A wave propagates on a string in the positive x -direction at a velocity υ . The shape of the string at t = t 0 is given by g ( x, t 0 ) = A sin( x / a ). Write the wave equation for a general time t .

A wave propagates on a string in the positive x-direction at a velocity υ. The shape of the string at t = t₀ is given by g(x, t₀) = A sin(x/a). Write the wave equation for a general time t.

The general equation is

Here,

Also,

So,

Comparing,

To sustain equality, the equation must be,

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