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A wave travelling in positive X – direction with $A = 0.2 m$ has a velocity of 360 m/sec. If $λ = 60 m,$ then correct expression for the wave

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$y = 0.2 \sin [π (6 t - \frac{x}{60})]$

$y = 0.2 \sin [2 π (6 t - \frac{x}{60})]$

$y = 0.2 \sin [2 π (6 t + \frac{x}{60})]$

$y = 0.2 \sin [π (6 t + \frac{x}{60})]$

answer is C.

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Detailed Solution

$Y = Asin (ωt - kx); ω = 2 πf; k = \frac{2 π}{λ}$

$Y = Asin (\frac{2 πvt}{λ} - \frac{2 π}{λ} x)$

$\Rightarrow Y = Asin \frac{2 π}{λ} (vt - x)$

$\Rightarrow y = 0.2 \sin [2 π (6 t - \frac{x}{60})]$

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