What happens when the phase difference is π in interference?

When the phase difference is π in interference, destructive interference occurs, resulting in a minimum or zero intensity.

In the phenomenon of wave interference, the phase difference plays a crucial role in determining the resultant wave's amplitude. When two waves interfere, they superpose, and the resultant wave's amplitude depends on the phase difference between the two interfering waves. If the phase difference is π (or 180 degrees), the waves are said to be in anti-phase. This means that the crest of one wave coincides with the trough of the other wave, and vice versa.

In this scenario, destructive interference occurs. The amplitudes of the two waves subtract from each other, leading to a minimum or even zero intensity at the point of interference. This is because the positive displacement caused by one wave is exactly cancelled out by the negative displacement caused by the other wave. The result is a point of minimal disturbance, often referred to as a 'node'.

This concept is fundamental in understanding various phenomena in physics, such as the pattern observed in a double-slit experiment, the noise-cancelling effect of certain headphones, and the formation of standing waves in musical instruments. In all these cases, the principle of superposition applies, and the phase difference between waves determines whether constructive or destructive interference occurs.

In summary, a phase difference of π in interference leads to destructive interference, where the amplitudes of the two waves cancel each other out. This results in a minimum or zero intensity at the point of interference, creating what is known as a 'node'. Understanding this concept is crucial for grasping various wave-related phenomena in physics.