A state trooper’s car sends out a radar signal at a frequency of 13.3 GHz. Find the wavelength of this signal. The wave speed is 2.998 × 108 m/s. Answer in units of m
lambda = distance = speed * time
Time = period = 1/ frequency
To find the wavelength of a signal, we can use the formula:
Wavelength = Speed of light / Frequency
In this case, the given frequency is 13.3 GHz, which means 13.3 x 10^9 Hz. And the speed of light is 2.998 x 10^8 m/s.
So, substituting the values into the formula:
Wavelength = (2.998 x 10^8 m/s) / (13.3 x 10^9 Hz)
Now, we can simplify the expression:
Wavelength = (2.998 / 13.3) x (10^8 / 10^9) m
Dividing 2.998 by 13.3 gives us approximately 0.2256.
Dividing 10^8 by 10^9 gives us 0.1.
Now, substitute these values back into the formula:
Wavelength = 0.2256 x 0.1 m
Multiplying the values gives us:
Wavelength = 0.02256 m
Therefore, the wavelength of the signal is approximately 0.02256 meters.