**The Wave Equation – Learn**

The wave equation relates the velocity, frequency and wavelength of a wave. It can also be useful to incorporate the relationship between the period of a wave and its frequency.

**Period and frequency:** The period of a wave is inversely proportional to its frequency.

and

Where:

= period of the wave in s (seconds)

= frequency of the wave in Hz (Hertz)

**Velocity, frequency, period and wavelength:** The relationship between velocity, frequency, period and wavelength is represented by the following:

and

Where:

= velocity of the wave in

= wavelength in m (metres)

= period of the wave in s (seconds)

= frequency of the wave in Hz (Hertz)

**Example 1:**

What is the velocity of a wave with a wavelength of 2.0 m and a frequency of 10 Hz?

Some questions will require the wave equation to be rearranged:

**Example 2:**

What is the frequency of a wave with a wavelength of 0.05 m and a velocity of 25?

, rearranged to give:

Some questions will require the units to be changed:

**Example 3:**

What is the velocity of a wave with a wavelength of 740 nm and a frequency of 400 kHz?

=

=

**Example 4:**

What is the period of a wave with a frequency of 2.5 kHz?

=