Measuring the speed of sound in air

Sound takes time to travel through air. Its speed can be estimated by measuring the distance it travels and the time it takes to travel that distance. The speed of sound in air is approximately $$330–350\ \mathrm{m/s}$$.

Measuring the distance and time

Place an observer a measured distance from a source that produces a sound and a visible signal at the same time. The observer starts a timer when they see the signal and stops it when they hear the sound.

Light travels much faster than sound, so its travel time is negligible compared with the sound travel time. The measured interval is therefore approximately the time taken for sound to travel from the source to the observer.

Calculating the speed of sound

Divide the measured distance by the measured time:

Here, $$v$$ is the estimated speed in metres per second, $$d$$ is the distance in metres, and $$t$$ is the time in seconds.

Repeat the measurement and average the results to improve the estimate. Repeats help reduce the effect of variation in the measured times, including variation caused by the observer's reaction time.

Progressive waves

A progressive wave is a disturbance that travels from one place to another, transferring energy as it moves.

When a progressive wave travels through a material, the particles oscillate about their equilibrium positions: their positions when they are not disturbed. Each particle moves back and forth as the disturbance passes, but it does not travel along with the wave. Energy is transferred through the material even though the particles do not make the journey with it.

Amplitude, frequency and period

The amplitude is the maximum displacement of an oscillating particle from its equilibrium position.

The frequency $$f$$ is the number of complete oscillations made per unit time. It is measured in hertz ($$\mathrm{Hz}$$), where one hertz means one oscillation per second. The period $$T$$ is the time taken for one complete oscillation, measured in seconds. They are related by:

A higher frequency means more oscillations each second, so the time taken for each oscillation is shorter.

Wavelength and wave speed

The wavelength $$\lambda$$ is the distance between successive points that are at the same stage of oscillation, such as two successive crests. It is measured in metres.

The wave speed $$c$$ is the distance travelled by the disturbance per unit time. It is not the speed at which an individual particle oscillates. In one period, the disturbance travels one wavelength, so its speed is wavelength divided by period. Since $$f = 1/T$$:

When $$f$$ is in hertz and $$\lambda$$ is in metres, $$c$$ is in metres per second.