When calculating how fast an object is moving, we use the velocity equation:

v = d t

That is velocity is equal to the displacement divided by time.

When calculating the velocity of a wave, we use the same idea. Velocity is equal to the displacement (wavelength) divided by the time (period).

This gives the equation for the velocity of a wave:

v = λ T

Since we know that f = 1 T we can substitute into this equation and get:

v = fλ

v = velocity (m/s)
f = frequency (Hz)
λ = wavelength (m)
T = period (s)

Examples:

1. What is the velocity of a 650 Hz sound wave that has a length of 52.8cm?

   Interactive popup. Assistance may be required.

   Givens

   f = 650 Hz    λ = 52.8 cm = 0.528 m    v = ? Interactive popup. Assistance may be required.

   Equation

   v = fλ Interactive popup. Assistance may be required.

   Solution

   v = fλ = (650)(0.528) = 343.2 m/s

2. What is the frequency of a 0.23 meter long wave that is traveling at 46 m/s?

   Interactive popup. Assistance may be required.

   Givens

   v = 46 m/s      λ = 0.23 m      f = ? Interactive popup. Assistance may be required.

   Equation

   v = fλ Interactive popup. Assistance may be required.

   Solution

   v = fλ
   f = v λ = 46 0.23 = 200 Hz

Important note: Even though both velocity and frequency describe the rate of motion of the wave, it is important to point out that frequency is how often a specific piece of the medium moves back and forth, and velocity is how quickly the energy of the wave moves from one place to another through the medium.