Answer

Verified

347.4k+ views

**Hint:**This question can be solved by substituting the expression for frequency and wavelength in the wave velocity equation. The expression of frequency can be obtained from the angular frequency equation and the wavelength expression from the angular wave number equation. These expressions then when substituted in the wave velocity equation will give the relation between angular frequency, angular wave number and wave velocity.

**Formula used:**$\omega = \dfrac{{2\pi \pi }}{T}$,$k = \dfrac{{2\pi }}{\lambda }$,$v = \upsilon \lambda $

**Complete step-by-step solution:**

Angular frequency is given by the equation $\omega = \dfrac{{2\pi }}{T} = 2\pi \upsilon $

Where, $\omega $ is the angular frequency, T is the time period and $\upsilon $ is the frequency

Let’s write the above equation in terms of $\upsilon $, $\upsilon = \dfrac{\omega }{{2\pi }}$……………… (1)

Angular wave number is given from the equation $k = \dfrac{{2\pi }}{\lambda }$

Where k is the wave number and $\lambda $ is the wavelength

Writing the above equation in terms of $\lambda = \dfrac{{2\pi }}{k}$………………. (2)

From the wave equation,$v = \upsilon \lambda $ ……………… (3)

Substituting the values of $\upsilon $ and $\lambda $ from equation (1) and equation (2) respectively in equation (3)

Therefore equation (3) becomes, $v = \upsilon \lambda = \dfrac{\omega }{{2\pi }} \times \dfrac{{2\pi }}{k}$

Simplifying the equation we get, $v = \dfrac{\omega }{k}$

Hence, this is the relation between angular velocity, angular wave number and angular frequency.

**Note:**This problem can also be solved by taking the ratio between angular frequency and angular wave number.

Angular frequency,$\omega = 2\pi \upsilon $ and wave number, $k = \dfrac{{2\pi }}{\lambda }$

Taking the ratio between angular frequency and angular wave number

We get, $\dfrac{\omega }{k} = \dfrac{{2\pi \upsilon }}{{\dfrac{{2\pi }}{\lambda }}}$

Simplifying the expression we get, $\dfrac{\omega }{k} = \upsilon \lambda $

Using the relation$v = \upsilon \lambda $, we get $v = \dfrac{\omega }{k}$

Using this method also we can derive a relation between angular frequency, angular wave number and wave velocity.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Guru Purnima speech in English in 100 words class 7 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Three liquids are given to you One is hydrochloric class 11 chemistry CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE