Vibration of Composite Strings
Category : JEE Main & Advanced
Suppose two strings of different material and lengths are joined end to end and tied between clamps as shown. Now after plucking, stationary waves are established only at those frequencies which matches with any one harmonic of both the independent string \[{{S}_{1}}\] and \[{{S}_{2}}\]
As the frequency of the wave in both strings must be same so
\[\frac{p}{2{{l}_{1}}}=\sqrt{\frac{T}{{{m}_{1}}}}=\frac{q}{2{{l}_{2}}}\sqrt{\frac{T}{{{m}_{2}}}}\]\[\Rightarrow \] \[\frac{p}{q}=\frac{{{l}_{1}}}{{{l}_{2}}}\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\sqrt{\frac{{{\rho }_{1}}}{{{\rho }_{2}}}}\]
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