Q.
A transverse sinusoidal wave moves along a string in positive x-direction at a speed of 10$cms^{- 2}$. The wavelength of the wave is 0.5 m and its amplitude is 10.cm at a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is
A) $\frac{\sqrt{3\pi}}{50}\widehat{j}ms^{- 1}$
B) $- \frac{\sqrt{3\pi}}{50}\widehat{j}ms^{- 1}$
C) $\frac{\sqrt{3\pi}}{50}\widehat{i}ms^{- 1}$
D) $- \frac{\sqrt{3\pi}}{50}\widehat{\mathsf{j}}ms^{- 1}$
Explanation
(a) Particle velocity $v_{p} = - v(slope\ of\ y - x\ graph)$
Here, v=+ve, as the wave is travelling in positive x-direction.
Slope at P is negative.
∴ Velocity of particle is in positive y (+$\widehat{\mathfrak{j}}$) direction.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.