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**Problem**: An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031 × 108 s−1 (103.1 MHz). What is the wavelength of these radio waves in meters?

###### FREE Expert Solution

###### FREE Expert Solution

We are being asked to calculate the wavelength with a frequency equal to of 1.031 × 10^{8} s^{−1}.

Wavelength, frequency, and the **speed of light** are connected by the following equation:

$\overline{){\mathbf{c}}{\mathbf{=}}{\mathbf{\lambda \nu}}}$

c = speed of light, m/s

λ = wavelength, in m

ν = frequency, Hz (Hertz)

We can rearrange the equation to isolate the wavelength (λ):

$\frac{\mathbf{c}}{\mathbf{\nu}}\mathbf{=}\frac{\mathbf{\lambda}\overline{)\mathbf{\nu}}}{\overline{)\mathbf{\nu}}}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{\lambda}}{\mathbf{=}}\frac{\mathbf{c}}{\mathbf{\nu}}}$

**Calculate the wavelength (λ):**

**Given:**

**ν = 1.031 × 10 ^{8} s^{−1} **

**c = 2.998x10 ^{8} m/s**

###### Problem Details

An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031 × 10^{8} s^{−1} (103.1 MHz). What is the wavelength of these radio waves in meters?

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