12.1.3 – The Wave Equation | Physics with Mr Shone

The Wave Equation
velocity = frequency × wavelength v = ƒ λ

The Wave Equation

velocity = frequency × wavelength

v = ƒ λ

when ƒ is given in Hertz, Hz,

λ is given in metre, m, (λ is the Greek Letter “lambda”)

the unit of v will be in m/s.

Deriving the Wave Equation (ENRICHMENT)

Consider a dipper placed into some water.

The dipper can be oscillated up and down to generate waves on the water surface.

A short time after starting the dipper, one complete wave will have been produced as shown in this diagram:

The furthest point of the wave will be one wavelength from the dipper. ie. the wave has travelled a distance λ at that point.

The time taken to generate a single wave is the period, T. Thus the time taken to travel this distance is T.

velocity = distance / time

velocity = λ / T

Or (as ƒ = 1/T)

velocity = ƒλ

Example
A ripple tank is used to generate water waves of wavelength 0.500 m. (a) If the dipper of the ripple tank vibrates with a frequency of 6.0 Hz, what is the speed of the waves? v = f λ = (6.0)(0.500) = 3.0 m s⁻¹ (b) If the frequency is adjusted to 2.5 Hz, and assuming that the speed of the water waves remains the same, what is the new wavelength? λ = v / f = (3.0) / (2.5) = 1.2 m

Example

A ripple tank is used to generate water waves of wavelength 0.500 m.

(a) If the dipper of the ripple tank vibrates with a frequency of 6.0 Hz, what is the speed of the waves?

v = f λ

= (6.0)(0.500)

= 3.0 m s⁻¹

(b) If the frequency is adjusted to 2.5 Hz, and assuming that the speed of the water waves remains the same, what is the new wavelength?

λ = v / f

= (3.0) / (2.5)

= 1.2 m

Example
Class95 is a Singapore radio station. The number in its name represents the frequency at which it broadcasts (in Megahertz). What is the wavelength of a radio wave of this radio station? frequency = 95 MHz = 95 × 10⁶ Hz Radio waves are em waves and thus will travel at 3.0 × 10⁸ m/s v = f λ 3.0 × 10⁸ = (95 × 10⁶ )(λ) λ = 3.16 m

Example

Class95 is a Singapore radio station. The number in its name represents the frequency at which it broadcasts (in Megahertz).

What is the wavelength of a radio wave of this radio station?

frequency = 95 MHz = 95 × 10⁶ Hz

Radio waves are em waves and thus will travel at 3.0 × 10⁸ m/s

v = f λ

3.0 × 10⁸ = (95 × 10⁶ )(λ)

λ = 3.16 m

2025 Physics Lessons