Question

The displacement of a transvers wave travelling on a string is represented by D1 = 4.2sin(0.84.x - 47t + 21) where D1 and x are in cm and t in s.Find an equation that represents a wave which, when traveling in the opposite direction, will produce a standing wave when added to this one

Answer 1

The equation for such type of wave is
`D_2 = sin(0.84.x + 47t + 21)`

Step-by-step explanation:

From the question we are told that

The displacement is
`D_1 = 4.2sin(0.84.x - 47t + 21)`

Here the wave number is k= 0.84

The angular frequency is
`w = 47`

The phase shift is
`\phi = 21`

Generally the equation that represents a wave which, when traveling in the opposite direction, will produce a standing wave when added to this one is mathematically represented as

`D_2 = sin(0.84.x + 47t + 21)`