2.1 Relation between phase difference $\left( \phi \right)$ and path difference $\left( {\Delta x} \right)$

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

1. Mathematically the phase difference between two different points $P$ and $Q$ separated by a distance $\left( {\Delta x} \right)$ is given by, $$\phi = \left( {\frac{{2\pi }}{\lambda }} \right)\Delta x$$ where,

$\phi $: Phase difference

$\Delta x$: Path difference

$\lambda $: Wavelength of wave

2. The phase difference between two waves generated by the same source when they travel along different path.

Lets the path difference between the two waves be $\Delta x$. Then the corresponding phase difference is given by, $$\phi = \left( {\frac{{2\pi }}{\lambda }} \right)\Delta x\quad or\quad \phi = k\Delta x$$

3. The phase difference at any point at two different time $t_1$ and $t_2$ $\left( {{t_2} > {t_1}} \right)$ is given by,$$\phi = \left( {\frac{{2\pi }}{T}} \right)\Delta t\quad or\quad \phi = \omega \Delta t$$ where

$\Delta t = {t_2} - {t_1}$

$\omega $: angular frequency

4. When a wave splits equally in two parts at point $A$ and travel along different path.

At point $B$, where the waves combine, there is a phase difference because of the path difference.

If $\lambda $ is the wavelength and $\Delta x$ is the path difference. Then the phase difference can be written as, $$\phi = \left( {\frac{{2\pi }}{\lambda }} \right)\Delta x$$