Final answer:
The particle velocity of a wave can be found by taking the derivative of its equation with respect to time. In this case, the derivative of the equation Y = 2sin(10t - x) is Y = 20cos(10t - x), which serves as the velocity of particle in motion along the wave.
Step-by-step explanation:
The motion of wave propagating along a string is described by the given equation Y = 2sin(10t - x). The particle velocity of a wave is essentially the speed at which a particular point on the wave — in this case, a particle on a string — is moving. You can find this by taking the derivative of the given equation with respect to time.
In this case, the derivative of the equation with respect to time would be: Y = 20cos(10t - x), which is the particle velocity of the wave. This is a general equation and can be used to find the velocity at any point and any time.
Learn more about Wave Motion