FM radio signals are electromagnetic waves transmitted between frequencies of 88 MHz and 107 MHz. Find the range of wavelengths for these signals.
largest___m
smallest___m
use the wave equation.
λ1 =c/f1 = 3•10^8/88•10^6 =3.4 m,
λ2 =c/f2 = 3•10^8/107•10^6 =2.8 m.
To find the range of wavelengths for FM radio signals, we can use the formula that relates wavelength (λ), frequency (f), and the speed of light in a vacuum (c):
c = λ * f
The speed of light in a vacuum is approximately 3 × 10^8 meters per second (m/s).
Given that the frequency range for FM radio signals is between 88 MHz and 107 MHz, we can convert these frequencies to their equivalent values in hertz (Hz):
88 MHz = 88 × 10^6 Hz
107 MHz = 107 × 10^6 Hz
Now, we can rearrange the formula above to solve for wavelength (λ):
λ = c / f
Substituting the values, we have:
λ = (3 × 10^8 m/s) / (88 × 10^6 Hz)
λ = 3.41 meters
This is the largest wavelength for FM radio signals.
Similarly, for the smallest wavelength:
λ = (3 × 10^8 m/s) / (107 × 10^6 Hz)
λ = 2.80 meters
Therefore, the range of wavelengths for FM radio signals is approximately 2.80 meters to 3.41 meters.