Question

An FM radio station broadcasts at a frequency of 9.86 × ${\mathbf{10}}^7{\mathbf{s}}^{-1}$(98.6 MHz). Calculate the wavelength of the radio waves.

Short answer

The wavelength of the radio wave is ${\text{3.04×10}}^{\text{14}}\text{\hspace{0.17em}m}$.

Step-by-step solution

Wavelength 

The wavelength represented by the symbol $\mathbf{\lambda }$is one of thecharacteristics of the wave, which is the distance between the two consecutive peaks formed when the wave travel.

Wavelength of radio waves  

The formula to calculate the wavelength of the radio wave is as follows:

$\text{wavelength}\left(\text{λ}\right)\text{=}\frac{\text{Speed\hspace{0.17em}of\hspace{0.17em}light\hspace{0.17em}(c)}}{\text{frequency}\left(\mathrm{\upsilon }\right)}$

Here:

• The speed of light is${\text{3×10}}^{\text{8}}\text{m/s}$.
• The frequency of the radio wave is${\text{9.86×10}}^{\text{7}}{\text{\hspace{0.17em}s}}^{\text{-1}}$.

Substituting the known value in the formula ofthe speed of the wave is done as follows:

$\begin{array}{c}\text{λ\hspace{0.17em}=\hspace{0.17em}}\frac{{\text{3×10}}^{\text{8}}\text{m/s}}{{\text{9.86×10}}^{\text{-7}}{\text{\hspace{0.17em}s}}^{\text{-1}}}\\ {\text{=\hspace{0.17em}3.04×10}}^{\text{14}}\text{\hspace{0.17em}m}\end{array}$