The Wave Equation (Edexcel International AS Physics)

The Wave Equation

• This equation links wave speed, frequency and wavelength

• Where:
  • v = velocity of the wave (m s^–1)
  • f = frequency of the wave (Hz)
  • λ = wavelength (m)

• The wave equation tells us that for a wave of constant speed:
  • As the wavelength increases, the frequency decreases
  • As the wavelength decreases, the frequency increases

 

The relationship between frequency and wavelength of a wave

Step 1: Write down the known quantities

• • Period, T = 1.0 μs = 1.0 × 10^–6 s
  • Velocity, c = 100 cm s^–1 = 1.0 m s^–1

Note the conversions:

• • The period must be converted from microseconds (μs) into seconds (s)
  • The velocity must be converted from cm s^–1 into m s^–1

Step 2: Write down the relationship between the frequency f and the period T 

f = 

Step 3: Substitute the value of the period into the above equation to calculate the frequency 

f = 

f = 1.0 × 10⁶ Hz

Step 4: Write down the wave equation

c = fλ

Step 5: Rearrange the wave equation to calculate the wavelength λ

λ = 

Step 6: Substitute the numbers into the above equation 

λ = 

λ = 1 × 10^–6 m