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

Answer ⇒ In Negative x-direction.

Explanation ⇒

Given,

Equation of the wave is,

y = c₁ Sin (c₂.x+c₃.t)

Taking c₂common inside the sine function, we will get,

y = c₁Sin[c₂(x + tc₃/c₂)]

Let c₂/c₃ = c (constant.)

∴ y = c₁Sin[c₂(c + t/c)]

Now, we can write this function as,

y = f(x + t/c)

We know Sine function is an increasing function, hence the wave will travel in negative x direction.

Hope it helps.