How noise-cancelling headphones work

When two waves overlap, they add together. If a crest of one meets a crest of the other they reinforce, called constructive interference; if a crest meets a trough they cancel, called destructive interference. This adding of waves is called superposition.

Noise-cancelling headphones use a tiny microphone to sample the noise coming in, then play a matching sound wave that is inverted, so its crests line up with the noise's troughs. Where the two meet at your ear they cancel, and the steady hum of an aeroplane cabin or an LRT carriage becomes much quieter.

It works best on steady, low tones, because sudden or complex sounds are harder to invert in time. This is the same interference seen when ripples from two stones cross on a pond.

In SPM you should explain interference using superposition and identify where waves add or cancel.

Waves

The physics behind it

When two waves overlap, the principle of superposition says the total displacement at any instant is the sum of the separate displacements. If one wave has a crest of +A where the other has a trough of −A, they add to zero, which is destructive interference.

For sound, complete cancellation needs the two waves to have equal amplitude and be exactly out of step.

Take a low hum at 100 Hz. Sound travels at about 340 m s⁻¹, so its wavelength is λ = v/f = 340 m s⁻¹ ÷ 100 Hz = 3.4 m.

A matching wave cancels it only when its crest lines up with the noise's trough, an offset of half a wavelength, here 1.7 m. That is a generous distance, which is why steady low tones are the ones these headphones handle best.

The amplitudes simply add: a pressure variation of +0.5 Pa from the noise meeting −0.5 Pa from the anti-noise gives 0.5 Pa + (−0.5 Pa) = 0 Pa at your eardrum. No pressure swing means no sound.

The energy is not destroyed; it is redistributed away from the point of cancellation.

See it in daily life

At home the steady drone of an air-conditioner compressor or a refrigerator is a good match for this technology. That hum is a low, unchanging tone, exactly the kind of wave a small microphone can sample and then match with an inverted copy.

Slip on a pair of noise-cancelling earphones while studying near such a machine, and the constant background hum drops away, leaving your music or your own thoughts clearer, even though a sudden clatter of a dropped spoon still gets through. The reason is that the electronics can predict and invert a repeating tone, but a sharp, one-off sound changes too quickly to cancel in time.

You can notice the wave idea without any electronics too. In a large empty hall, walk slowly while a steady tone plays from two speakers, and you pass through places that sound loud and places that sound faint.

Those quiet places are where the two waves partly cancel by the same destructive interference the headphones create on purpose.

How this comes up in SPM

In Paper 2 this idea is examined with command words such as explain, describe, state and compare. You may be asked to explain constructive and destructive interference, to state the principle of superposition, or to describe how a path difference decides whether waves reinforce or cancel.

Within the same Waves chapter, interference sits beside diffraction, because a real interference pattern is usually produced after waves spread through two gaps. It also builds on the fundamentals of waves, where wavelength, frequency and the relationship v = fλ are defined, and it links to the behaviour of sound waves.

A common task is to describe a two-source interference experiment with water waves or sound, and to relate the positions of loud and quiet points to the path difference in whole or half wavelengths. Keep your reasoning tied to crests meeting crests or crests meeting troughs, and use v = fλ with correct units whenever a wavelength must be found.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)