Question Detail
Question
The particle velocity (u) of a wave, as discussed in the document, is the time derivative of the displacement y(x,t). Given y(x,t) = Asin(kx - ωt + φ), what is the expression for the particle velocity u(x,t)?
Correct Answer
Option A is the correct answer.
Detailed Explanation
On page 6, under 'Particle Velocity, Slope of y(x,t) with respect to x', the document provides the partial derivative of y(x,t) with respect to time as ∂y(x,t)/∂t = -Aωcos(kx - ωt + φ). This derivative is defined as the particle velocity u.
Hint
Particle velocity is defined as the partial derivative of displacement y(x,t) with respect to time t. Refer to the 'Particle Velocity' section on page 6.