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Show that the equation, y = a sin(ωt - kx) satisfies the wave equation ∂^2y/∂t^2 = v^2(∂^2y/∂x^2).

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Show that the equation, y = a sin(ωt - kx) satisfies the wave equation ∂2y/∂t2 = v2(∂2y/∂x2). Find speed of wave and the direction in which it is travelling.

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We can write these two equations as,

The negative sign between ωt and kx implies that wave is travelling along positive x-direction.

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