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Consider a plane progressive wave propagating along negative x-direction whose frequency is f. At t = t₀ the displacement associated with the wave is given by the following equation:
$y (x, t = t_{0}) = Acoskx$
Displacement associated with the wave as a function of x at t = 2t₀ can be represented by equation.

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$Acos (kx + 4 {πft}_{0})$

$Acos (kx + 2 {πft}_{0})$

$Acos (kx - 2 {πft}_{0})$

$Asin (kx + 2 {πft}_{0})$

answer is A.

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Detailed Solution

$y (x, t = 2 t_{0}) = A \cos [k x + ω t_{0}]$ $y (x, t = t_{0}) = Acoskx$

$∴ y (x, t) = A \cos k [x + v (t - t_{0})]$

$y (x, t) = A \cos [k x + ω t - ω t_{0}]$

$at t = 2 t_{0}$

$y (x, t = 2 t_{0}) = A \cos [k x + ω t_{0}]$

$y (x, t = 2 t_{0}) = A \cos [k x + 2 π f t_{0}]$

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