Wave Speed Formula

A wave is described as a type of disturbance in moving media, such as the ocean waves, which travel in a medium and may be seen as wave crests moving from one place to another over time. An object’s motion may be characterised in terms of speed, which represents the object’s velocity.

When a source vibrates and disrupts a particle in the medium, it creates a wave. This is commonly seen in the case of tuning forks or ripples in water when a body is dumped, among other things.

The frequency is the number of waves that travel in one second, and the time period is the reciprocal of the frequency. The distance between the equivalent spots in any two successive waves is known as the wavelength.

Wave Speed Formula

v = f λ

Where,

v is the velocity of the wave

f is the frequency of the wave

λ is the wavelength

Derivation of Formula

The formula for wave speed, which includes wavelength and frequency, is as follows:

The equation for the magnitude of velocity is: v = Δx/Δt

If the magnitude of the displacement of the wave equals the wavelength of the wave, λ, then the time for

that to occur is the period, T

v = Δx/Δt = λ/T

We know frequency and period are inversely related: f = 1/T

Therefore, the equation for the magnitude of the velocity of a wave is: v = Δx/Δt = λ/T = f λ 

v = f λ

Sample Problems

Problem 1: A light wave travels with a wavelength of 600 nm. Determine its frequency.

Solution

Wavelength λ = 600 nm

Velocity of light = 3 x 10⁸ m/s²

The frequency is calculated by,

f = v / λ

= 3 x 10⁸ / 600 x 10^-9

=5 x 10¹⁴ Hz

Problem 2: A sound wave has a wavelength of 1.5 mm. Determine its frequency.

Solution

Wavelength λ = 1.5 mm,

Velocity of sound v = 343.2 m/s.

The frequency is calculated by,

f = v / λ

= 343.2 / 1.5 × 10^-3

= 228 × 10³ Hz 

Problem 3: A wave has a frequency of 50 Hz and a wavelength of 10 m. What is the speed of the wave? 

Solution

Frequency f= 50 Hz

Wavelength λ = 10 m

The speed of the wave is calculated by,

v = λ × f 

= 10 m × 50 Hz

= 500 m/s

Problem 4: A wave has frequency of 5 Hz and a speed of 25 m/s. What is the wavelength of the wave? 

Solution

frequency f = 5 Hz

Speed of the wave v = 25 m/s

The wavelength is calculated by,

λ = v / f

= 25 / 5

= 5 m

Problem 5: A wave has wavelength of 10 m and a speed of 340 m/s. What is the frequency of the wave? 

Solution

Wavelength λ = 10 m

Speed of the wave = 340 m/s

The frequency is calculated by,

f = v / λ 

= 340 / 10

= 34 Hz