Question

A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz (MHz), where 1 MHz = 10⁶ Hz and 1 Hz = 1s⁻1.

Calculate the broadcast wavelength of the radio station 103.1 FM.
a) 2.9 meters
b) 3.4 meters
c) 3.0 meters
d) 3.2 meters

Answer 1

The broadcast wavelength for the radio station 103.1 FM is calculated using the speed of light and the frequency of the station. Substituting the given frequency into the wavelength formula yields a wavelength of approximately 2.91 meters, which means the closest answer is 2.9 meters (a).

Step-by-step explanation:

To calculate the broadcast wavelength for a radio station frequency, we can use the relationship between speed, frequency, and wavelength, which is given by the equation:

v = f × λ

Where v is the speed of light (approximately 3.00 × 10⁸ m/s in a vacuum), f is the frequency, and λ is the wavelength.

The frequency for 103.1 FM is 103.1 MHz, which is 103.1 × 10⁶ Hz. Using the speed of light, we then rearrange the formula to solve for wavelength λ:

λ = ν / f

λ = (3.00 × 10⁸ m/s) / (103.1 × 10⁶ s⁻¹)

λ ≈ 2.91 meters.

Therefore, the closest answer to the wavelength of the radio station 103.1 FM is (a) 2.9 meters.