Sound – beats, the Doppler effect and sonic booms

When two or more sound waves occupy the same space, they affect one another. This is known as sound wave interference. Sound waves combine by simple addition. The resulting wave depends on how the waves line up.

When two sound waves strike our eardrums at the same time, we hear the direct combination of the two waves. For example, when two sounds with the same frequency (pitch) and amplitude (volume) line up and strike our ears (like diagram A in the image below), we hear a sound twice as loud as either sound alone. When we hear the two sounds shown in diagram B, we hear neither sound because they cancel each other out. This is how noise-cancelling headphones work. 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.

When two sounds are nearly the same pitch, such as the sounds shown in diagram D, the result is a phenomenon known as beats. We notice it as the unpleasant sound when two instruments are slightly out of tune. Looking closely at the waves in diagram D, you can see why beats occur. The waves are aligned peak to peak at the beginning, but as the waves progress, the slight difference in the length of the waves causes them to line up peak to trough, cancelling each other out. Then the waves begin to align peak to peak again, and the pattern repeats. You can clearly hear beats when two pure tones such as 440 Hz and 441 Hz are sounded at the same time.

Beat patterns

Sound waves in air travel out in all directions from the source, and the phenomenon of beats can be observed in the image below. In the diagram on the left, the two sounds are coming from sources that are at the same location. Notice the blurry concentric rings caused by the waves destructively interfering. A microphone probe (red circle) shows the beat pattern. The diagram on the right shows the same two sound sources separated by a small distance. Notice the pattern of blurry circles indicating the asymmetric shape of the beat pattern.

Doppler effect

A different effect happens when the source of the sound is moving. A sound wave travels at a specific speed in a given material. In air, that speed is approximately 340 metres/second. The wave patterns are similar to the water waves that would be made by a duck swimming in one direction and bobbing up and down in the water. The duck would be moving towards the waves in front of it – creating shorter waves towards the front – and racing away from the waves behind – leaving longer waves in its wake.

When a stationary observer (red circle in the image below) observes the sound approaching, they would perceive more waves striking their ears every second, and the pitch of the sound would appear higher than it really is. When the sound passes, they would observe fewer waves in each second and therefore hear a lower pitch. You may have observed this effect when an ambulance streaks past and the sound of the siren appears to change pitch as it passes you.

Sonic boom

A phenomenon that is related to the Doppler effect is called a sonic boom. A sonic boom occurs when an object literally outruns is own sound waves. When an object travels faster than the sound waves it produces, no sound is heard in front of the object.

The image below shows the sound waves made by a supersonic jet. The red circle indicates the position of an observer. When the jet takes off, it quickly begins to outrun its own sound. In the third image, the observer would have seen the jet fly past but not yet have heard the sound. The sound waves literally pile up into a very high intensity V-shaped shockwave trailing the jet. When the edge of the wave strikes the observer, they hear (and feel) a violent boom, which has enough force to break windows. After the concentrated waves pass, the observer would hear the regular sound of the jet.