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Wave Speed

The speed of a wave is very similar to the speed of a particle. For particles, we track the movement of material, but for waves, we track the movement of energy. In progressive waves, we see this as the propagation of peaks and troughs. For a standing wave, no energy is transferred, peaks and troughs do not propagate and so they have zero speed.

The image below shows part of a wave propagating at 1 m/s.

The displacement-position graph for a wave pulse is shown at three different times. The pulse consists of one peak and one trough propagating with a speed of one meter per second. After one second its peak and trough have moved by one meter, relative to their initial positions. After two seconds they have moved two meters. For all three times, at positions ahead of the pulse the displacement is zero until the pulse arrives. Similarly, for positions behind the pulse the displacement returns to zero after it has passed. Below this diagram, similar graphs are shown for wave pulses with different wave speeds. For faster speeds the peak and trough travel further in the same amount of time.

Figure 1: Displacement-position graph for a wave pulse at three different times.

The speed, v, of the wave can be related to the frequency, f, and wavelength, λ, through the expression: v = fλ. It can also depend on the medium the wave is traveling through. For example, sound waves traveling through the air have a wave speed of 343 m/s, while light waves which propagate through oscillating electric and magnetic fields travel at around 300,000,000 m/s in a vacuum. This is why when lightning strikes, we see the lightning bolt before we hear the thunder clap!The speed of the wave can be related to the frequency and wavelength through the expression: speed equals frequency times wavelength. It can also depend on the medium the wave is traveling through. For example, sound waves traveling through the air have a wave speed of 343 m/s, while light waves which propagate through oscillating electric and magnetic fields travel at around 300,000,000 m/s in a vacuum. This is why when lightning strikes, we see the lightning bolt before we hear the thunder clap!