How does change of medium effect standing wave ? Please give an example of two strings of different linear mass densities in which a wave originates which further results in a standing wave?

If the tension is kept the same and only the mass density per length changes, then the frequency of the standing wave should change (as evidenced by the behavior of real strings). Thus to "sweep" the same range of displacement per cycle, a heavier string should be moving more slowly and y(t) is "stretched" in time.