Question

A sound wave of fixed frequency is going through a medium in the X direction. Ignore the velocities of the particles due to thermal motion and assume that the layers of the medium perform simple harmonic motions about their mean positions. Graph in the figure represents displacements of the particles from their mean positions (plotted on Y axis) at a particular instant of time. Some of the particles are labeled by alphabets a - s. Velocity of the particle G is directed negative at that instant. Points C, I and 0 correspond to maximum displacement at that instant.

(I) The sound wave is travelling along the negative X direction.

(II) The sound wave is travelling along the positive X direction.

(III) Particles C, I and 0 are possessing maximum kinetic energy at the given instant.

(IV) Particles F, Land R are possessing maximum kinetic energy at the given instant.

(a) Only I and IV are correct. 

(b) Only II and III are correct.

(c) Only I and III are correct. 

(d) Only II and IV are correct.

Answer 1

Correct option: (b) Only II and III are correct.

Explanation: 

y = a sin(wt–kx) when wave is moving towards + x axes

dy/dx = v = aw cos (wt–kx)

of y = max then sin (wt–kx) = 1 => (wt–kx) = 90°

so when y = max then velocity will be zero

At, F, L and R K.E. will be max

At G, velocity s negative

V = aw cos (π + wt. – kx) = – aw cos wt

so wave is moving towards + x axis