Question

Curve 'yx' 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 ${53}^{\circ }$ .

• 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 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

If the wave moves towards left, the peak must shift towards left which means that all points to the left of peak must be going upwards and others to the right must be going downwards. Hence point A will move upwards.

Also for a travelling wave on a string, the velocity of a point $A$ is related to wave velocity by slope at that point,

$\frac{v_A}{v_{wave}}=tan\left(\theta \right)=tan\left({53}^0\right)=\frac{5}{3}>1$

Hence, $v_A>v_{wave}$.