Standing Waves

Stareling werves Equation of standing waves when two waves having sa- me amplitude same frequen- +ve x direction -ve x clineciin y and same wavelengin are travelling in opposite directi- y Y2 formed. on. Then standing waves are y: Displacement of standing wave Antinode y y=y,ty, y. = Asin (wt - -Kx) y. = Asin (cret +KX) y= A sin (wt-kx)+ A sin Y=A [sin(ust-kx) + sin(with)] Nodes Properties of stand sinA + sinB = =2sin(AIB) cos A-B 2 ing waves. -The OLD particles are in SHM y= (2sin 2 with different amplitude. cos - - particles which have maxim- (Wt-kx- cut-kx- (wt t xx) 2 um amplitude are called,Anti- nocles - particles having 'o' amplitu- y= = 2ASinuet Cos (-KX) de are nodes. stand - particles of one segmant are - y = 2A05KX sincest ng in very allin same phase butinadju- K = 211 scent segment particles are Co= 2TT V= w A in opposite phase. K - All particle reaches the m- As = 2Acoskx aximum displacement and mean position simultaneocy- ly.

standing waves ina Stretched string Fundamental Frequency - Ist harmonics . - Ist mo- cle -- IS- segment X/2 V=fA f= = V & a D= 7/2 2 A=21 - fi = V 2l fi= I 21 T/4 M 1th mode nth hormones fn=nv 21 nth overtone (n+1) node (n+1)2 f = (nii) V 2D

211/2 l f2 = V a l = 27 2 2=21 2 f2 = V 21 2 f2 = 2V 27 f2 = 2f, 2nd harmonics 3rd harmonics -> 3rdseg- most, 2nd or vertone 3rd harmonics f3=3f1 f3= 3V 2l 7th harmonics f 7= 7v 2l 8th overtone f = av 2p are harmonics on A present

P1 : fz if3 1 2:3