AM radio signals are broadcast at frequencies between 540 kHz and 1585 kHz (kilohertz) and travel 3.0 X 10^8 m/s.
a. What is the range of the wavelengths for the signals? (from shortest to longest).
b. FM frequencies range between 88MHz and 108 MHz (megahertz) and travel at the same speed. What is the range of FM wavelengths?
Wavelength LAMBDA= Light speed/Frequency =
3x10^8/540x100 = ....
To find the range of wavelengths for AM radio signals, we can use the formula:
Wavelength = Speed of Light / Frequency
a. For the AM radio signals with frequencies between 540 kHz and 1585 kHz, we need to convert the frequencies from kilohertz to hertz (Hz) since the speed of light is given in meters per second (m/s).
The range of wavelengths can be calculated as follows:
- Convert the lower frequency to hertz:
540 kHz = 540,000 Hz
- Convert the higher frequency to hertz:
1585 kHz = 1,585,000 Hz
- Plug the values into the formula:
Wavelength (lower) = 3.0 x 10^8 m/s / 540,000 Hz
Wavelength (higher) = 3.0 x 10^8 m/s / 1,585,000 Hz
b. Similarly, for FM radio signals with frequencies between 88 MHz and 108 MHz, we convert the frequencies from megahertz to hertz:
The range of wavelengths can be calculated as follows:
- Convert the lower frequency to hertz:
88 MHz = 88,000,000 Hz
- Convert the higher frequency to hertz:
108 MHz = 108,000,000 Hz
- Plug the values into the formula:
Wavelength (lower) = 3.0 x 10^8 m/s / 88,000,000 Hz
Wavelength (higher) = 3.0 x 10^8 m/s / 108,000,000 Hz
By performing the calculations, you will get the values for the lower and higher wavelengths in both cases.