Physics > Superposition of Waves > 4.0 Longitudinal stationary wave in an organ pipe
Superposition of Waves
1.0 Introduction
2.0 Interference of Waves
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
3.0 Standing or Stationary 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
4.0 Longitudinal stationary wave in an organ pipe
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
5.0 Beats
6.0 Questions
4.1 Open organ pipe
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
3.2 Vibrations in a stretched string
3.3 Melde's Experient
3.4 Resonance
4.2 Closed organ pipe
4.3 End correction
4.4 Resonance tube
4.5 Energy in a stationary wave
- In an open organ pipe both ends are open.
- In an open organ pipe at both ends displacement antinode or pressure node is formed.
| Normal modes of an organ pipe | Pressure Diagram | Displacement diagram | Explanation | Wavelength | Frequency |
First mode or first harmonic or fundamental tone |
|
| $$\frac{\lambda }{2} = L$$$$\lambda = 2L$$$$\frac{v}{f} = 2L$$$$f = \frac{v}{{2L}}$$ | $$\lambda = 2L$$ | $$f = \frac{v}{{2L}}$$ |
Second mode or second harmonic or first overtone |
|
| $$\frac{{2\lambda }}{2} = L$$$$\lambda = L$$$$\frac{v}{f} = L$$$$f = \frac{v}{L}$$ | $$\lambda = L$$ | $$f = \frac{v}{{L}}$$ |
$n^{th}$ mode or $n^{th}$ harmonic or $(n-1)^{th}$ overtone |
|
| $$\frac{{n\lambda }}{2} = L$$$$\lambda = \frac{{2L}}{n}$$$$\frac{v}{f} = \frac{{2L}}{n}$$$$f = \frac{{nv}}{{2L}}$$ | $$\lambda = \frac{{2L}}{n}$$ | $$f = \frac{{nv}}{{2L}}$$ |
Note: In this case, $n$ is equal to the number of loops.
