1. Wave Equation II and Solution

3. Length of the curved element

4. Perpendicular force on the element

5. Equation of motion of small element Wave equation  = mass density

6. Gen. Wave equation (String wave) (Elastic wave) (Acoustic wave through fluid)  : compressibility  0 :equilibrium density

7. Therefore, (nothing but wave equation) General Solution

8. Physical significance of  =f(ct+x) wave moving to the left

9. For a sinusoidal plane wave Therefore, : frequency of oscillation in time

11. C: wave velocity

12.  : period of oscillation

13. Different forms of solution of wave equations

14. Particle velocity :

15. Dispersion Relation A link between spatial and temporal oscillations For wave equation Plane wave solution Frequency of oscillation

16. For monochromatic wave in a non-dispersive medium Plot dispersion relation Slope (c)  phase velocity of the wave   = ck k

17. Wave equation in spherical polar coordinates (r, ,  ) For spherically symmetric wave

18. Solution of spherically symmetric wave

19. Wave equation General solution of wave equation

20. Solution of Plane wave of form  wavelength c : wave velocity a : amplitude

21. 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