Question

An organ pipe $P_{1}$ closed at one end vibrating in its first overtone and another pipe $P_{2}$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_{1}$ and $P_{2}$ is

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

Answer 1

Answer: (C)

3 : 8

Answer 2

First overtone of closed organ pipe

$n_{1} = \frac{3v}{4l_{1}}$

Third overtone of open organ pipe

$n_{2} = \frac{4v}{2L_{2}}$

$n_{1} = n_{2}$ (Given) $\Rightarrow$ $\frac { 3 v } { 4 l _ { 1 } } = \frac { 4 v } { 2 l _ { 2 } } \Rightarrow$ $\frac{L_{1}}{L_{2}} = \frac{3}{8}$