What is the evidence that sound travels as abt (bx37h ez)n wave?

What is the evidence that rno)k.7sk 9)eq3fgp rm43sfmsound is a form of energy?

Children sometimes play with a homemade “cnc:y7he 9ab 1telephone” 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 clearcb9n1 :ce7ahy ly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, nyprfywd 1i. g(3 k23gdo you expect the frequency or wavelength rwipn gy2dgf k331y( .to change?

What evidence can yol ccuy7-k1e2zr+1 ts 1sluu zvh /pb4w2ldx9:u give that the speed of sound in air does not depend significantly on frequencc: xszlr24z-w/us 7 21b ek19 yhutl+ uv1cpdly?

The voice of a person who has inhaled helium sounds very h xbpl1vanq+ 4i3* cu6iigh-pitched. Why?

How will the air temperature in a room affect the pitchg xux0h-i,* qx of organ pipes?

Explain how a tube might be used as a filter to red1 qja(d n nlu(0u)b1lx(qm v+buce the amplitude of sounds in various frequnmlln0bjq)qud1 +1(bu a(x(v ency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced z3dtscp(ak;c(* v9dkcloser together as you move up the fingerboard toward the bridgec pavs*k(3dzc9 td(k ;?

A noisy truck approay/ b0l;ujm7y+qyb3.p7 ;.mum ur bkbxches you from behind a building. Initially you hear it but cannot see it. u+y3.7myq0ymb/jl pu b7bu xr. kb;;m When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacjwqqu9 o/0 2jge,” whereas beats can be said to be due to “interference ijgjq0 wq92 /uon time.” Explain.

In Fig. 12–16, if the fr2/oc:2qrls(fg q pns)equency of the speakers were lowered, would the points D and C (r cpqqo(/s)gf n: 22lswhere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in ar(xev 1)kk.an veas with very high noise levels have consisted mainv xkn1ka).ev(ly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Ea9,ct(xtnq-2 frwr -il ch wave can be thought of as a superposition 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? n,rxtw-f-c( ql2t 9 riExplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and ttx uq;(g..ijobserver move in the same direction, with the same velocity? Expla. i.utx(gtqj;in.

If a wind is blowing, will this alter the frequency of the sound heaqx- +pdi8oao 3lquu,pb2s5d 4rd by a person at rest with respect to the source? Is the wavelength2od5,pxp+ qo4b iqdu3u8- lsa or velocity changed?

Figure 12–32 shows various positions of a child in motion on a se-h 1r k7v,jrjwing. A monitor is blowing a whistle in front of the child on the ground. At whichkhrev7r j,-j 1 position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengti8qjvk1 .8::onhny cxh of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after . :okq:cyjhvn8x in18shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his sht1e c3lb isn6oq o+*n/dkad o 569lwhn;6kf3j ip just below the waterline. He hears the echo of the sound reflected from the ocean 361i6j6f olh*d; sl+w3no5eok9k cqand/nt b 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 wavelengthstame hbi*3 ; a+ypw9xp2+k*pf 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 iswt 3q7 adm,c9u drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is hetuq,7 ad w39mcard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking*gz*8-2 +rcdmj jkuni7r+d da the water below is heard 3. 2dnmu+zd*7r g8j+cdkrj a*- i5 s later. How high is the cliff?    m

