Wave Speed

Wave speed tells us how fast a disturbance travels from one point to another. It is not the speed of the particles of the medium, but the speed at which the wave pattern or energy moves forward.

I like to imagine tapping one end of a rope: the ripple you create travels along the rope even though the rope itself doesn’t move forward. That moving ripple is what wave speed describes.

Definition: Wave speed is the distance travelled by a wave in one second.

It tells how quickly the disturbance moves through the medium and is usually written as \( v \).

Wave speed is closely connected to how often the wave repeats (frequency) and how long each wave is (wavelength). The basic formula is:

Here:

• \( v \) = wave speed
• \( f \) = frequency (waves per second)
• \( \lambda \) = wavelength (length of one complete wave)

This formula works for all types of waves — water, sound, light, or waves on a string.

The formula \( v = f\lambda \) is easy to understand if you think of it like this:

• Frequency tells how many waves pass in one second.
• Wavelength tells how long each wave is.

So if each wave is \( \lambda \) metres long, and \( f \) such waves pass each second, the total distance covered per second is \( f\lambda \).

The speed of a wave depends strongly on the medium through which it travels. For example:

• Sound travels faster in solids than in liquids, and faster in liquids than in air.
• Water waves travel faster in deep water compared to shallow water.
• Light travels fastest in vacuum and slows down in glass or water.

The medium decides how easily particles interact and pass the disturbance forward.

The wave moves forward, but the particles do not. They only oscillate around a fixed position.

For example, in a sound wave, air particles simply vibrate back and forth, but the sound travels outward rapidly. This distinction is important when visualizing wave behaviour.

Wave speed shows up in many everyday situations:

• Echoes depend on the speed of sound in air.
• Communication signals rely on the speed of electromagnetic waves.
• Tsunamis travel very fast across oceans because water waves move faster in deep regions.
• A guitar string vibrates, and the speed of the wave along the string affects the pitch.

Wave speed helps explain how waves behave across distances, materials, and situations.

Knowing wave speed helps in understanding reflection, refraction, resonance, and many other wave phenomena. It also plays a crucial role in sound engineering, communication systems, optics, and even earthquake studies.

Once the connection between speed, frequency and wavelength becomes clear, most wave problems become much easier to understand.