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Different Forms of Equations

Equation of p...

Question

Equation of progressive wave is given by $y = 0.2 cos π (0.04 t + 0.02 x - \frac{π}{6})$ . The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of $\frac{π}{2}$ ?

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 C $25 cm$
Comparting with $y = a cos (ω t + k x - ϕ)$
We get $k = \frac{2 π}{λ} = 0.02 π$
$\Rightarrow λ = 100 cm$
$Δ ϕ = \frac{π}{2}$ . Hence, path difference between them
$Δ x = \frac{λ}{2 π} \times Δ ϕ$
$= \frac{λ}{2 π} \times \frac{π}{2}$
$= \frac{λ}{4} = \frac{100}{4} = 25 cm$

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