What is the evidence thn5dfddn25 p v6at sound travels as a wave?

What is the evidence that sound i)/ inzlq-)rz;4asw; aokwo; m s a form of energy?

Children sometimes play with a homemade “telephone” by attaching k :,3w n :7 7u9qmepjncmygno6a string to the bottoms of two paper cups. When the string is stretched and a child speaksng 6:enqmkmuyn,cpj w 93o 7:7 into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from airga +;qis 7q:.w sl2omu into water, do you expect the frequency or wavelength to change?sl2wu + maoqgqi:;7.s

What evidence can you give that 3skr x s0xe2g2the speed of sound in air does not depend significantly on freqx3e02xs gskr2 uency?

The voice of a person who has i/giu,m8k j.1 4m3hw7tvwngnn1hvzba1gnr4 2nhaled helium sounds very high-pitched. Why?

How will the air temp*nnma lyl-j lzvu8vpo05c75 -erature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter toicog( j8 5n/bb*nter41n6vlb reduce the amplitude of sounds in various freqji1b4rbb5 / 6(tlngnoevnc 8 *uency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clo:1a.l5 pl6mxcrt r9n1yoq k4+,g cs wtser together as you move up the fingerb w1tp ox91ln4smcart:6 g y,lqr5kc+. oard toward the bridge?

A noisy truck approaches you from behind a building.f(sd oc23)v,xksn8z z 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. [Hs ,83vzoxn(f kdc2sz) int: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas betyk jxfd3;(3z ats can be said to be due to “interference int3;k 3xyfz(jd time.” Explain.

In Fig. 12–16, if the frequlm.fp,k (goj( 7x+itwency of the speakers were lowered, would the points D and C (where destructive and constructive intefg it(wokpx.,l +mj7(rference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in v*u1 i7u(u m;g2/ ki ipst0gb5 jp:rba0l0src areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relative7:2sp(kilui*u /0 r0vm bjir5 tp1 agbucs0g; ly new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a supuzb3b8j)g ( xperposition 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 frequenb8z3uj)g pbx( cies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer fd5 kkrr*yj9* move in the same direction, with the same 5kdyk*r f* rj9velocity? Explain.

If a wind is blowing,)y5 2d8vtddh 4 *asqke, ojd7d will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength )8j,* 2ed o4ysvhda 57qddt kdor velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monao ,v-g y05mr e7b4b57tyylmgitor 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 fogg4l- 5bmo,7r5 v0b7maytyey r the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout r))k bjx*nd4uv;x em4 leflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length ob)duvn4xe )*;x lk j4mf the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below (;op /ea8bqdg ebl ks:k7v/o;the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How d ko oq;bv:8e/ldpge7/b;k a(seep 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 wavelengtz8 e rdac 5.t/4xxymu6hs 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 tuna on a foggy da07 qr8menz,gz3d/ty t y. Without warning, an engine backfire occurs ,q 8 3ndtg zemtzy7r/0on 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 top of a cliff. The splash ioo 4 sacud ckmatc:ju)ut0fs326vkn (a4f62 )t makes when striking the water beloas6 ( 6kdfku c)2j3o v4ncc2ousu40at fm):at w is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, s5 m-o5a2m zfymees a huge stone strike the concrete pavement. A moment later two sounds are heard from the a2 y-5fm5zmomimpact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distancoy2p/rf;/ v o2 hwvnm9e by the “5-second rule” for estimating the distance from a lightnyown 9/ vfvr2 pmo/;h2ing strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atdep2.h xtsv*sh2 t64o 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 c:g. x 8lmb:,5yiv t+hq1vcoqsound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 xlv5ir w-o3cgwp. ;+jdB when fired simultaneously at a vowj5 +ixw- c3gl.;r pcertain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with a+hb4 fmoyki90yr c 82four 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, not9o2r80ahc i+bm y4kyf dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 5m:5iv4 vrhw7fg3q lt78 dB, whereas for a CD player it is 95 dB. What is :4lwg3 7 iv7tm5hvrf qthe 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 :m y9ge6x*au *ncsl2f a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on thye 6gua m*x2 l9s*:cfne 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 qv cji.ug3.qh: :t0ddan eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modestg/7ina1t3m h* k nanwn;,7so s amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to eac mnk,wt17sin o/an3 7;sgha* nh 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 registeredht b;; nm79 rg/ kiy+t)(d5 zd,vi5renk2essj 130 dB when placed 2.8 m in front of a loudspeaker on trnbj57 k dtt9 negsdy z2vie(,h5/k)mrs+ ;; ihe stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What isc w56h5ym3 mdy the ratio of the a c 5wyh653mdymmplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor fb( koj 9a( p;jfu8xeqxhj0/. will the intensity in(ja ;(.jb xeok0h xpj9q8f /ufcrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement a0rr;go+qditu7g-nb .gi9 2n amplitudes, but one has twice the frequency of the other. What is the rat;o7iugr+ g gi q dra09bn.2nt-io of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds5 gzpk75o7:t)fusy dv to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 H 5 f)v k75s7:dptogyzuz?    dB

  A 6000-Hz tone must have what sound level to sev9q7/x5;yd ojh) vlot em as loud as a 100-Hz tone that has a 50-dB sound level? (dql9xvvto )5o 7;yj/hSee Fig. 12–6.)    dB

What are the lowest and highest frequencies that -nt-dj(4z,k sna k4.vtwasn 3an ear can detect when the sound level is 30 dB?s-wtadnt4, 4 kn.(s-k3njza v (See Fig. 12–6.)

