4.3 End correction

1.1 Principle of superposition

2.1 Relation between phase difference $\left( \phi \right)$ and path difference $\left( {\Delta x} \right)$
2.2 Interference of waves from coherent sources
2.3 Interference of waves from incoherent sources
2.4 Reflection and transmission of a wave
2.5 Motion of wave during reflection
2.6 Expression for the reflection and transmission of wave

3.1 Transverse stationary wave on a stretched string
3.2 Vibrations in a stretched string
3.3 Melde's Experient
3.4 Resonance

4.1 Open organ pipe
4.2 Closed organ pipe
4.3 End correction
4.4 Resonance tube
4.5 Energy in a stationary wave

The displacement antinode at the open end of a tube is not formed exactly at open end but a little outside. This is known as end correction.

It is denoted by $e$.

Also, $e=0.6r$, where $r$ is the radius of the organ pipe.

$$\begin{equation} \begin{aligned} L + e = \frac{\lambda }{4} \\ \frac{v}{f} = 4(L + e) \\ f = \frac{v}{{4(L + e)}}\quad {\text{or}}\quad f = \frac{v}{{4(L + 0.6r)}} \\\end{aligned} \end{equation} $$

$$\begin{equation} \begin{aligned} L + 2e = \frac{\lambda }{2} \\ \frac{v}{f} = 2(L + 2e) \\ f = \frac{v}{{2(L + 2e)}}\quad {\text{or}}\quad f = \frac{v}{{2(L + 1.2r)}} \\\end{aligned} \end{equation} $$