WAVES

Wave Equation

Elastic Wave A Rod made of elastic substance ©SB/SPK

Disturbance in the rod

Young’s Modulus ©SB/SPK

Elasticity : Spring constant

i i-1 i+1 ©SB/SPK

Displacement of ith mass satisfies differential equation

a: separation between the masses a  where 0 Let a: separation between the masses a  where 0 is a function of two continuous variable x and t

In the Continuum limit

Notation of partial derivatives : variation of with t while x is kept constant : variation of with x while t is kept constant

Taylor series expansion

and

Longitudinal wave in elastic rod Y: Young’s modulus A: Cross sectional area r=mass density Wave equation cs: wave velocity

For disturbance propagating in all directions (Laplacian operator)

Summary Wave equation

Reference 1. LECTURE NOTES FOR PHYSICS I SASTRY AND SARASWAT 2. THE PHYSICS OF VIBRATIONS AND WAVES AUTHOR: H.J. PAIN IIT KGP Central Library Class no. 530.124 PAI/P