Maxwell's Rainbow — Question 6

Question 6

A microwave echo has a round-trip delay and a finite range resolution

A microwave radar records an echo 12.0 microseconds after transmission. Its receiver adds 1.0 microsecond of processing delay. The transmitted pulse duration is 0.20 microsecond. Use c=3.00 times 10 to the 8 m/s and ignore motion.

1. Find the target range after subtracting the processing delay.

2. Using separation of nonoverlapping echo pulses as the criterion, find the minimum radial separation of two targets.

Question 6 - Solution

A microwave echo has a round-trip delay and a finite range resolution

(a) Method and calculation

$$\Delta t_{\mathrm{flight}}=12.0-1.0=11.0\,\mu\mathrm s,\quad2R=c\Delta t_{\mathrm{flight}}.$$$$\boxed{R=1.65\times10^3\,\mathrm m}.$$

(b) Interpretation and further calculation

$$2\Delta R/c\ge\tau\Rightarrow\Delta R_{\min}=c\tau/2.$$$$\boxed{\Delta R_{\min}=30.0\,\mathrm m}.$$

Physical check

The factor of two belongs to both ranging and radial resolution because the wave travels outward and back.