Final answer:
The wavelength of a radio signal broadcasted at 106.9 kHz is approximately 2.806 x 10^12 nm, calculated by dividing the speed of light by the frequency and then converting the result to nanometers.
Step-by-step explanation:
The wavelength of a radio signal can be calculated using the formula λ = c / f, where λ is the wavelength in meters, c is the speed of light in a vacuum (approximately 3 x 108 m/s), and f is the frequency in hertz. To find the wavelength corresponding to a frequency of 106.9 kHz (which is 106.9 x 103 Hz), we first convert the frequency to hertz and then use the formula. Therefore, the wavelength λ is given by λ = (3 x 108 m/s) / (106.9 x 103 Hz), which simplifies to approximately 2806 meters. Since 1 meter equals 1 x 109 nanometers (nm), we then convert this result to nanometers by multiplying by 1 x 109, giving us a wavelength of approximately 2.806 x 1012 nm.