Question 8-5A1

To avoid range ambiguity in a RADAR system, the echo from the most distant target must be received before the next pulse is transmitted. If a new pulse is sent too soon, a distant echo could be misinterpreted as a closer target hit by a subsequent pulse. This sets an upper limit on the Pulse Repetition Frequency (PRF). The time it takes for a pulse to travel to a target 5 nautical miles away and return is calculated as: $T_{roundtrip} = \frac{2 \times \text{Range}}{\text{Speed of Light}}$ Given: Range = 5 nautical miles = 5 * 1852 meters = 9260 meters Speed of light (c) $\approx 3 \times 10^8$ meters/second $T_{roundtrip} = \frac{2 \times 9260 \text{ m}}{3 \times 10^8 \text{ m/s}} = \frac{18520}{3 \times 10^8} \text{ s} \approx 6.173 \times 10^{-5} \text{ s}$ The Pulse Repetition Interval ($T_{PRI}$) must be at least this long. Since $PRF = \frac{1}{T_{PRI}}$, the maximum PRF is: $PRF_{max} = \frac{1}{T_{roundtrip}} = \frac{1}{6.173 \times 10^{-5} \text{ s}} \approx 16200 \text{ Hz} = 16.2 \text{ kHz}$ Therefore, for a range of 5 nautical miles, the RADAR pulse repetition frequency must be 16.2 kHz or less to ensure unambiguous range measurements. Options A, B, and C are incorrect as they either specify an incorrect frequency range or an incorrect relationship (e.g., "or more" instead of "or less").