Answer :
The longer wavelength is from the 960 AM radio station, with a wavelength of approximately 312.5 meters, while the 89.1 FM radio station has a wavelength of approximately 3.37 meters.
1. First, let's understand that AM (Amplitude Modulation) and FM (Frequency Modulation) are two different types of the radio wave modulation.
2. AM radio stations are identified by their frequency in kilohertz (kHz), while FM stations are identified by their frequency in megahertz (MHz).
3. To compare the wavelengths, we'll need to convert the frequencies to the same unit, so let's convert 89.1 MHz to kHz: 89.1 MHz × 1000 = 89100 kHz.
4. Now, we can use the speed of light (c) to determine the wavelengths. The formula is: wavelength (λ) = speed of light (c) / frequency (f). The speed of light is approximately 3 × 10^8 meters per second (m/s).
5. Calculate the wavelength for 960 AM: λ = (3 × 10^8 m/s) / (960 × 10^3 Hz) ≈ 312.5 meters.
6. Calculate the wavelength for 89.1 FM: λ = (3 × 10^8 m/s) / (89.1 × 10^6 Hz) ≈ 3.37 meters.
The wavelength of a radio wave is inversely proportional to its frequency, so the radio wave on 960 on the AM dial has a lower frequency than the radio wave on 89.1 on the FM dial. This means that the radio wave on 960 on the AM dial has a longer wavelength than the radio wave on 89.1 on the FM dial.
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