Defining a piecewise function of two variables

I need to plot the solution of a wave equation in three dimension. The solution is in this form: u(x,t)= sin(xt) if x>t; 0 if x<=t. The problem is I am not able to define such function of two variables. While searching I got the way to define functions using the command "piecewise" but it is not working in my case. More precisely, I tried the following code:

x=linspace(0,1,50);
t=linspace(0,1,50);
[x,t]=meshgrid(x,t);
z= piecewise(x>t, sin(x*t), x<=t, 0)
mesh(z,x,t)

Please advice.