An open pipe, when closed at one end, can resonate in its third harmonic with a frequency which is 100   Hz more than its fundamental frequency as an open pipe. If the fundamental frequency of the pipe when it is open at both ends is 50 n   Hz , then the value of n is

Step-by-step solution

Length of the organ pipe is same in both the cases. Fundamental frequency of open pipe is f 1 = v 2 l Frequency of third harmonic of closed pipe will be. f ⁡ 2 = 3 v ⁡ 4 l ⁡ Given that, f ⁡ 2 = f ⁡ 1 + 1 0 0 or f ⁡ 2 - f ⁡ 1 = 1 0 0 or 3 4 v ⁡ l ⁡ - 1 2 v ⁡ l ⁡ = 1 0 0 ⇒ v ⁡ 4 l ⁡ = 1 0 0 ∴ v ⁡ 2 l ⁡ or f ⁡ 1 = 2 0 0 Hz 50 . n Hz ⇒ n = 4 Therefore, fundamental frequency of the open pipe is 200 Hz. and n = 4