  A person, with his ear to the ground, see (+nupwb 00:jitr es-rs a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air (tbs-:ru00rn pwj i+ eand 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-second 8y;43. tci u ,eiqxnlw(p72b8wgy 6g a7fvq oxrule” for estimating the distance from a lightning strike if the temper4fvgaye2 cu6w; ,op38.qxn q wli87t (y7igxbature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity oo: moa4c,l j2rf 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 level .y6 fcn9l0 ujkof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when 6j7 3uziz;csyei, g0k fired simultaneously at a certain place, what will be the sou s;yk zz 3e6,0g7iiujcnd level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy j,w.4g yx*hm: wuuzna-et engines is experiencing a sound level bordering on hw- :wu *u.az,gx myn4pain, 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 xbi1 kh(/l xs3s34wfl of 58 dB, whereas for a CD player it is i1 lhx(34lx3/ bfks ws95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nor.t6w( ;g;g9l8u; n2hwtw 9g qbfraruqmal conversation. Use Table 12–2. Assume the sound spreads rtq8;rq;a. g;w w l(rb gw296utuhng f9oughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum wu2qq m 1h3)vhqhose 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 thogle -60cruql3.rhr 1e more modest amplifier B is rated at 40 W. (a) Estimate the sound level 30eqclrou1 - lrrhg.6 in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter 65 3pbomb+6pdfsp9mxvu7 6lp)xuyn-registered 130 dB when placed 2.8 m in front of a loudspeakexo5m x fu6d9+v nm 6-bpl6pp3ypb 7)usr 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 ly4b uiz, 4grgmu 7s/;ievel of 2.0 dB. What is the ratio of the amplitudes of two sou, 7/ sgy giu4i4rum;bznds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (. mg6gf0 +um) /oyhtjfa) by what factor will the intensity increase? Increase by a factgjy+gf hotfmu .60)/m or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice e9ketja,hq* +ua:dwxib*r l*v )3lh( the frequeb wkuj*9)i ra ,:a*l+ldev t*x3(q ehhncy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) oxvvmm y i18/d9f a sound wave in air that corresponds to a displacement amplitude of vibm 9m /di18yvvxrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sejs0(oszj (gw )em as loud as a 100-Hz tone that has a 50-dB souz0s o s(g)(jwjnd level? (See Fig. 12–6.)    dB

What are the lowest and highpa+wlp*h*tc hpb9 ;c;( xf n.rest frequencies that an ear can detect when the sound level is 30 dB? (Seehl 9rh;aw cp+c *bt. pnx*fp;( Fig. 12–6.)

  Your auditory system can acf 2perx4 fi 3em98:bn7aetu7 icommodate a huge range of sound levels. What is the ratio nu7rfe7 bx3:948 mifap2ei teof 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 fundamej(g aqd1/eks/ o7xa(of3t 6h untal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass o6ooetdu/as1gqkf 3 x/ja(7( hf 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm v bf7p5; msa5eb8d2ndlong. What are the fundamental and first three audible overtones if the pipe in2 s5;df7 5b veadp8bms
(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 frequencyc tg,t2g-: xn*wi5d/jcb+wu k would you expect from blowing across the top of an eg-5di*/uj2 :cx,+kt n cw gtwbmpty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipy 9y2kzw+2kn3 2hye bae organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of 3yyb2k ae 292ywz+k hnthe 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 itfagql 4r0:cj;mj0q6paluxr ; m:q9t : s third harmonic. What will be its fundamen6:qr4 x:lp mq ajtr9c:q;lfamj0;g0utal 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 a0 x5jncs ,g1ghbove middle C (330 Hz)xg 1c5s,0gnjh.
(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 orgati2.dl 5epv,h xt;21b gl.oetn pipe that emits middle C (262 Hz) when the temperature is 2.i e2.e2p h5l t ;1tobvdgt,lx1 $^{\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 arnb 4xq7 w)yz(t 20 $^{\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 hole )q yzfzt .38mp* * jrwzr4dam.be that must be uncovered to play D above middl mz3z8.mjrz) ypta4*r. *fqdwe 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 616 Hz, but p5wf tv9xz8xdvvnq 0jmz. : f24clqe6n 7f8m8 not at any other frequencies in between. (a) Show why this is an open oq07d pq8 jmwlzvvf tv4z :8fnx2c.mx8e9n5f6r a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two suc04rsom5c 9 k njnk hh(u.xbf3-ceho fr905-kb j (cmn3 .nuh4ksxssive 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 q9 -*:nuy :piar aiy(z$^{\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 withi;agqv3 q52ekfjom +: in the audible range for a 2.14-m-long organ pipe atao f23 kq5v+jqim;:g e 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately ;oyrz q*p ra rh8z/p/7j;j2a e2.5 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 standz jyqp/*heo ;r ar2zj8p7;ra/ing 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 one beat every 2.0 s when trying to adjust two strin 4evhxe1zen/kv:p:72 gme1 r(ziws5zgs, one of which is sounding 440 Hz. Howze 14vep 21gk :e/5zwhzmxi7rs(e:n v far off in frequency is the other string? ±    Hz

