What conditions lead to destructive interference?

Destructive interference occurs when two waves of the same frequency are out of phase by 180 degrees or half a wavelength.

In more detail, destructive interference is a fundamental concept in wave theory, which is applicable to all types of waves, including light, sound, and water waves. It is a phenomenon that occurs when two or more waves combine to produce a wave of lesser amplitude, or in some cases, completely cancel each other out. This happens when the waves are of the same frequency and are out of phase by 180 degrees or half a wavelength.

The term 'out of phase' refers to the situation where the peaks and troughs of the waves do not coincide. In the case of destructive interference, the peak of one wave aligns with the trough of another, causing them to cancel each other out. This results in a wave of lesser amplitude or, in some cases, no wave at all.

The conditions for destructive interference can be easily visualised if you imagine two waves on a string. If you create a wave pulse on one end and an identical wave pulse on the other end at the same time, but in the opposite direction, when the two pulses meet in the middle, they will cancel each other out. This is because the upward displacement of one pulse is exactly cancelled by the downward displacement of the other pulse.

In terms of light waves, destructive interference can result in dark bands in interference patterns, such as in the famous double-slit experiment. This is because the light waves from the two slits can cancel each other out when they are half a wavelength out of phase.

In conclusion, the key conditions for destructive interference are that the waves must be of the same frequency and must be out of phase by 180 degrees or half a wavelength. This results in the waves cancelling each other out, leading to a decrease in amplitude or complete cancellation.