Joe is a carpenter with a few screws loose. Told to measure the length of a board, he takes a 12 inch ruler, places it end to end until he is all the way done, but records only the number of inches showing on the ruler, which is 3. Joe does not understand why the number is so small. He then takes a 13 inch ruler and does the same measurement, recording only the number of inches showing on the ruler, which is 8 this time. Now Joe is very confused as to why the numbers are different. Assuming the distance Joe measured is less than 156 inches, can you tell Joe what distance he measured?
After you do this problem, please note the following. Use of a particular pulse repetition frequency is analogous to using a ruler. The length of the ruler is measured in units of range bins, assuming range bin width is unchanged from one PRI to the next during the measurement. A pulse repetition interval of 12 range bins is mathematically analogous to the 12 inch ruler and a PRI of 13 range bins is analogous to the 13 inch ruler in this problem.