  What is the beat frequen7x u2/zw)asa3eld s.+w qpjb8cy 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 awtx5a (v 2v3wjnother (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5003v2v jwxa5w(t0 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 fork anukbza* ;/ fmhixz2ovmy*91x9h ;zr m 7d 9 beats/s when sounded with a 355-Hz tuning *m* 92ky; mxa/ho zrxf1h7 u9vb;ziz mfork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The ten ccnl an8tm5c )37m7wdsion 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. 11–1mml t )3 8c75wndc7nca3.]    Hz

  How many beats will be heard if two iden7 7my 1wfa2 pwt+wij:+n(oqcqtical flutes each try to play middle C (262 Hz), 2yn7awjq 7o :+c(1ftwiqwmp +but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 445k gy60atk pjhe79sa *1 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 soun5kga9 0kh6psy7*teaj ded 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: b7bl uxz9ymon .d*(1t0wnxi 3.50 m from the othe:bwydmn bx(7uto*l zi1n .09 xr.
(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, buoe3s,mdl; u0fr 1x1hd t a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the u1;0for3,lxsdm e 1dhfrequency 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* p0;tvh4ijfzc8-ows x5iu) s: s o 0dzvvyl27 per second will be heard? (Assume T =uh780ocd*ws xl54ov2if0tzsvyv; jzs :p-)i 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certvk9 8h j;i(1th9 mjfxgain fire engine’s siren is 1550 Hz when at rest. Whaf;(kj1xm9 98 i hjgvtht frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency -msu;- xl3g hbdo5pb6wss7 6jdo you detect if a fire engine whose siren emits at 1550 Hz moves al bu- g6dspxbms-h5o3j 6;w 7st 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 sou5,(wbk,1kj;1jzdr s(x2 j u(dtsb uve rce is moving toward you at 15 m/1,sjtwd 5jdu2rkj ((s b( vu,ekb; x1zs versus 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 wiii c2cowvqyig 72/n )2th 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 frcv)y272iq2giicnow / equency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultra rzs k3p +;k*0- ou-(mdjfczrsw15cdgsonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound15dwz-o u+c3r; sk cg srz p0*kfmdj(- frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at ;wq1r o-9q+l6d vpsvu a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency doespqwuvq1ov- r d 9s6;+l the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimen):e7wql4sqaz 0r- iqp ts, a tuba was played on a moving flat trai:e s i)a7 l0q-pqr4qzwn car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves n92 y(g-rg29 ldqv owhto measure blood-flow speeds. Suppose the device e9ogyh qn-2l2(9rw g dvmits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraso/ejjrg.zb i m5 6/ud45 qxbc3onic 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 tlc dh s0u :plch85b;f 9tg+k3lhe wind velocity is 12 m/s from the north, what frequency willl c8hc350 9:ls;pdulgh tfk +b observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if ibs4 zr31 ej0msts 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 of souv upj.x,isw*-nd is 310 m/s (a) What is spwv* x.,jiu-the angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of souo 7k,o qry73o ls(vkf:ik :/yyqk; fl2nd is only about 35 m/s o27 ofkyvkf qs r:ll;,7(ik3ky/o:qy
(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 b.qsr1s7l) cl 8500 m/s strikes the ocean. Determine the shock wave angle it produc7.crqls1l) s bes
(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 +6w:/envl ,awpcizh 6,lt:beea qs70$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pli48ex5v d5f- xdnqh l:ane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the 8qlhxxf4v-55nid e: d sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz 3+u5kn 6xtghg 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 tiggxu6khnt5 3+me between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human a hog8s0 01qw11v( . es bk31tzg4ecyfelxekg7udible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of s0;nl, j0hwvrmany plal0j vn;0r hw,sstic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sol/ )pav8r1-6esrj2rs n2qe )l.r w1(wnni ac gund close to the threshold of human hearing (0 dB). What will be vjr-)n)pr61 8lee2qlrs.w ir(ca2sg wa/ n n1the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when a-yxp.jl4nd io/u9(l m n 82-dB sound and an 87-dB sound are heard simultaneousl(y.9-xdjmi 4 u/pl only?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,1lv mlh*l5; po is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equall lvp;lo5l* hm1y in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Tms wyx)6o8/ugm h-l+xieuc42nct 6 c -he power output drops by 10 dnx8u)u2 l6mot-c cgx4cy/ime s-h6 +wB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thzfh 4 zres5:)bc0g lv)eir 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 r4z gz0b rc5 s)hv)lfe:adius 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 communicata kqtcj 1x/aw:)c,w: b,earyr7*:gxept(g3 sions 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 violin is tuned to a frequency 1+w7l8iq lsy/la- / pct$\frac{1}{2}$ 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 fundamdc4;qqg)pk z) ental frequency of 440 pgk)qz; q) cd4Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tg / 4lv4hb5rxjube 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 agaivb4/45lj gxhr n at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass9 rl0zn*v hd7orhuk +2 2.10 g is near a tube that is open at one end and als+z0 h *hkuvl7 nd2r9roo 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 re h7q/s,zub2 bcsonate 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 froc,bwkj,opl2ree ( 25a m two sources. The sound is loudest at pointo( lra,e,j2pkew 5cb2s 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 of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on vibulkl 5 o10(suq30a the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of theoal v0 u0bi13usl5 qk( moving train?   m/s

