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. What is the fundamental frequency of the open pipe? 

(A) 240 

(B) 200 

(C) 300 

(D) 480

Answer 1

The correct option is (B) 200.

Explanation:

Fundamental frequency of open pipe is f₁ = (V / 2ℓ) 

Frequency of third harmonics of closed pipe is f₂ = 3 (V / 4ℓ) 

Given f₂ – f₁ = 100 Hz 

∴ (3V / 4ℓ) – (V / 2ℓ) = 100 Hz 

∴ (V / 4ℓ) = 100 Hz 

∴ (V / 2ℓ) = 200 Hz = fundamental frequency of open pipe.