Chapter 26.2, Problem 17PP

To determine

The frequency of an electromagnetic wave having wavelength $2.2\times {10}^{-2}\text{m}$ .

Answer to Problem 17PP

The frequency of an EM wave is $\boxed{f=1.36\times {10}^{10}\text{Hz}}$ .

Explanation of Solution

Given:

Wavelength of an electromagnetic wave is $\lambda =2.2\times {10}^{-2}\text{m}$ .

Formula used:

The wavelength of electromagnetic waves is expressed as

  $f=\frac{c}{\lambda }$  ...... (1)

Here, $c$ and $\lambda$ are speed of light in vacuum and frequency of an EM wave.

Calculation:

Substitute $3.0\times {10}^8{\text{ms}}^{\text{-1}}$ for $c$ and $2.2\times {10}^{-2}\text{m}$ for $\lambda$ in equation (1)

  $f=\frac{3.0\times {10}^8{\text{ms}}^{\text{-1}}}{2.2\times {10}^{-2}\text{m}}$

  $\boxed{f=1.36\times {10}^{10}\text{Hz}}$

Conclusion:

Hence, the frequency of an EM wave is $\boxed{f=1.36\times {10}^{10}\text{Hz}}$ .