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------------------------------------------------ A local FM radio station broadcasts at a frequency of 99.8 MHz. Calculate the wavelength at which it is broadcasting.

Wavelength = _____ meters

(Note: 1 MHz = \(10^6\) s\(^{-1}\))

The wavelength at which a local FM radio station broadcasts at a frequency of 99.8 MHz is 3.00 meters, calculated using the speed of light and the frequency of the broadcast.

Explanation:

To calculate the wavelength at which a local FM radio station broadcasts at a frequency of 99.8 MHz, we can use the formula c = λf where λ is the wavelength, f is the frequency, and c is the speed of light in a vacuum (approximately 3.00 × 108 m/s). Given that 1 MHz equals 106 s−1, we first convert the frequency from MHz to Hz by multiplying the given number by 106. Thus, the frequency in Hertz is 99.8 × 106 Hz. Next, rearrange the formula to solve for λ: λ = c / f. Plugging in the converted frequency and the speed of light, we get λ = 3.00 × 108 m/s / 99.8 × 106 Hz = 3.00 m. Therefore, the wavelength at which the radio station is broadcasting is 3.00 meters.