INTERFERENCE BETWEEN THE WAVES FROM TWO POINT SOURCES

Next, we shall consider two small balls, which oscillate on the water surface. Every ball excites the wave, which interferes with the wave from the other ball. As a result we see on the water surface a typical interference pattern. Let us derive the equation for this interference.

The wave from every ball is described by the formula:

s 1=A 1 cos(w t - kr 1); s 2=A 2 cos(w t - kr 2);

where A 1 and A 2 are the amplitudes of the waves in the points of excitation (balls), r 1 and r 2 are the distances from ball 1 and ball 2 to the point of observation, k = w/v, v is the speed of the waves propagation.

Because the difference D =r 2-r 1 is much less than each radius r 1 and r 2 we can consider r 1» r 2 and A = A 1 » A 2. Superposition of the waves s 1 and s 2 can be described as follows:

We can see from this equation that in the points where r 2 - r 1 = l (1/2+n) the water surface does not oscillate. These node points (lines) are clearly seen in the animated picture.