Question

Wave Question?

A traveling wave on a string is described by `y(t)=Asin(kx−ωt)`. Let `A=8 mm, k=2π,`and `ω=42` rad/s. How long will take for a point on the string to move from `y = 3 mm` to `y = -3 mm.`?

Answer 1

See below.

Explanation:

Taking the point `x_0` as reference point we have

`arcsin(y_1/A) = k x_0 - omega t_1` and
`arcsin(y_2/A) = k x_0 - omega t_2`

now substracting we have

`t_2-t_1 = 1/omega(arcsin(y_1/A)-arcsin(y_2/A))`