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

Calculate the time period of a wave with a frequency of 5 Hz.

T = \frac{1}{f}

T = 1 \div 5

T = 0.2~s

Question

Calculate the time period of a wave with a frequency of 400 Hz.

T = 1 \div 400

T = 0.0025~s

Calculating wave speed

Wave velocity, the speed of a wave, can be calculated using the equation:

wave speed = frequency × wavelength

v \ = f \ \lambda

This is when:

  • wave speed (T) is measured in metres per second (m/s)
  • frequency (f) is measured in Hertz (Hz)
  • wavelength (λ ) is measured in metres (m)
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 wave speed if the frequency is 50 Hz and the wavelength is 6 m?

v \ = f \ \lambda

v \ = 50 \times 6

v \ = 300 \ m/s

Question

What is the speed of a wave with a frequency of 0.2 Hz and a wavelength of 25 m?

v \ = f \ \lambda

v \ = 0.2 \times 25

v \ = 5 \ m/s

The speed of sound in different materials

Sound is a mechanical longitudinal wave. The wave is passed on by collisions between particles, so the speed the wave moves depends on the density of the particles.

MediumStateSpeed of sound
SteelSolid6,000 m/s
WaterLiquid1,500 m/s
AirGas330 m/s

When sound moves from one medium into another, the change in speed will also cause a change in wavelength, frequency is unaffected.

wave speed = frequency × wavelength

Constant frequency means that the wavelength will be proportional to the wave velocity.