1. WAVES

2. Wave Equation

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

4. Disturbance in the rod

5. Young’s Modulus
©SB/SPK

6. Elasticity : Spring constant

7. i
i-1
i+1
©SB/SPK

8. Displacement of ith mass satisfies differential equation

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

10. In the Continuum limit

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

12. Taylor series expansion

13. and

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

16. For disturbance propagating in all directions
(Laplacian operator)

17. Summary
Wave equation

18. 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  PAI/P