# A wave with an amplitude of 1.94 m interferes with a second wave with an amplitude of 0.85 m....

## Question:

A wave with an amplitude of 1.94 m interferes with a second wave with an amplitude of 0.85 m. What is the largest resulting wave that could occur if these two waves destructively interfere?

## Waves:

The amplitude of a wave is the maximum displacement from the equilibrium position. Destructive interference results in the algebraic difference of the two waves interfering. Therefore, for two identical waves interfering, for example, they give a resultant wave of zero amplitude (complete cancellation of the waves).

The resultant of two waves interfering destructively is found from superposition as the algebraic difference of the two waves. That is, corresponding parts of the two waves are subtracted out from each other. For the largest resulting wave the two waves must be perfectly out of phase. Then, a trough (deep) will meet a crest (peak) and the result will be the difference of the two. Therefore, the resultant wave will have an amplitude = 1.94 m - (0.85 m) = 1.09 m. Thus, the largest resulting wave will have an amplitude of 1.09 m. 