15. Two traveling Waves!  
We have chosen the
xaxis to have a length of exact number of halfwavelengths (four (l/2) in this case. By pressing the F9
key, you can see how at both ends (and also for values of x = n l/2, n = 0, 1, 2,..), we always
have the same value with opposite signs for the two waves; therefore the
second wave can be thought of as the ‘hard’ reflected wave at the
right end. This is the situation we have for a transverse vibration set
up in a stretched string with fixed end.
Note at x = (n+1/2) l/2 they have exactly the same y value with the same sign. 

wave15 