Question

The y-x curve at an instant for a wave travelling along x-axis on a string is shown below, if the slope at point $A$ on the curve is 53°. Which of the following is/are correct?

• 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, $V_p$ is positive.

$V_p=-\frac{dy}{dx}\cdot V_w$
$\frac{V_p}{V_w}=-\tan \theta$
As $\tan \theta$ ( given slope is positive) and $V_w$ ( as wave is moving along x-axis)are positive $V_p$ is negative.
and $\left(-\tan \theta \right|>1$(as given angle ${53}^{\circ }$ > ${45}^{\circ }$)
$\therefore V_P>V_W$