x-y curve at an instant for a wave travelling along x axis on a string is shown. Slope at the point A on the curve, as shown, is $53^{o}$ .

Transverse velocity of the particle at point A is positive if the wave is travelling along the positive x axis.

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Transverse velocity of the particle at point A is positive if the wave is travelling along the negative x axis of the particle at point A

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The magnitude of transverse velocity of the particle at point A is greater than the wave speed.

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The magnitude of the transverse velocity of the particle at point A is lesser than wave speed.

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Solution

The correct options are
B Transverse velocity of the particle at point A is positive if the wave is travelling along the negative x axis of the particle at point A
C The magnitude of transverse velocity of the particle at point A is greater than the wave speed.
As shown in the curve, if the wave is moving along the negative x axis, $V_{p}$ is positive.
$\frac{V_{P}}{V_{W}} = - tan θ$
Given $θ = 53^{o} \Rightarrow | - tan θ | > 1$
$∴ V_{P} > V_{W}$

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x-y curve at an instant for a wave travelling along x axis on a string is shown. Slope at the point A on the curve, as shown, is 53o.

x-y curve at an instant for a wave travelling along x axis on a string is shown. Slope at the point A on the curve, as shown, is $53^{o}$ .