Question

y - x 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 $\tan {53}^{\circ }$

• A. Transverse velocity of the particle at point A is positive if the wave is travelling along positive x axis.
• B. Transverse velocity of the particle at point A is positive if the wave is travelling along negative x axis.
• C. Magnitude of transverse velocity of the particle at point A is greater than wave speed.
• D. Magnitude of transverse velocity of the particle at point A is lesser than wave speed.

Answer 1

Answer: (B), (C)

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

As shown in the curve, if wave is moving along -x axis, $V_p$ is positive.

$\frac{V_p}{V_w}=-\tan \theta \Rightarrow |-\tan \theta |>1\Rightarrow \therefore V_p>V_w$.

Also, if $V_w$ is negative (travelling along negative x-axis), then $V_p$ is positive.