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

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

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

Step 6: Substitute the numbers into the above equation

λ?= 1 × 10–6?m