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

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) 200 (B) 300 (C) 240 (D) 480

Tardigrade Admin · Accepted Answer

Length of the organ pipe is same in both the cases. Fundamental frequency of open pipe is

f_{2} = 3 (\frac{v}{4 l})

Given that,

f_{2} = f_{1} + 100

or

f_{2} - f_{1} = 100

or

\frac{3}{4} (\frac{v}{l}) - (\frac{1}{2}) (\frac{v}{1}) = 100 \Rightarrow \frac{v}{4 l} = 100

∴

\frac{v}{2 l}

or

f_{1} = 200 Hz

Therefore, fundamental frequency of the open pipe is 200 Hz.

Q. 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

200

300

240

480

Length of the organ pipe is same in both the cases. Fundamental frequency of open pipe is f2​=3(4lv​) Given that, f2​=f1​+100 or f2​−f1​=100 or 43​(lv​)−(21​)(1v​)=100⇒4lv​=100 ∴ 2lv​ or f1​=200Hz Therefore, fundamental frequency of the open pipe is 200 Hz.