A state trooper’s car sends out a radar signal at a frequency of 14 GHz.
Find the wavelength of this signal. The wave speed is 2.998 × 108 m/s.
Answer in units of m
speed= frequency*wavelength.
wavelength = speed / frequency
F = 14 GHz = 14*10^9 Hz = 14*10^9 cycles/second.
Wavelength = V/F = V * 1/F = 2.998*10^8 / 14*10^9 = meters.
To find the wavelength of the signal, we can use the formula:
wavelength = wave speed / frequency.
Here, the wave speed is given as 2.998 × 10^8 m/s, and the frequency is given as 14 GHz (14 × 10^9 Hz).
Now, we can substitute these values into the formula:
wavelength = (2.998 × 10^8 m/s) / (14 × 10^9 Hz).
Simplifying the expression:
wavelength = (2.998 / 14) × (10^8 / 10^9) m.
wavelength = 0.2141 × 10^-1 m.
Converting the scientific notation to decimal notation:
wavelength = 0.02141 m.
Therefore, the wavelength of the radar signal is 0.02141 meters.