JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Waves & Sound

A transverse sinusoidal wave moves along a string in the positive

x

-direction at a speed of

10 cm / s

. 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

Answer: (A)

Solution

For a sinusoidal wave:

y = A sin (ω t \pm ϕ)

and particle velocity

v = A ω cos (ω t \pm ϕ)

.

Given:

y = 5

cm =

A /2

(where

A = 10

cm), so

sin (ω t \pm ϕ) = 1/2

, giving

ω t \pm ϕ = 30°

.

Angular frequency:

ω = 2 π \frac{v}{λ} = 2 π \frac{0.1}{0.5} = \frac{2 π}{5}

rad/s

Particle velocity:

v = A ω cos (30°) = \frac{10}{100} \times \frac{2 π}{5} \times \frac{3}{2} = \frac{π 3}{50}

m/s

From the figure, the wave is moving right and point P is moving upward (positive

\hat{j}

direction).

JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Single correct option