A closed organ pipe and an open organ pipe have the same length. When the 2^ nd overtone of the closed pipe and the 1^ st overtone of the open pipe are sounded together, they produce 4 beats per second. The fundamental frequency of the closed pipe is:

Step-by-step solution

Let the length of both pipes be L and the speed of sound be v . The fundamental frequency of the closed pipe is f_c = v 4L . The 2^ nd overtone of a closed pipe corresponds to the 5^ th harmonic. Its frequency is: f₁ = 5 ( v 4L ) = 5f_c The fundamental frequency of the open pipe is f_o = v 2L = 2f_c . The 1^ st overtone of an open pipe corresponds to the 2^ nd harmonic. Its frequency is: f₂ = 2 ( v 2L ) = v L = 4 ( v 4L ) = 4f_c The beat frequency is the difference between these two frequencies: f_ beat = |f₁ - f₂|