Final answer:
The range of wavelengths for AM radio, given its frequency range of 540 to 1600 kHz, is approximately 555.2 meters to 187.4 meters. For FM radio with a frequency range of 88.0 to 108 MHz, the range of wavelengths is about 3.406 meters to 2.776 meters.
Step-by-step explanation:
Calculating the Range of Wavelengths for AM and FM Radio
To calculate the range of wavelengths for AM radio with a frequency range of 540 to 1600 kHz, we use the formula for the wavelength (λ): λ = c / f, where λ is the wavelength, c is the speed of light (approximately 2.998 x 108 m/s), and f is the frequency. For the AM frequency range, we do the following calculations:
- Longest Wavelength (at lowest frequency 540 kHz): λ = 2.998 x 108 m/s / 540 x 103 Hz = 555.2 meters (approximately).
- Shortest Wavelength (at highest frequency 1600 kHz): λ = 2.998 x 108 m/s / 1600 x 103 Hz = 187.4 meters (approximately).
Therefore, the range of wavelengths for AM radio is from about 555.2 meters to 187.4 meters.
For FM radio with a frequency range of 88.0 to 108 MHz, we perform similar calculations:
- Longest Wavelength (at lowest frequency 88.0 MHz): λ = 2.998 x 108 m/s / 88.0 x 106 Hz = 3.406 meters (approximately).
- Shortest Wavelength (at highest frequency 108 MHz): λ = 2.998 x 108 m/s / 108 x 106 Hz = 2.776 meters (approximately).
The range of wavelengths for FM radio is therefore from about 3.406 meters to 2.776 meters.