Physics - Laws of Traverse Vibrations

Laws of Traverse Vibrations

The fundamental frequency of a stretched String fixed at both end is given by

$n\, =\, \frac {1} {2l}\sqrt {T/m}\, \, \, \, where\, l\, =\, length,\, T\, =\, tension,\, m\, =\, linear\, density$

First Law or Law of Length :

When the tension (T) and linear density (m) are constant, the frequency of Vibration (n) of a streched String vibrating in one segment is inversely proportional to its length (l)

$n\propto \frac {1} {l}\, \, \, or\, nl\, =\, constant\, or\, {n}_{1}{l}_{1}={n}_{2}{l}_{2}$

Second Law or Law of Tensions :

When the length (l) and the linear density (m) are constant, the frequency of Vibration (n) of a streched String vibrating in one segment is inversely to the square root of the tension (T) in the wire

$n\, \propto \, \sqrt {T}\, i.e\, \frac {n} {\sqrt {T}}\, =\, constant\, i.e\, \frac {{n}_{1}} {{n}_{2}}=\sqrt {\frac {{T}_{1}} {{T}_{2}}}$

Third Law or Law of Linear Densities :

When the length (l) and Tension (T) are constant, the frequency of a streched string vibrating in one Segment is inversely proportional to square root of linear density.

$n\, \propto \, \frac {1} {\sqrt {m}}\, \, \, i.e\, n\sqrt {m}\, =\, const.$

$\frac {{n}_{1}} {{n}_{2}}=\sqrt {\frac {m2} {m1}}$

Post By : Ashish Maurya 17 May, 2020 271 views Physics

Physics - Laws of Traverse Vibrations

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