PHYSICS 231INTRODUCTORY PHYSICS ILecture 22Simple PendulumTraveling ave!L"ngitudinal# Tran!ver!eSinu!"idal $aveSpeed# %re&uenc'# $avelengt(Last Lecture gL maxcos(t ) y Acos 2xmft

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1]1v f Speed of a Wave in a Vibrating StringTi! ten!i"n)Pitc( * %re&uenc'+ v Twhere mL f v 1TExample 13.9, !tring i! tied tig(tl' -et$een p"int! , and . a! a c"mmunicati"n device) I% "ne $ant! t" d"u-le t(e $ave !peed# "ne c"uld+ a/ D"u-le t(e ten!i"n-/ 0uadruple t(e ten!i"nc/ U!e a !tring $it( (al% t(e ma!!d/ U!e a !tring $it( d"u-le t(e ma!!e/ U!e a !tring $it( &uadruple t(e ma!!Superposition PrincipleTraveling $ave! can pa!! t(r"ug( eac( "t(er $it("ut -eing altered)y(x,t ) y1(x,t ) + y2(x,t )Reflection!ixed EndRe%lected $ave i! invertedReflection!ree EndRe%lected pul!e n"t inverted"#apter 1$S"undSound WavesSound is longitudinal pressure (compression) waves Range of hearing: 20 Hz to 20,000 Hz1R20U2NCY D23OSpeed of SoundLi&uid! and 4a!e!+ . i! -ul5m"dulu!# i! ma!!6v"lumeS"lid!+ Y i! Y"ung7! m"dulu!331 m6! i! v at 89 C:T i! t(e a-!"lute temperature)v Bv Yvair (331 ms)T273 KExample 1$.1;"(n .r"$n (it! a !teel railr"ad rail $it( a (ammer).et!' .r"$n# !tanding "ne mile d"$n t(e trac5# (ear!t(e -ang t(r"ug( t(e c""l 32 1 air $(ile (er t$in !i!ter .""p!ie i! l'ing ne