Question

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic
of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open
pipe. The fundamental frequency of the open pipe is
(A)
200Hz
(B)
300Hz​

Answer 1

Answer:

Frequency of mth harmonic in an open organ pipe       νm=2Lmv

Fundamental frequency  in an open organ pipe i.e m=1           ν1=2Lv

Frequency of nth harmonic in a closed organ pipe    νn′=4Lnv

Frequency of 3rd harmonic in a closed organ pipe    ν3′=4L3v

Now    ν3′−ν1=100

4L3v−2Lv=100⟹Lv=400

Thus fundamental frequency  in an open organ pipe            ν1=2Lv=2400=200Hz