# 6.1.3 The Wave Equation

### The Wave Equation

• Wave speed is defined as:

The distance travelled by a wave each second

• Wave speed is given the symbol ν and is measured in metres per second (m/s)
• Wave speed is the speed at which energy is transferred through a medium
• Transverse and longitudinal waves both obey the wave equation:

• Where:
• v = wave speed in metres per second (m/s)
• f = frequency in Hertz (Hz)
• λ = wavelength in metres (m)
• The wave speed equation may need to be rearranged, which can be done using this formula triangle:

#### Worked Example

A wave in a pond has a speed of 0.15 m/s and a time period of 2 seconds.

Calculate:

a) The frequency of the wave

b) The wavelength of the wave

Part (a)

Step 1: List the known quantities

• Time period, T = 2 s

Step 2: Write out the equation relating time period and frequency

Step 3: Rearrange for frequency, f, and calculate the answer

f = 1 ÷ T = 1 ÷ 2

Frequency, f = 0.5 Hz

Part (b)

Step 1: List the known quantities

• Wave speed, v = 0.15 m/s
• Frequency, f = 0.5 Hz

Step 2: Write out the wave speed equation

v = f × λ

Step 3: Rearrange the equation to calculate the wavelength

λ = v ÷ f

Step 4: Use the frequency you calculated in part (a) and put the values into the equation

λ = 0.15 ÷ 0.5

Wavelength, λ = 0.30 m

#### Exam Tip

When stating equations make sure you use the right letters:
For example, use λ for wavelength, not L or W

If you can’t remember the correct letters, then just state the word equations

Be careful with units: wavelength is usually measured in metres and speed in m/s, but if the wavelength is given in cm you might have to give the speed in cm/s

Likewise, watch out for frequency given in kHz: 1 kHz = 1000 Hz

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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