3.3 Melde's Experient

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

In longitudinal mode, the prongs of the tuning fork vibrate in a direction parallel to the length of the string.

In the longitudinal mode when tuning fork completes one vibration, the string completes only half the vibration. So, the frequency of the string is half of that of the fork. $$\begin{equation} \begin{aligned} {f_s} = \frac{{{f_f}}}{2}\quad ...(i) \\ \frac{{n\lambda }}{2} = L \\ \frac{v}{{{f_s}}} = \frac{{2L}}{n} \\ {f_s} = \frac{n}{{2L}}\sqrt {\frac{T}{\mu }} \quad ...(ii) \\\end{aligned} \end{equation} $$ From equation $(i)$ & $(ii)$ we get, $${f_f} = \frac{n}{L}\sqrt {\frac{T}{\mu }} $$

In transverse mode, the prongs of the tuning fork vibrate in a direction perpendicular to the length of the string.

In the transverse mode when tuning fork completes one vibration, the string also completes one vibration. So, the frequency of the string is equal to that of the fork. $$\begin{equation} \begin{aligned} {f_s} = {f_f}\quad ...(i) \\ \frac{{n\lambda }}{2} = L \\ \frac{v}{{{f_s}}} = \frac{{2L}}{n} \\ {f_s} = \frac{n}{{2L}}\sqrt {\frac{T}{\mu }} \quad ...(ii) \\\end{aligned} \end{equation} $$ From equation $(i)$ & $(ii)$ we get, $${f_f} = \frac{n}{{2L}}\sqrt {\frac{T}{\mu }} $$

Note: The number of loops in the transverse mode is twice that in the longitudinal mode.