When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz.When the string is also clamped at its midpoint, the lowest four resonant frequencies are:
A)50, 100, 150, and 200 Hz
B)50, 150, 250, and 300 Hz
C)100, 200, 300, and 400 Hz
D)25, 50 75, and 100 Hz
E)75, 150, 225, and 300 Hz

Question

Quizplus · Accepted Answer

When a string is clamped at its midpoint in addition to both ends, it effectively halves the length of the vibrating sections of the string. This results in a doubling of the frequencies of the resonant modes because the frequency of a vibrating string is inversely proportional to its length. Therefore, the lowest four resonant frequencies double to 100, 200, 300, and 400 Hz.

When a Certain String Is Clamped at Both Ends, the Lowest