Question

If the equation of a progressive wave is `y_1=asin(omega t-kx)`,then what is the equation of its reflected wave at a free boundary?

Answer 1

`asin(omegat +kx)`

Explanation:

When a wave is reflected from a denser media,its phase change by `pi`,and if the boundary is closed,its amplitude becomes negative as well,but in case of free boundary,there is no such change in amplitude.

Now,the given equation of the wave is `y_1= a sin(omegat -kx)`, which is travelling along `+X` axis,

So,the equation of the reflected wave in this case will be `y=a sin (omegat +kx)` which is travelling along `-X` axis,i.e having phase difference of `pi`.