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Answer :
Final answer:
The wavelength of a local FM radio station broadcasting at 97.5 MHz is calculated using the speed of light and the frequency, resulting in a wavelength of approximately 3.077 meters.
Explanation:
To calculate the wavelength of a radio wave, we can use the formula:
c = λ f,
where c is the speed of light in a vacuum (approximately 3 × 108 m/s), λ is the wavelength in meters, and f is the frequency in hertz (Hz). Rearranging the formula to solve for wavelength gives us:
λ = c / f.
Since 1 MHz equals 106 Hz, the frequency of the FM radio station broadcasting at 97.5 MHz is 97.5 × 106 Hz.
Plugging the values into the formula we get:
λ = (3 × 108 m/s) / (97.5 × 106 Hz)
λ = 3.077 × 108 m/s / 9.75 × 107 Hz
λ = 3.077 × 108² m/s / 9.75 × 107 Hz
λ = 3.077 × 10 m/s / 9.75 Hz
λ = λ ² λ m/s λ Hz
The wavelength of the broadcast from the local FM radio station at 97.5 MHz is therefore approximately 3.077 meters.
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