1. Wave Equation & Solutions
Transverse Waves

2. Transverse wave on a string
String Wave

4. Length of the curved element

5. Perpendicular force on the element

6. Equation of motion of small element
Wave equation

7. Wave equation
General Solution

8. Therefore, (nothing but wave equation)

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

10. For simple harmonic displacement of an oscillator

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

14. C: wave velocity

15. t: period of oscillation

16. Different forms of solution of wave equations

17. Particle velocity :

18. Dispersion Relation A link between spatial and temporal oscillations
For the wave equation
Plane wave solution
Oscillation frequency

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

20. Summary
Wave equation
General solution of wave equation

21. l: wavelength c : wave velocity a : amplitude
Solution of Plane wave of form
l: wavelength
c : wave velocity
a : amplitude

22. 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