  Your auditory system can accommodate3 jxl:v68crtipcz v- gldn3: / a huge range of sound levels. What is the ratio of highesl3-dz : /6:c v3l8ipcgnvjx rtt 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 44s-gugcn.i yry1z3km +h+ o1x,0 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Unde+n 13cs r+oy, g.ygxz hik-m1ur what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three ifx(lnq k7i/j+13iup audible ov7iip3uj n +i1f/kx lq(ertones 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 blowiq8 :9i qjry)jhng across the top of an empty soda bottle that is 18 cm deep, if you ahj9 y)q8 ri:jqssumed 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 pipe organ q:66zb/djm cuwith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required d6b:cj6u/ mqz? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third h(o zc3a5cozq)v/ 0bpoarmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original l) p 3oc/5z(0bvzoqo acength?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play yy6 o-/7t5l cwrldnufgb 8s0, ez3/puE above middle C (330 / reusz yl6g3y-,clt87 n wofbp5/0duHz).
(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 m+t1 c)w/ycn fthat emits middle C (262 Hz) when the temperat+tnyccwfm )1 /ure 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 a-gwxk (4ms j9yt 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 be 2:/:jhg.m n gu,pv jy k:vfso9that must be uncovered to play D 2h. fyg/jvpm:ko:s, vjgn:u9 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 aqtqu 3;v50zkcfu92w616 Hz, but not at any other ;t9qckwu5afvq 2uz30frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both eny zyo352 /aq6h+6.in; ,w1ead r4 nnskvarhbeds. It resonates at two succeek4oyqanz,h.arydv/r wb; n ehs+i3 56 n261assive 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 gfhm11a/gorqv42 1k 3ge u ty3$^{\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 thel*a ge +x3p pel)/j4nm audible range for a 2.14-m-long organ pipeej)m+lelxg43p*a n/ p at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsv76n 0lqbft;u ide and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationshqtb6n ;lf 7v0uip 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 strings, oqbcd;y pt3hay ft748+ ne of which is sounding 440 Hz. How far off in frequency is the other string? hc3qp yadt 78+b4; ytf±    Hz

  What is the beat frequency if middle C (262 H1 6r,gnxdojx 2z) 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 (branvx t59*yt8 -3csv c vg;k4kr9hyv4qlwd 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 playe kx9lcv qyvhgyv;t v4s59 t84-*k3 rwcd simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fo9z:6ai; .5 tbnw-lvx he7sya zrk and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Expwnax-zvs5.h;i:e zl 9y7a6bt lain your reasoning.    Hz

