91Ó°ÊÓ

The number of waves that moves a fixed point in unit time is known as frequency.

$f=\frac{1}{T}$

Where,T =Time period in

The frequency, wavelength, and speed of light of any wave are related by the wavelength-frequency relationship.

The wavelength-frequency relationship is:

$$\begin{gathered} c=\mathrm{λ}f \\ ⇒f=\frac{c}{\mathrm{λ}} \end{gathered}$$

Where,c is the speed of light which is equal to $3×{10}^8\mathrm{m}/\mathrm{s}$,$\mathrm{λ}$ is the wavelength andf is the frequency.

The wavelength is inversely proportional to the frequency.

$\mathrm{λ}=\frac{c}{f}$or $\frac{v}{f}$

Where, v is velocity of wave in m/s.

The wavelength-frequency relationship is:

$$\begin{gathered} c=\mathrm{λ}f \\ ⇒f=\frac{c}{\mathrm{λ}} \end{gathered}$$

Forrole="math" localid="1664348819222" $\mathrm{λ}=5.0\mathrm{Km}$

$$\begin{gathered} \mathrm{f}=\frac{3×{10}^8}{5×{10}^3} \\ =6×{10}^4\mathrm{Hz} \end{gathered}$$

For$\mathrm{λ}=5.0\mathrm{μ}m$

$$\begin{gathered} \mathrm{f}=\frac{3×{10}^8}{5×{10}^{-6}} \\ =6×{10}^{13}\mathrm{Hz} \end{gathered}$$

For$\mathrm{λ}=5.0nm$

$$\begin{gathered} \mathrm{f}=\frac{3×{10}^8}{5×{10}^{-9}} \\ =6×{10}^{16}\mathrm{Hz} \end{gathered}$$

Hence, frequency of a wave with a wavelength of

i . For$\mathrm{λ}=5.0\mathrm{Km}$ is $6×{10}^4\mathrm{Hz}$.

ii . For$\mathrm{λ}=5.0\mathrm{μ}m$ is $6×{10}^{13}\mathrm{Hz}$.

iii . For$\mathrm{λ}=5.0nm$ is $6×{10}^{16}\mathrm{Hz}$.

The wavelength is inversely proportional to the frequency.

$\mathrm{λ}=\frac{c}{f}$

For gamma rays of frequency $6.50×{10}^{21}\mathrm{Hz}$:

$$\begin{gathered} \mathrm{λ}=\frac{3×{10}^8}{6.50×{10}^{21}} \\ =4.62×{10}^{-14}m \end{gathered}$$

For AM station radio wave of frequency 590 KHz:

$$\begin{gathered} \mathrm{λ}=\frac{3×{10}^8}{590×{10}^3} \\ =508\mathrm{m} \end{gathered}$$

Hence, wavelength of

i. For gamma rays of frequency $6.50×{10}^{21}\mathrm{Hz}$is $4.62×{10}^{-14}\mathrm{m}$.

ii. For an AM station radio wave of frequency 590 KHz is 508 m