Wave period and wave speed

The time period of a wave can be calculated using the equation:

time~period = \frac{1}{frequency}

T = \frac{1}{f}

This is when:

  • time period (T) is measured in seconds (s)
  • frequency (f) is measured in Hertz (Hz)

Example calculation

Calculate the time period of a wave with a frequency of 50 Hz.

T = \frac{1}{f}

T = 1 \div 50

T = 0.02~s

Question

Calculate the frequency of a wave with a time period of 0.05 seconds.

0.05 = 1 \div f

f =  1 \div 0.05

f = 20~Hz

Calculating wave speed

The speed of a wave can be calculated using the equation:

wave speed = frequency × wavelength

v = f~ \lambda

This is when:

  • wave speed (v) is measured in metres per second (m/s)
  • frequency (f) is measured in Hertz (Hz)
  • wavelength ( \lambda ) is measured in metres (m)

The equation shows that wavelength is directly proportional to velocity of a wave which is moving at a constant frequency (for example, when water waves are refracted in a ripple tank).

Formula triangle demonstrating v equals f times lambda. V at the apex of triangle, f in bottom-left corner and lambda in bottom-right. Also demonstrates f equals v over lambda, lambda equals v over f.

Example calculation

What is the speed of a wave that has a frequency of 50 Hz and a wavelength of 6 m?

v = f~\lambda

v = 50 \times 6

v = 300~m/s

Question

What is the frequency of a wave with a speed of 5 m/s and a wavelength of 25 m?

f = \frac{v}{\lambda}

f = 5 \div 25

f = 0.2~Hz