Question

What is the relation between wavelength, frequency, and velocity?

Answer 1

Step 1: Definition

1. The number of vibrations per second is known as frequency. It is denoted by $\mathrm{f}$.
2. The wavelength seems to be the shortest distance over which the wave may be repeated. It is denoted by $\mathrm{\lambda }$.
3. The velocity of a wave would be the distance it may travel in one second $\text{v}$.

Step 2: Finding the relation between wavelength, frequency, and velocity

According to the above definitions,

$\mathrm{Wavelength}=\mathrm{Distance}\mathrm{traveled}\mathrm{by}\mathrm{the}\mathrm{wave}\mathrm{in}\mathrm{one}\mathrm{time}\mathrm{period}$ that is in $\mathrm{T}\mathrm{second}$.

Or,

$\mathrm{Wavelength}=\mathrm{Wave}\mathrm{velocity}\times \mathrm{Time}\mathrm{period}$

Or,

$\mathrm{\lambda }=\mathrm{v}\times \mathrm{T}$

Or, we know $\left[\mathrm{T}=\frac{1}{\mathrm{n}}\right]$

$\mathrm{\lambda }=\mathrm{v}\times \frac{1}{\mathrm{n}}$

So,

$\mathrm{v}=\mathrm{n\lambda }$

Therefore, the relation between wavelength, frequency, and velocity is $\mathrm{v}=\mathrm{n\lambda }$.