Question

An FM radio station broadcasts at 99.5 MHz. Calculate the wavelength of the corresponding radio waves.

Short answer

The wavelength of the radio waves corresponding to the 99.5 MHz broadcast is approximately \(3.015 \times 10^3\) meters.

Step-by-step solution

Convert frequency to Hz

The radio station broadcasts at a frequency of 99.5 MHz. To convert this frequency to Hz, multiply by 1,000,000 (since there are 1,000,000 Hz in 1 MHz): (99.5 MHz) × (1,000,000 Hz/MHz) = 99,500,000 Hz

Use the formula to find the wavelength

The formula that relates frequency (f), wavelength (λ), and the speed of light (c) is: c = f × λ We'll rearrange the formula to solve for the wavelength (λ): λ = c / f The speed of light (c) is approximately 3 × 10^8 meters per second (m/s). We can now plug the values into the formula: λ = (3 × 10^8 m/s) / (99,500,000 Hz)

Calculate the wavelength

Now, perform the calculation: λ ≈ (3 × 10^8 m/s) / (99,500,000 Hz) ≈ 3015.075 m/s / Hz

Simplify and express the answer

To simplify the result, we can express the wavelength in meters: λ ≈ 3.015 × 10^3 m So, the wavelength of the radio waves corresponding to the 99.5 MHz broadcast is approximately 3015 meters.