How is interference applied in noise-cancelling headphones?

Interference is applied in noise-cancelling headphones by producing sound waves that cancel out unwanted ambient noise.

Noise-cancelling headphones utilise the principle of superposition to reduce unwanted ambient noise. This principle states that when two or more waves meet, the resulting wave is the vector sum of the individual waves. In simpler terms, the resulting wave is the combination of the individual waves.

In the context of noise-cancelling headphones, they have a built-in microphone that picks up the ambient noise. The headphones then produce a sound wave that is the exact opposite (or 'anti-noise') of the ambient noise. This is achieved by inverting the waveform of the ambient noise. When the anti-noise meets the ambient noise, they interfere destructively, effectively cancelling each other out. This is because the peak of one wave aligns with the trough of the other, resulting in a net amplitude of zero.

This process is an example of active noise cancellation, where the headphones actively produce sound waves to interfere with and cancel out the ambient noise. It's important to note that this process is most effective with consistent, low-frequency noise, such as the hum of an aeroplane engine. It's less effective with sudden, high-frequency noise, such as someone talking nearby, because the headphones may not react quickly enough to produce the necessary anti-noise.

In addition to active noise cancellation, noise-cancelling headphones also typically include passive noise cancellation features, such as sound-absorbing materials and a snug fit around the ears, to further reduce ambient noise.

In conclusion, the application of interference in noise-cancelling headphones is a practical example of wave superposition in action. It demonstrates how understanding the fundamental principles of physics can lead to innovative solutions to everyday problems.