Question 8-5A6

To avoid range ambiguity in a radar system, the next pulse must not be transmitted until the echo from the most distant target of interest has returned. This ensures that a single echo can be uniquely associated with its originating pulse. For a range of 10 nautical miles, we need to calculate the time it takes for a pulse to travel to the target and return (round trip). The speed of radio waves is approximately $3 \times 10^8$ meters per second. One nautical mile is 1852 meters. So, the target is at $10 \times 1852 = 18520$ meters. The round trip distance is $2 \times 18520 = 37040$ meters. The time taken for this round trip (the minimum Pulse Repetition Interval, PRI) is: $PRI = \text{Distance} / \text{Speed} = 37040 \text{ m} / (3 \times 10^8 \text{ m/s}) \approx 0.00012347 \text{ seconds}$ This is approximately 123.47 microseconds. The maximum Pulse Repetition Frequency (PRF) is the inverse of the minimum PRI: $PRF = 1 / PRI = 1 / 0.00012347 \text{ s} \approx 8100 \text{ Hz}$ This is approximately 8.1 kHz. Therefore, the PRF must be 8.1 kHz *or less* to ensure that echoes from targets at 10 nautical miles are received before the next pulse is transmitted, preventing range ambiguity. * **A) Approximately 8.1 kHz or less.** This is correct, as calculated. * **B) 900 Hz.** While 900 Hz would avoid ambiguity, 8.1 kHz is the *maximum* permissible PRF for this range. "8.1 kHz or less" correctly defines the limit. * **C) 18.1 kHz or more.** A PRF higher than 8.1 kHz would mean the next pulse is sent before the echo from 10 nmi returns, causing range ambiguity. * **D) 120.3 microseconds.** This is a time duration (PRI), not a frequency (PRF). While close to the calculated PRI, it doesn't answer the question for PRF.