+megl vnp,rsus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped wlsi0/h ;5ygxt0*g;gf2zh ce iith the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horn0i ;hgh;tsfg 05xly/g * zcie2s emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves ab4g e+sdw6 ,vat 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivedva b+gw4de ,s6 sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As n 52nv-t5kxhxit flies, the bat emits an ultrasonic sound wave with h 2 5xk-5tvnnxfrequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler wi6;9:wupogt experiments, a tuba 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 approau twp;9ogi:w6 ched the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter use jph1y*:guwv- s ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequep-yug *v:h w1jncy if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultboo5e v/f5df7r ca* llc;/ zu:rasonic 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 wz72ohl2 y3ci75 4kaitg l qh+cind velocity is 12 m/s from the north, what +2c3oi 52k7 c4ztilahg7lhyq 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 o(z12t y pm8 ,eh9ogqgozuc;c5 n land 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 whel-)syp3o rv+z re the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’l3o s rp)-vzy+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 -hbbsr -pb7e :where the speed of sound is oerps b :h-b7-bnly 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 wawf* gankc2n2 :a y4jyy n8y.3vve angle it pjy :.k*2c gnwany3y4nf v 28ayroduces
(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 m3i8) emi/uebtgun .ah47f* eyf 1 *kj$/theta$ 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 exactly 1.5 km above the ground fl3 fh:,v:jmah0x.l z. vus tdi4ying faster than the speed of sound. By the time you hear the sonic boom, the planx: aid.j0s.z lhh4 tmu3:fv,ve has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 2 l/1)ym ./wgyfld rhphjs8m, ,0,000-Hz sound pulses downward from the bottom of the boat, and th/rmhh/,yl.,d)sf w1g pljm8y en 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)?    s

  Approximately how many octaves are there in the human audibt qg4i3 j t whxrp52d7p*,h+lble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sg7w2)g1soprb h lt2 ;uymphony. It consists of many plastic pipes of various lengths, which are open on bgwl)217;usp bht r g2ooth 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 closlb hk,8 h+g0,eyxzr4 xe to the threshold of human hearing (0 dB8gke ,ryhzb4xx,+0lh). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound zi6ik4nlj9u )are heard simulu9n6z4)i kiljtaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1 k;2(sn9 wpioo3flxy t44+:o qujhzau2z/db6 05 dB. What is the acoustic power output (W) of the:s42qx zwj i6u;+hy /afupb2zd( o39l 4oo knt speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outputx0xhi .ue( ddo;xzl*bh el/1 cdq ;k90 at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts ax;xexliezq;c*/h0 0kbl 9 dd(1d o.hut 15 kHz?    dB

  Workers around jet aircraft typically wear protective deviceo6i )y75dz mcjs 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 average human ear has an effective radius of 2.0 cm. What would be the power intercepted by d6mocy7 z)ji5 an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the 930lpu lxmlxl0 5)5b, m az8+xxjn xpdgain, $\beta$ 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 frequ7ag b6(5,7xodndcz tju n4xy1 ency 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 cdfpbx-z gm5rd) zh : gz1q:5o0m long between fixed points with a fundamental frz xz055:bgg) dp hdqz-rf:1omequency of 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 vip4 0kcle k2dtor(: o,ubration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube 2:l,to0c4rpu ke (ko dabove 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 (ad7u )r rlr0khvv 0*zmass 2.10 g is near a tube that is open at one end and alh 0ra *rrd7l)vkv 0(zuso 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 observeq7 b.s a/gkf5+4t ez 4qy6qstmd 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 sourcesajyk0cbmf 8(li3+t5 d. The sound is loudest at points equidistant from the kldb3580yi jfc(+amt two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Onf )q6ysenp +onjos(49y)q) k de 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 oo4spqj(dkqo fs+ 6))) eny n9yf the moving train?   m/s

  The frequency of a steam train whistle as it app6 i j8lwof -9 /8/xtumtn5df0vmr z0waroaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train x-9/zm fditw8uo mwlj5nf8t 60av/ 0rmoving (assume constant velocity)?    m/s

  At a race track, you can est9g,vew9hqc 0 j9fw 5vkimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straig0v,99fhecwq9k wv jg5htaway. How fast is it going?    m/s

  Two open organ pipes, /g7:nm pprd/x sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lon/dxprgmp: 7/ ng. How long is the other?    m

Two loudspeakers are at oppos tjt4x.84zpe47:dk ul1wz) e 2jguajkite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound 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, (bt euxkz2atl)k4d 1j .ezwgjj:p7 u84 4) 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 flowlylcy/+ ebq jmw*rcp:( + 8)zw in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed (lc8mj*z/l e+qw y)r+ :wbpycof $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at slir;op ;u11vf2d0a ua4pg vhk8 ; e6/xtuos1 fpeed 6.5 m/s while 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 refli ;o kffvt2vruh6p1 /1ul8e pa04odga1 ;xs;uects off the moth?    kHz

  A bat emits a series of high frequencye2kf8fms/7 ol sound pulses 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 echo from one chirp 7/o2k8m eflfsreturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38:vn*v o87z mgbn- g)tz) was once used to send signals from one Alpine village to another. Since lower frequency sounds ):n8zgt7bnzv-movg* 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 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 listenixr(h5xhv +0 w-doa/zdff,r+ing can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this rooma d(f+,df iwozhrx/+ 5x0vhr-.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv,)khq xfway fk,9g 5g4olves 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-long rod, k4fg 5x h)9qg,kya wf,
(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 hear-c qjta4gs jr 06th.3s0* eqbcing for the human ear at a frequency of about 1000 Hz ctceb300qg .jt rqh4s a sj6*-is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground heasda- k ;k/c r550fpc9thv zx3prs the sonic boom 1.5 min after the plane passes direv0 pd z5chaf5r ;t9xsk c/-pk3ctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is y ;4kpw twv+8c b1+syl15 $^{\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