  The frequency of a steam train whistlesqf r mi.a4( qk3)ig)bs, paxe9;) aib as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train mq sa9asr)fm.q( )g,ba) iie;i 3k4xbpoving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of carcny e4rl)6u 3hs just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the 6)l u4nh3cr yesound 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 togetherp;wt/ 1jz/e pz, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thjz;etp/ /w 1pze other?    m

Two loudspeakers are 0kj ,9 jmmpiki38bnh1vzl**a at opposite ends of a railroad car as it moves past a stationary observer*,a8mk 3 m0pk1z jvliijhbn9* 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 f 00dw,4;b t/dhddpkj ilow 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 frodb d40i; j,/0pwhkdtdm 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 moth7r gd 5ikjd)k+ is flying toward the bat at speed 5 m/s The bat emit5dj dk)7 igrk+s a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound puls)rk8tf1vu erb2-+ lj qxe r2r* (z0jui+ ba5oses 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 fromj e bt +f5j r12s0x(8au r+iurb2-lv*oqk)rze one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38ht- 84u;oi0 acjejt5n) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long c t hina5-tjejuo;804 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 listening can be compromised by the presence of stand+ t4*wa-eyoa 39h twtkelf*6fing 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 fundytaok*f et4 hatw*-e 6f93lw +amental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calle2luncfue ); eaa t99;zd “singing rods,” involves a long, slender aluminum rod held in the hand near tft eu9l)e uc ;z29;naahe 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,
(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 freq uz7:zhde/j,)zc k :ixuency of ab cz,jixu)eh7 /zdk::zout 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the x(hi/fq19ig nt8*aa5wjxx: ve hi0p+ 9v8sehsonic boom 1.5 min afxfse*x98 58 ivg1xtav+ph 9a0hq/ win:e i(j hter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatf-+ rx8zs vyvbnl1c4 s s6.ie dfs48/t is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h