The equation of a progressive wave is given by $y = 2 s i n (π t - 0.5 π t)$ where x and y are in metre and t is in second. The velocity of the particle at t = 1 second and x = 1 m is

2 m s^{- 1}

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Z e r o

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4 m s^{- 1}

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0.5 m s^{- 1}

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Solution

The correct option is B $Z e r o$
The particle velocity is given by $v p = ω \sqrt{A^{2} - y^{2}}$
Comparing the given equation with the standard form
$y = A s i n (ω t - k x)$ we get;
$A = 2 m, ω = π r a d s^{- 1}$
At x = 1 m and t = 1 s, $y = 2 s i n (π - 0.5 π)$
$= 2 s i n 0.5 π = 2 m$ .
$∴ v_{p} = π \sqrt{2^{2} - 2^{2}} = 0$

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