Final answer:
The ratio of the wavelength of the radio wave in air to its wavelength in water, considering equal frequency in both mediums, is 2:1, because radio waves travel faster in air than in water.
Step-by-step explanation:
The question asks to compare the wavelength of a radio wave in air with its wavelength in water, given that the frequency remains the same in both mediums. The relationship between wavelength (λ), frequency (f), and the speed of the wave (v) is given by the equation v = λ × f. As the frequency remains constant (500,000 Hz), the ratio of the wavelengths depends on the ratio of the speeds of the wave in the two different mediums. Since electromagnetic waves (including radio waves) travel faster in air than in water, the wavelength in air will be longer than in water. Therefore, the answer to this question is c. 2:1. This ratio implies that the wavelength in air is twice the wavelength in water.