  Two violin strings are tuned to the same frequen a/wfxj2 fe40tr;o :ejcy, 294 Hz. The tension in one string is then decreased by 2.0%. What will 2xj/rf4ewtfo0:;e j abe the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C (1zf1k.bpfcx s:k*p)our1. a w262 Hz), but one is at 5.0°C and :kc xa.11zurfw1*.fkop)p b sthe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency o eig z+07io7tbc2 hxp/l8oi h3f 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 C7x/oteih 7 +3iz2o80ihg cblp ? 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 3.0(a3 q gah)n8gu0 m from one speaker and 3.50 m fr)ugaah 3qn g(8om 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 su: nu4wans p/spz*( uzyqq)+j7pposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one apu)s jynz:+s7q*p(z wun /q4 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 oxx f680mu zvtn,yn8m/f wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 8x y,6 uv8zn0mn/fxtm20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a tpp/)lco8n0ksd j: al h/ 8tn.certain fire engine’s siren is 1550 Hz when at res: atsl /po8p d8k.ct)l n/n0hjt. What 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 do you det7ku*:c)cp/hq4i -lp; x hgtpkect if a fire engine whose siren emits at 1550 Hz mocc /k pxlpgh q7; :4)ik-tuh*pves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at 1 hj9n1 pmof4/y,ai+/i j31jiezi( vkp5 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly theakzf i mojen4pi+1(1iyi/9vj3,p j h / 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 equippedf) 6 pmk1dzk:b with the same single frequency horn. When one is at rest and the 6p) :kd1k bmzfother 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 horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waacf417 ,hcozt ves at 50.0 kHz and receives them returned from 4 ,ct ohz71fcaan 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 g6/ .9y oro kn)dt8-bveazf *va speed of 5 m/s As it flies, the bat emits an ultrasonic sound don9)/yr.ez b 6k -v *8gtoavfwave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played 8cjgafed 44rgps (4)c 0byj6oon a moving flat train car at a frequency of 75 Hz, and a second identical tuba playeajpb6ry4c8g s40o 4(ej)cd fg d 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 blood-flow speeds./bspu*cm7j3i.x2zh o Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing *7ub2j iz/s o.3pm cxhin large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of b izj 1wkxtj h cq5h9+)qkxs12ee)x;.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 vewk7wtlio1, gi . m9lh,ig,zi, locity is 12 m/s from t iz l.7owwh ilgg9,1mik, i,,the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its s jkguqff l 256ct3()ohpeed 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 (puvea9, fp/ vthe speed of sound is 310 m/s (a) What is t9/ep(vf avp ,uhe 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 obk+fft-3ci6 i f sound is only aboi -6b 3fkci+tfut 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 wave anglzuc w+5d2)7 dzmxa3 qt g91wnle i71 la5nwzq3cu+md dgz9w x )t2t produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle sd(,5yjspu (,kkmh9f$/theta$ 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 e/+pe gfp 8.4pu; wtquaxactly 1.5 km above the ground flying faster than the speewpu/fu g+p4 q.ep8a t;d of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonaak51vit 4e7vx enzzj)(.x/ jgr device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum jkz/xv e7 zt(45 ainjgx1).ev depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how man*xyr2 6xqio+vs5x8 nay octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cav:irilwmw1 m9gln 9wo8(88nl lled a sewer pipe symphony. It consists of many plast lirg8l 18lwwvm:98onmw9 in( ic 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 sound closea;fgr p kk;+d, 95d*acm)rznfr);j ow to the threshold of human hearing (0 dB). What will be the sound level of 1000 suc rnowrp k) ,z9afagdk; f5+dj m)cr;*;h mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound 8ubk a1,+rv gband an 87-dB sound are heard simulta au,v1brg +kb8neously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, isc o;bndbo: j// 105 dB. What is the acoustic o;d/b coj/:b npower output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is */94k: tun 9jxptfjr shb8w1urated at 150 W output at 1000 Hz. The power output drops by 10 dB tj8 nk 9*u41btufhrp:/sj9wx at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective6/2q qycgn8*x*sugd:q fln -7 u0z ztk devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be t*k c7xq26d- :yu uz*fgsgn08tn qzq /lhe power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, th lm6aoctb80 v+e 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 violins;91 nn fvuoq) is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a viol28ez 0,vg :edwzmt ,(iz+odq xin is 32 cm long between fixed points with a fundamental frequenc2 qzgtzzdi,m0ee(wxo,:d v8+ y 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 vibration above a vertical open tube fillenonr 024in5rr. 2 hdqed 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 reson nr4 q2hodnnr2r0 ie5.ate 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 stih(xc u:. c ys n0qkwr2or1v6q9+ nrl:ring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in itcv1rk:lwn 02orhc+q:qx6 9ys.(ui r ns fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to rp8v hnn h/)c-+trr,aoesonate 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-m7gyr2cts4b* em 3yv6f3zu y 1Hz 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 ivgs4m u*yy13c7fz6 2by e3mrts the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor onfr nivi 24/76v)a junwwia3j8 the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tra7v6wif/ji)n a3n4riw8uvj 2 ain?   m/s

  The frequency of a steam train whistle as it appraou(c)qttt/5tdng cq 9z) ;i9oaches you is 538 Hz. After it passes you, its frequ; c )z9 ottnq(qaiu)cgd59tt/ency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed qfdh9;:d*xxz(d 2 u hfof 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 (frequenc;zq xhdfx29dfu*dh(: y halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, producevtx3zmxap sj)b-)2 / s a beat frequency of 11 Hz. The shorter one is 2.40 m long. H v/bs xzxmt 2-j)ps)a3ow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastrk-m0 th5. ly2heg 7vt a statile2 -rhy0tkm.vh75t gonary 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, at C?

  If the velocity of blood flow in thni:fx2nxzb )x g:6+ x-8ay axmn0ssc 7e 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 an6xc)b i:xnm 87s as 20x:+xyxg-aznnfd reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while th(s w75i ingakv8va;d,e 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 thatw8k ai;igv(nsv7 da,5 wave reflects off the moth?    kHz

  A bat emits a series of high frequq6) hc.srx6z fency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. )hfr.z cs66xqHow far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine v34w6,b fk,f6iga ;ybsbrxmxo//8 m wkillage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is abou4wmfkbw im f,b6 ;ba//xsxo6,g 8rk3y t 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 r mx9;j+ j ks*q4r,oakbe 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 9jk+mx, ;rjskoqa4* rfundamental 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, slender alumik9k r+rza .o1tnum 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. Fo .a+1zk9r roktr 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 thresholk+ l6g kf4-zdad of hearing for the human ear at a frequency of about 1-gl 6akzk4 fd+000 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 grounahe1qhd .b2. e(5ibubd hears the sonic boom 1.5 min after the plane passes directly overhead. Whe hbqib dub.e5(1ha 2.at is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is r44 zwty9mbch). zg* f15 $^{\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