FM radio signals are electromagnetic waves transmitted between frequencies of 88 MHz and 107 MHz. Find the range of wavelengths for these signals.
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To find the range of wavelengths for FM radio signals, we need to use the formula:
wavelength (λ) = speed of light (c) / frequency (f)
The speed of light (c) is approximately 3 x 10^8 meters per second.
The frequency range for FM radio signals is between 88 MHz and 107 MHz.
Let's first convert these frequencies to hertz (Hz) by multiplying them by 10^6:
Lower frequency = 88 MHz = 88 x 10^6 Hz
Upper frequency = 107 MHz = 107 x 10^6 Hz
Now, we can calculate the range of wavelengths using the formula:
Lower wavelength = c / Lower frequency
Upper wavelength = c / Upper frequency
Plugging in the values:
Lower wavelength = 3 x 10^8 m/s / (88 x 10^6 Hz)
Upper wavelength = 3 x 10^8 m/s / (107 x 10^6 Hz)
Simplifying:
Lower wavelength ≈ 3.409 m
Upper wavelength ≈ 2.804 m
Therefore, the range of wavelengths for FM radio signals is approximately 2.804 meters to 3.409 meters.