Final answer:
Assuming the radio station frequency of 106.9 Hz is a typo and should be MHz, the wavelength of the broadcast radio wave can be calculated using the speed of light formula. After converting the frequency to Hz and applying the formula, the wavelength is approximately 2.807 meters, which equals roughly 2.807 x 10^9 nanometers.
Step-by-step explanation:
To find the wavelength of a radio wave broadcast with a given frequency, you can use the formula for the speed of light (c) as follows: c = frequency (f) × wavelength (λ). The speed of light (c) is approximately 3 × 108 meters per second (m/s). Since radio station frequencies are usually given in megahertz (MHz), you should convert the frequency from Hertz to MHz by multiplying by 106.
In the case of a radio station broadcasting at 106.9 Hz, first, you should recognize that there is likely a typo in the frequency provided, as radio stations typically broadcast in the MHz range. Assuming it meant 106.9 MHz, the frequency in Hz is 106.9 × 106 Hz. Now, you can solve for the wavelength by rearranging the formula: λ = c/f.
λ = (3 × 108 m/s) / (106.9 × 106 Hz)
λ = (3 × 108) / (106.9 × 106) meters
λ = 2.806 × 108 / 106.9 meters
λ ≈ 2.807 meters
To convert this to nanometers (nm), recall that 1 meter is equal to 109 nanometers:
λ ≈ 2.807 × 109 nm