If a vibrating object, anchored at both ends, is shortened while tension remains constant, what change occurs?

When a vibrating object is anchored at both ends and has its length shortened while maintaining constant tension, the fundamental frequency of vibration increases. This is because the frequency of a vibrating string is inversely proportional to its length—the shorter the string, the higher the frequency of vibration.

As the length of the vibrating object decreases, it leads to an increase in the number of vibrations per second, which corresponds to a higher pitch. This relationship is governed by the equation for the frequency of a vibrating string, where frequency is directly proportional to the square root of the tension and inversely proportional to the length of the string.

Thus, when the length is decreased, the frequency increases, resulting in a higher pitch.