Wave Equation & Solutions

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Presentation transcript:

Wave Equation & Solutions Transverse Waves

Transverse wave on a string String Wave

Length of the curved element

Perpendicular force on the element

Equation of motion of small element Wave equation

Wave equation General Solution

Therefore, (nothing but wave equation)

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

For simple harmonic displacement of an oscillator

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

C: wave velocity

t: period of oscillation

Different forms of solution of wave equations

Particle velocity :

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

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

Summary Wave equation General solution of wave equation

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

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

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