Write the function that describes this wave travelling in the positive x direction.

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Solution

We know that the equation of a sinusoidal wave travelling along +X direction is given by-

$y = A sin (k x - ω t)$

$ω = 2 π f = 2 π \times 50 = 100 π / s$

$A = \frac{15}{2} c m$ since amplitude is maximum vertical displacement from mean position and it is half the displacement between valley and peak.

There are 4 waves in 6m length.

$λ = \frac{6}{4} = 1.5 m = 150 c m$

$k = \frac{2 π}{λ} = \frac{2 π}{150}$

$⟹ y = 7.5 sin 2 π [\frac{x}{150} - 50 t] c m$

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