If all the strings on guitar in picture were plucked and allowed to vibrate freely string at top would produce highest pitched sound. What could be concluded about rate of vibr?

The rate of vibration, also known as frequency, is inversely proportional to the length of the string. In other words, the shorter the string, the higher the frequency of vibration and the higher the pitch of the sound produced.

Since the string at the top is the shortest, it will vibrate at the highest frequency and produce the highest pitched sound. The strings below it will be progressively longer, resulting in lower frequencies and lower pitches.