Wave Velocity

Wave Velocity is one of the common topics of all the exams that test students on the parameters of physics. Students normally find it hard to deal with this topic as it is a little complex in nature. Although, if studied well, the same topic could be very scoring for the students from exam point of view. To bridge the gap between students and their learning Vedantu has come up with an article prepared by a team of dedicated teachers on wave velocity.  Wave Velocity - Formula, Properties, Examples could also be found in the PDF format from the website. The students can download it on their devices and study from the comfort of their homes. The resource is free of cost and doesn’t require any prior registration fee. 

A wave is a result of external perturbation in a plane surface. We can define a wave as - a wave is a disturbance propagating in space with transportation of energy and momentum from one point to another without transfer of the matter. The most commonly used examples for waves are the ripples in a pond, Sound that reaches us propagates through wave motion, TV signals, etc.  The waves are classified into different types depending upon the type of medium, propagation energy, dimensions, and the vibration of particles.

What is Wave Velocity?

Now, we are constantly talking about the term wave velocity. To understand the wave velocity first, let us look at the meaning and define wave velocity.

• The wave velocity definition is given as the velocity associated with the disturbance propagating in the given medium or in other words, wave velocity is the distance traveled by waves per unit time.

• The wave velocity depends upon the nature of the medium used.

• The wave velocity is also known as phase velocity  

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Now the formula of wave velocity is given as follows. The wave velocity formula says it is the product of wavelength and the frequency of the wave. I.e.,

Wave velocity (v) mathematically is given by,

\[\Rightarrow v = \frac{w}{k} \]……….(1)

 Where,

 w - The angular velocity

 k - the angular wavenumber or propagation constant

We know that,

The value of the angular velocity = w =  \[2\pi \nu \]; where \[\nu\] - Frequency of the wave

The value of the wavenumber = k = \[\frac{2\pi}{\lambda}\]; where \[\lambda\] - The wavelength

 Substituting these value in equation (1) we get,

 \[\Rightarrow = \frac{2\pi\nu}{2\pi\lambda} = \lambda\nu  \]

Therefore, we have,

\[\Rightarrow =  v = \lambda\nu \]…….(2)

Where,

\[\lambda\]- The wavelength

\[\nu\] - Frequency of the wave

Equation (2) is known as the equation of wave velocity or wave velocity formula.

Wave Velocity Formula:

In wave motion, the perturbations travel through the medium due to repeated periodic oscillations of the particles. The velocity of the wave will be different from the velocity of the particles with which they vibrate about their mean positions. The wave velocity will always be constant but the particle velocity will be changing with time periods.

Properties of Wave Velocity:

The wave velocity in a given medium is always constant.

The wave velocity is independent of the time and source of the wave, but the wave velocity depends on the wavelength of the propagating wave in a given medium.

The wave velocity depends on the medium used.

Examples:

1. How to Calculate Wave Velocity for a Given Periodic Wave with a Wavelength of 3m Has a Frequency 6Hz?

Sol: Given,

The wavelength of the periodic wave = \[\lambda\] = 3m

The frequency of the given periodic wave = \[\nu\] = 6Hz

We have to calculate the wave velocity of the given periodic wave. From the equation of wave velocity we have,

\[\Rightarrow v = \lambda\nu \]

Where, 

\[\lambda\] - The wavelength

 \[\nu\]  - Frequency of the wave

Substituting the corresponding values in equation (1) we get, 

\[\Rightarrow\]  v = (3)(6) = 18 m/s 

Therefore, the wave velocity of a given periodic wave is 18 m/s.

2. How Do You Find the Velocity of a Wave with a Wavelength of 20m has a Frequency 70Hz?

Sol: Given,

The wavelength of the periodic wave = \[\lambda\] = 20m

The frequency of the given periodic wave = \[\nu\] = 70Hz

We have to calculate the wave velocity of the given periodic wave. From the equation of wave velocity we have,

\[\Rightarrow v = \lambda\nu \]

Where, 

\[\lambda\] - The wavelength

 \[\nu\]  - Frequency of the wave

Substituting the corresponding values in equation (1) we get, 

⇒ v = (20)(70) = 1400 m/s

Therefore, the wave velocity of a given periodic wave is 1400 m/s.

3. The Velocity of Wave 70m/s. If the Wavelength of the Wave is 1m then Calculate the Frequency of the Given Wave.

Sol: The wavelength of the wave = \[\lambda\] = 1m

The wave velocity of the given wave = v = 70m/s

We have to calculate the Frequency of the given wave. From the equation of wave velocity we have,

\[\Rightarrow v = \lambda\nu \]...... 1

Where, 

\[\lambda\] - The wavelength

 \[\nu\]  - Frequency of the wave

On rearranging the equation (1) for the frequency of the wave, 

\[\Rightarrow \nu = \frac { v}{λ} \]……(2) 

Substituting the given values, 

\[\Rightarrow  \nu = \frac {70}{1} \]……(2) 

 = 70 Hz

Therefore, the frequency of the given wave is 70Hz 

4. A Wave with a Frequency 450Hz is Traveling at a Speed of 200m/s. Then Calculate the Wavelength of the Wave. 

Sol: The frequency of the wave = \[\nu\] = 450Hz

The wave velocity of the given wave = v = 200m/s 

We have to calculate the wavelength of the given wave. From the equation of wave velocity we have,

\[\Rightarrow v = \lambda\nu \]...... 1

Where, 

\[\lambda\] - The wavelength

 \[\nu\]  - Frequency of the wave

On rearranging the equation (1) for the wavelength of the wave, 

\[\Rightarrow \lambda = \frac { v}{\nu} \]………(2) 

Substituting the corresponding values in (2) we get, 

\[\Rightarrow  \lambda = \frac {200}{450} \]………(2)

 = 0.44m 

Therefore, the wavelength of the given wave is 0.44m.

Revision remedy

The Wave Velocity - Formula, Properties, Examples article developed by Vedantu is a perfect tool for revision for the students. It is advised that when the exams are near, you should choose to revise from the wave velocity PDF. The article precisely mentions all the details with complete clarity to the students. One may even choose to make notes from the above content and enhance her chances to score well in the exams.  On the other hand, just underlining the keywords would suffice too. All one has to do is look at the keywords.  If feasible, taking a printout is also a convenient idea.

Making the Notes and Underlining 

As it is common knowledge, having good revision notes is the best policy for scoring well in exams.  One can use the wave velocity article to make the revision notes. Note down all the keywords and important definitions that are relevant from the exam point of view.