A transverse wave travels towards the positive x-direction with speed v and is written in the general form y = f(x-vt). If the local slope of the string at a point is ∂y/∂x, which relation gives the transverse particle velocity uᵧ at that point?
Options

Question

A transverse wave travels towards the positive x-direction with speed v and is written in the general form y = f(x-vt). If the local slope of the string at a point is ∂y/∂x, which relation gives the transverse particle velocity uᵧ at that point?

Options

G1 Physics · Accepted Answer

For y = f(x−vt), differentiate with respect to x: ∂y/∂x = f'. Differentiate with respect to t: ∂y/∂t = −vf'. Therefore, uᵧ = ∂y/∂t = −v∂y/∂x. Correct option: B.

A transverse wave travels towards the positive x-direction with speed v and is written in the general form y = f(x−vt). If the local slope of the string at a point is ∂y/∂x, which relation gives the transverse particle velocity uᵧ at that point?