Question

For the wave of part b, write the equations for the transverse velocity of a particle at point x. Express your answer in terms of a, Ω, x, t, and k.

Answer 1

The transverse velocity of a particle at point x experiencing a transverse wave is given by the derivative of the wave function with respect to time, resulting in v(x, t) = -AΩ cos(kx - Ωt).

Step-by-step explanation:

The question seeks the transverse velocity equation for a particle at point x on a string experiencing a transverse wave, using the wave function y(x, t) = A sin(kx - Ωt), where 'A' represents amplitude, 'Ω' the angular frequency, 'k' the wavenumber, 't' time, and 'x' the position along the string.

To find the velocity, we take the partial derivative of the wave function with respect to time, 't'. This gives us:

v(x, t) = ∂y/∂t = -AΩ cos(kx - Ωt)

This equation represents the transverse velocity of the medium at point x at time t, where the velocity is perpendicular to the wave's direction of travel.