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Physics-

General

Easy

Question

A transverse sinusoidal wave moves along a string in positive x-direction at a speed of 10 $c m s to the power of negative 2 end exponent$ . The wavelength of the wave is 0.5 m and its amplitude is 10.cm at a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is

$\frac{\sqrt{3 π}}{50} \hat{j} m s^{- 1}$
$- \frac{\sqrt{3 π}}{50} \hat{j} m s^{- 1}$
$\frac{\sqrt{3 π}}{50} \hat{i} m s^{- 1}$
$- \frac{\sqrt{3 π}}{50} \hat{j} m s^{- 1}$

The correct answer is: $fraction numerator square root of 3 pi end root over denominator 50 end fraction stack j with hat on top m s to the power of negative 1 end exponent$

Particle velocity $v subscript p end subscript equals negative v open parentheses s l o p e blank o f blank y minus x blank g r a p h close parentheses$
Here, v=+ve, as the wave is travelling in positive x-direction.
Slope at P is negative.
∴ Velocity of particle is in positive y (+ $stack j with hat on top$ ) direction.

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