Question

An organ pipe P₁ closed at one end vibrating in its first harmonic and another pipe P₂ open at both ends vibrating in its third harmonic are in resonance with given tuning fork. The ratio of the length of P₁ to that of P₂ is 

(a)  8/3

(b) 3/8

(c)  1/6

(d) 1/3

Answer 1

Correct option (c) 1/6 

Explanation:

for pipe closed at one end, Frequency of first harmonic, f₁ = v/4l₁

For pipe open at both ends, frequency of third harmonic f₂ = 3v/2l2