Question

The 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, as shown, is ${53}^{\circ }$. Select the correct statement(s).

• 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 of the particle at point A.
• 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)

The correct options are
B Transverse velocity of the particle at point A is positive if the wave is travelling along negative x axis of the particle at point A.
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, $V_A$ is positive because as the peak shifts left all particles on left move upward.

$\frac{V_A}{V_W}=-tan\theta$
$|-tan\theta |>1$ $\therefore V_A>V_W$