Question

A closed organ pipe is vibrating in first overtone and is in resonance with another open organ pipe vibrating in third harmonic. The ratio of lengths of the pipes respectively is :

• A. 1 : 2
• B. 4 : 1
• C. 8 : 3
• D. 3 : 8

Answer 1

The correct option is A 1 : 2

First overtone in closed pipe $3{\nu }_c=\frac{3\nu }{4L_1}$

Third harmonic of open pipe $3{\nu }_o=\frac{3\nu }{2L_2}$

Now, according to problem

$3{\nu }_c=3{\nu }_o$

$\frac{3\nu }{4L_1}=\frac{3\nu }{2L_2}$

$\frac{L_1}{L_2}=\frac{2}{4}=\frac{1}{2}$.