The ratio of frequencies of the first overtone produced by an open pipe to that of a closed pipe having the same length is

Step-by-step solution

Frequency ratio of first overtones for open and closed pipes For an open pipe of length L , the first overtone (second harmonic) has frequency f_ open = 2 v 2L = v L . For a closed pipe of the same length, the first overtone (third harmonic) has frequency f_ closed = 3 v 4L = 3v 4L . The ratio is therefore f_ open f_ closed = v/L 3v/(4L) = 1 3/4 = 4 3 . The frequencies are in the ratio 4:3 .