Interference of Sound – Interference

We can see the antinodes and the nodal lines better from a bird’s eye view. How do we apply frequency, amplitude, and phase to describe this “new” wave structure, a product of interfering sound waves that originate from two tuning forks, at a particular point in space?

To this end, let us assign a spinning wheel to each sound wave. We now have two sound waves that interfere at point B. Let us represent that interference by a combination of two wheels. Mathematically, the interference is defined as a sum of the two sound waves. This is the same as adding the vectors of the two phasors. At point B, both phasors point in the same direction. The phase difference is zero degrees. When we add the two radii, the amplitude doubles. The two sound waves produce maximum reinforcement, and the constructive interference can be heard due to the increase in volume.

The point B moves further, which means that the path difference δ is one-half wavelength. Both phasors now point in the opposite directions. The phase difference is 180°. When we add together the two phasors, the result is zero, which means that the amplitude of the resultant wave is likewise zero. The destructive interference at this point is perceived as silence.

Point B moves one more time by one-half wavelength, so that both phasors point again in the same direction. The acoustic effect which follows is, again, a doubling of the amplitude. The phase difference is 360°. It corresponds to the path difference of precisely one wavelength. δ equals λ.