What Is the Equation of a Wave Reflected from a Rigid Boundary?

[Amith2006]

Sir,
Consider a progressive wave represented by the equation,
y = A[sin(wt – kx)]
If it is reflected from a wall, what will probably be the equation of the reflected wave?
I think it is y = A1[sin(wt + kx)]
Is it right? Should a negative sign be given to the expression? Will there be a phase change of pi assuming the wall to be rigid boundary?

 

[maverick280857]

Sir,
Consider a progressive wave represented by the equation,
y = A[sin(wt – kx)]
If it is reflected from a wall, what will probably be the equation of the reflected wave?
I think it is y = A1[sin(wt + kx)]
Is it right? Should a negative sign be given to the expression? Will there be a phase change of pi assuming the wall to be rigid boundary?

There will be a phase change of \pi if the wall is of a denser medium than the incident medium. Since the wall is rigid, this is correct. A_{1} is determined from considerations of boundary conditions. That will tell you whether there should be a minus sign or not. You don't have to "give" it a negative sign.