Question

A string vibrates according to the equation

y' = (0.30 cm) sin[(π/3 cm-1)x] cos[(55π s-1)t]

What is the speed of a particle of the string at the position x = 1.5 cm when t = 9/8 s?

Answer 1

This is a standing wave.
y at constant x = 1.5
=.3 sin [1.5(pi/3-1)] cos t(55 pi -1)
so
dy/dt at constant x = 1.5

={.3 sin [1.5(pi/3-1)]} * {(1-55pi)sin [(9/8)55pi-1)] }

Answer 2

I kinda wrote my equation wrong so heres a new version:

y' = (0.30 cm) sin[(π/3 cm^(-1))x] cos[(55πs^(-1))t]

Answer 3

I thought it was messed up. The method I gave you is how to go about it anyway.