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Question
The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given f(t) = A sin (t/T). The wave speed is v. Write the wave equation.
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Solution
Given,
Equation of the wave travelling in the positive x-direction at x = 0:
\[f\left( t \right) = A\sin\left( \frac{t}{T} \right)\]
Here,
Wave speed = v
Wavelength, λ = vT
T = Time period
Therefore, the general equation of the wave can be represented by
\[y = A\sin\left[ \left( \frac{t}{T} \right) - \left( \frac{x}{\nu T} \right) \right]\]
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