Wave Velocity Formula

A wave occurs when a planar surface is disturbed from the outside. A wave is a disturbance that propagates in space and transports energy and momentum from one point to another without transferring substance. The ripples in a pond, the sound that reaches us via wave motion, TV signals, and so on are some of the most widely utilized examples of waves. The kind of media, propagation energy, size, and particle vibration all contribute to the classification of waves. In this article, we’ll discuss how to compute wave velocity.

What is Wave Velocity?

Wave velocity is defined as the speed at which a disturbance propagates in a given medium, OR In other words, the distance traversed by waves per unit time.

The nature of the media utilized determines the wave velocity. Phase velocity is another name for wave velocity.

Precise periodic oscillations of the particles cause perturbations in wave motion, which move across the medium. The wave’s velocity will differ from the particle’s velocity as they oscillate around their mean places. The wave velocity remains constant over time, whereas the particle velocity varies. 

SI unit of the velocity of the wave is m/s.

Formula for Wave Velocity 

Wave velocity is calculated using the following formula:

V = λν

where,

• V is the velocity of wave (m/s),
• ν is the Frequency of wave, and
• λ is the Wavelength.

Derivation of Wave Velocity

The product of the wave’s wavelength and frequency, according to the wave velocity formula.

V = w/k    …(1)

where, 

• w is the Angular velocity, 
• k is the Angular wavenumber.

We have, w = 2πν 

where 

• ν is the Frequency of wave.

And k = 2π/λ

where 

• λ is the Wavelength.

Substitute w and k in equation (1),

V = (2πν) / (2π/λ)

= (2πνλ) / (2π)

V = λν

Sample Questions

Question 1: What Factors Have an Impact on Wave Velocity?

Answer:

The following factors affect the wave’s velocity:

• The medium that was used.
• In a certain medium, the wavelength of a propagating wave.

Question 2: Write two Properties of Wave velocity.

Answer:

Properties of Wave velocity are,

• In given medium, the wave velocity remains constant.
• The wave velocity is independent of the wave’s time and source, but it is affected by the propagating wave’s wavelength in a given medium.

Question 3: How to calculate the wave velocity of a 10 m wavelength periodic wave with a 16 Hz frequency?

Answer:

Given : ν = 16 Hz, λ = 10 m

Since,

V = λν

V = 16 × 10

= 160 m/s

Question 4: If the wavelength of a wave is 6 m and the frequency of a wave is 12 Hz then Calculate the Velocity of the wave.

Answer:

Given : f = 12 Hz, λ = 6 m

Since,

V = λν 

= 12 × 6

= 72 m/s

Question 5: The Wave’s Velocity is 120 m/s. Calculate the frequency of the given wave if the wave’s wavelength is 13 m.

Answer:

Given : V = 120 m/s, λ = 13 m

Since,

V = λν

ν = V/λ

= 120/13

= 9.23 Hz

Question 6: A wave with a frequency of 120 Hz is traveling at a speed of 287 m/s. Then determine the wave’s wavelength.

Answer:

Given : V = 287 m/s, ν = 120 Hz

Since,

V = λν

or 

λ = V/ν

= 287 / 120

= 2.39 m