# 1-9 Interference of waves

Two sinusoidal waves y_{1}(x,t) and y_{2}(x,t)

### Constructive and Destructive interference

moving in the same medium interfere to
produce the resultant wave y_{res}(x,t)

We say that the two waves

**interfere destructively**
if the resultant wave has an amplitude of

zero, which is the minimum possible amplitude the
resultant wave can have. Thus destructive interference occurs when

Destructive interference occurs when the phase difference between wave 1
and wave 2 is an odd integer multiple of p,or equivalently, the path difference between them is
an odd integer multiple of l/2.

We say that the two waves

**interfere constructively
**
if the resultant wave has an amplitude of

2y_{m},
which
is the maximum possible amplitude the resultant
wave can have.
Thus constructive interference occurs
when

Constructive interference occurs when the phase difference between wave 1
and wave 2 is an integer multiple of 2p,or equivalently, the path difference between them is
an integer multiple of l.