How can I apply a phase shift to an amplitude-time graph?

I am using x=randn(100,1) and plot(x) to generate a graph that looks similar to an amplitude time graph obtained from an ultrasound transducer. I need to be able to produce synthetic data that has exhibited a phase shift in the signal due a temperature rise but am unsure how to do so.

Would there perhaps be an easier way of plotting such a graph that is easier to phase shift?