A progressive wave is represented as $y = 0.2 cos π (0.04 t + 0.2 x - \frac{π}{6})$ where distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of $\frac{π}{2}$ ?

4 cm

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8 cm

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25 cm

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12.5 cm

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Solution

The correct option is D 25 cm
On comparing the given equation with
$y = a cos (ω t + k x - ϕ)$
we get, $k = \frac{2 π}{λ} = 0.02$
and $λ = 100 c m$
It is given that phase difference between particles $△ ϕ = \frac{π}{2}$
So, the path difference between them,
$△ p = \frac{λ}{2 π} \times △ ϕ$
$= \frac{λ}{2 π} \times \frac{π}{2} = \frac{λ}{4} = \frac{100}{4} = 25 c m$

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