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Phase Difference

Equation of a...

Question

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

4 cm

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8 cm

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25 cm

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10 cm

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Solution

The correct option is C $25 cm$
Given:
$y = 0.2 cos π (0.04 t + 0.02 x - \frac{π}{6})$
On comparing with standard equation of progressive wave,
$y = A cos (ω t + k x + ϕ)$ ,
Wave number, $k = 0.02 π {cm}^{- 1}$
So, wavelength, $λ = \frac{2 π}{k} = \frac{2 π}{0.02 π} = 100 cm$
We know phase difference,
$Δ ϕ = \frac{2 π}{λ} Δ x$
$\Rightarrow Δ x = \frac{Δ ϕ λ}{2 π} = \frac{\frac{π}{2} \times 100}{2 π} = 25 cm$

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y = 0.2 cos π (0.04 t + 0.02 x - \frac{π}{6})

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y = 0.2 cos π (0.04 t + 0.02 x - \frac{π}{6})

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y = 0.2 cos π (0.04 t + 0.02 x - \frac{π}{6})

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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

y = 0.2 cos π (0.04 t + 0.2 x - \frac{π}{6})

\frac{π}{2}

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