Traveling Sound Waves

The beat frequency is given by the absolute difference in the frequencies of the two pipes: where is the frequency of the longer pipe, and is the frequency of the shorter pipe. We are given: - The beat frequency , - The length of the first pipe, , - The length of the second pipe, . For open pipes, the frequency is inversely proportional to the length , i.e., Thus, we can write: Now, substituting the lengths of the pipes: Now, we know the difference in their frequencies is equal to the beat frequency: Substitute into the equation: Solving for : Thus, the frequency of the shorter pipe is .