On closing an open organ pipe from one end, it is noticed that the frequency of third harmonic is 50 ~Hz more than the fundamental frequency of vibration in open organ pipe. The fundamental frequency of open organ pipe is

Step-by-step solution

Frequency of m ^ th harmonic in an open organ pipe is f_m= m v 2 L Fundamental frequency in an open organ pipe, for m=1 f₁= v 2 L Frequency of nth harmonic in a closed organ pipe, f_n^ = n v 4 L Frequency of 3rd harmonic in a closed organ pipe, f^ ₃= 3 v 4 L Now, f₃^ -f₁=50 3 v 4 L - v 2 L =50 v L =200 Thus, fundamental frequency in an open organ pipe, f₁= v 2 L = 200 2 ~Hz =100 ~Hz