Wave Equation II and Solution. Length of the curved element.

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Presentation transcript:

Wave Equation II and Solution

Length of the curved element

Perpendicular force on the element

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

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

Therefore, (nothing but wave equation) General Solution

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

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

C: wave velocity

 : period of oscillation

Different forms of solution of wave equations

Particle velocity :

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

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

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

Solution of spherically symmetric wave

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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