A string, fixed at both ends, vibrates at a frequency of 12 Hz with a standing transverse wave pattern containing 3 loops. What frequency is needed if the standing wave pattern is to contain 4 loops?
A) 48 Hz
B) 16 Hz
C) 36 Hz
D) 18 Hz
E) 12 Hz

Question

Quizplus · Accepted Answer

The frequency of a standing wave in a string fixed at both ends is directly proportional to the number of loops (or harmonics). If 3 loops correspond to 12 Hz, then 4 loops (which is 4/3 times more) will correspond to a frequency that is 4/3 times 12 Hz, which equals 16 Hz.

A String, Fixed at Both Ends, Vibrates at a Frequency