Question

What is the wavelength of the radio waves transmitted by an FM station at 90 MHz? (Radio waves travel at \(3.0 \times 10^{8} \mathrm{m} / \mathrm{s} .\)

Short answer

Answer: The wavelength of the radio waves transmitted by an FM station at 90 MHz is 3.33 meters.

Step-by-step solution

Write down the wave speed formula

The wave speed formula is: speed = frequency × wavelength or v = f × λ Where v is the speed of the radio waves, f is the frequency of the radio waves, and λ is the wavelength of the radio waves.

Rearrange the formula to solve for wavelength

To find the wavelength, we need to rearrange the equation: λ = v / f

Convert the given frequency to Hz

The frequency is given in MHz, which is megahertz. We need to convert it to hertz (Hz) for our calculations: 90 MHz = 90 × 10^6 Hz

Plug in given values and solve for wavelength

Now, we can plug in the values for the speed of radio waves (v = 3.0 × 10^8 m/s) and frequency (f = 90 × 10^6 Hz) into the rearranged equation: λ = (3.0 × 10^8 m/s) / (90 × 10^6 Hz)

Calculate the wavelength

Now, we can perform the calculation: λ = (3.0 × 10^8 m/s) / (90 × 10^6 Hz) = (3.0 / 90) × 10^2 m = 0.033 × 10^2 m = 3.33 m The wavelength of the radio waves transmitted by an FM station at 90 MHz is 3.33 meters.