Physics
Physics
Problem
1. Describe how you would arrange for a string that is kept under tension, with both ends fixed, to vibrate in its second harmonic mode. 2. Draw the shape of the string when it is vibrating in its second harmonic mode.Intuitive explanation
The key to exciting the second harmonic is understanding that you need exactly two half-wavelengths to fit along the string's length. Pluck or drive the string at its midpoint—this is the antinode for the second harmonic—while the two quarter-points become nodes where the string barely moves. The string will then naturally oscillate in two opposing "humps" that meet at the center, creating that characteristic figure-eight motion when viewed over time.
Intuitive explanation
The key to exciting the second harmonic is understanding that you need exactly two half-wavelengths to fit along the string's length. Pluck or drive the string at its midpoint—this is the antinode for the second harmonic—while the two quarter-points become nodes where the string barely moves. The string will then naturally oscillate in two opposing "humps" that meet at the center, creating that characteristic figure-eight motion when viewed over time.