PhysicsAn open pipe 30 cm long and a closed pipe 23 cm long, both of the same diameter, are each sounding their first overtone are in unison. The end correction of these pipes is

An open pipe 30 cm long and a closed pipe 23 cm long, both of the same diameter, are each sounding their first overtone are in unison. The end correction of these pipes is

A
0.5 cm
B
0.3 cm
C
1 cm
D
1.2 cm

Solution:

First over tone $n_{1} = \frac{2 V}{2 (l_{0} + 2 e)}$
Closed pipe length l_c = 23 cm
First overtone $n_{lc} = \frac{3 V}{4 (l_{e} + e)}$
Unison $n_{l_{0}} = n_{l_{c}}; \frac{2 V}{2 (l_{0} + 2 e)} = \frac{3 V}{4 (l_{c} + e)}$
3(l₀ + 2e) = 4(l_e + e) $\Rightarrow$ e = 1 cm