Melde's Experiment
Category : JEE Main & Advanced
(1) It is an experimental representation of transverse stationary wave.
(2) In Melde's experiment, one end of a flexible piece of string is tied to the end of a tuning fork. The other end passes over a smooth pulley carries a suitable load.
(3) If p is the number of loop's formed in stretched string and T is the tension in the string then Melde's law is \[p\sqrt{T}=\]constant \[\Rightarrow \] \[\frac{{{p}_{1}}}{{{p}_{2}}}=\sqrt{\frac{{{T}_{2}}}{{{T}_{1}}}}\] (For comparing two cases)
Two arrangements of connecting a string to turning fork
| Transversely | Example |
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| Prongs of tuning fork vibrates at right angles to the thread. | Prongs vibrated along the length of the thread. |
| Frequency of vibration of turning fork: frequency of vibration of the thread. | Frequency of turning fork \[=2\times \] (Frequency of vibration of thread) |
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If number of loops in string is P then \[l=\frac{p\lambda }{2}\Rightarrow \lambda =\frac{2l}{p}\] \[\Rightarrow \] Frequency of string \[=\frac{v}{\lambda }=\frac{p}{2l}\sqrt{\frac{T}{m}}\]\[\left( \because \,v=\sqrt{\frac{T}{m}} \right)\] \[\Rightarrow \] Frequency of tuning fork \[=\frac{p}{2l}\sqrt{\frac{T}{m}}\] \[\Rightarrow \] If l, m, n \[\to \] constant then \[p\sqrt{T}=\] constant |
It number of loop so in string is p then \[l=\frac{p\lambda }{2}\Rightarrow \,\lambda =\frac{2l}{p}\] \[\Rightarrow \]Frequency of string \[=\frac{v}{\lambda }=\frac{p}{2l}\sqrt{\frac{T}{m}}\] \[\Rightarrow \]Frequency of turning fork \[I=\frac{P}{l}\sqrt{\frac{T}{m}}\] \[\Rightarrow \]If l, m, n \[\to \] constant then \[p\sqrt{T}=\]constant |
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