Sound – wave interference

Sound waves are longitudinal or compression waves that transmit sound energy from the source of the sound to an observer. Sound waves are typically drawn as transverse waves, with the peaks and troughs representing the areas of compression and decompression of the air. Sound waves can also move through liquids and solids, but this article focuses on sound waves in air.

When a sound wave travels out from a source, it travels outwards like a wave produced when a stone is dropped into water. The sound wave from a single clap is similar to a stone dropped in water – the wave spreads out over time. The wave pattern formed by a series of steady vibrations would look like a series of concentric circles centred on the source of the vibration.

Detecting sound waves

Sound waves are not visible. To detect them, we can use our ears or we can position a microphone (probe) and observe the sound using an oscilloscope, computer or smartphone app.

In the image below, the microphone is detecting the sound of the note A at two different octaves – one vibrating at 440 vibrations per second and the other at 220. The number of vibrations per second is also known as frequency or pitch and is measured in hertz, which has the symbol Hz (named after Heinrich Hertz).

Notice that the wavelength for the 220 Hz wave is longer than the wavelength for the 440 Hz wave. As the wavelength increases, the frequency decreases according to the formula:

Wave interference

When two or more sound waves occupy the same space, they affect one another. The waves do not bounce off of each, but they move through each other. The resulting wave depends on how the waves line up.

With constructive interference, two waves with the same frequency and amplitude line up – the peaks line up with peaks and troughs with troughs as in diagram A above. The result is a wave that has twice the amplitude of the original waves so the sound wave will be twice as loud.

Destructive interference is when similar waves line up peak to trough as in diagram B. The result is a cancellation of the waves. Noise-cancelling headphones work on this principle. They detect the sounds coming into the ear and produce sounds with equal volume but with the peaks and troughs reversed, resulting in near silence.

The result of any combination of sound waves is simply the addition of the various waves. When we hear the sound of two different musical notes, as shown in diagram C, we hear a complex waveform we think of as harmony.

Diagram D shows beats – when two sound waves are nearly the same frequency but slightly different. The resulting wave has points of constructive interference and destructive interference. A sound wave with the beat pattern in diagram D will have a volume that varies at a regular rate – you can hear a pulse or flutter in the sound.

Sound waves and pitch

Because sound travels outwards from a central source, waves interact in interesting patterns. When the same pitch or frequency sound wave is produced from two sources, a pattern of interference is produced.

In the image below, two sources – labelled Sound 1 and 2 – are aligned one above the other. The waves interfere with each other so that there is constructive interference in some areas (left-hand picture) and destructive interference in other areas (right-hand picture).

As the spacing between the sources is increased, the interference pattern changes and more zones of destructive interference are created.

These interference patterns can easily be observed by placing two sound sources in close proximity (0.5–2 metres apart) in a large open space and setting each to emit the same pitch. When you walk around listening to the sound, distinct areas of loudness and softness can be observed.