Equation of a progressive wave is given by

$y = 0.2 c o s π ⟮ 0.04 t + .02 x - \frac{π}{6} ⟯$

The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of p/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 C
25 cm

Comparing with $y = a c o s (w t + k x - ϕ)$ ,

We get $k = \frac{2 π}{λ} = 0.02 \Rightarrow λ = 100 c m$

Also, it is given that phase difference between particles $△ ϕ = \frac{π}{2}$ . Hence path difference between them

$△ = \frac{λ}{2 π} \times △ ϕ = \frac{λ}{2 π} \times \frac{π}{2} = \frac{λ}{4} = \frac{100}{4} = 25 c m$

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