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Differential Equation of Wave Motion

The general equation of a simple harmonic wave is

y=a  sin 2π/λ (vt-x)

 

Differentiating equation (1) with respect to time

-dy /dt = 2πav/λ  cos (vt-x)

 

Again differentiating equation (2) with respect to time

To find the value of compression, differentiate equation (1) with respect to x

To find the rate of change of compression with respect to distance, differentiate equation

(4) with respect to x

From education (2) and (3)

Equation (7) represents the differential equation of wave motion.

 

The general differential equation of wave motion can be written as

Thus, knowing the value of K, the value of the wave velocity can be calculated.