Question

An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is :

• A. 1:2
• B. 4:1
• C. 8:3
• D. 3:8

Answer 1

Answer: (A)

1:2

For the closed organ pipe, the first over tone frequency is given by
${\nu }_{c2}=\frac{3v}{4l_1}$
The frequency of the third harmonic of an open pipe
${\nu }_{o3}=\frac{3v}{2l_2}$.
For resonance to happen,
${\nu }_{c2}={\nu }_{o3}$
Thus
$\frac{3v}{4l_1}=\frac{3v}{2l_2}\Rightarrow \frac{l_1}{l_2}=\frac{1}{2}$