Question

A wave is represented by an equation y = c₁ sin (c₂.x+c₃.t). In which direction is the wave going? Assume that c₁, c₂ and c₃ are all positive.

Answer 1

y = c₁ sin (c₂.x+c₃.t)

→y = c₁ sin {c₃.(t + c₂.x/c₃)}

→y = c₁ sin [c₃.{t + x/(c₃/c₂)}]

→y = c₁ sin [c₃.(t + x/c)] = (t + x/c), where c = c₃/c₂.

So the wave is travelling in the negative x-direction.