The frequency n of vibration of a stretched string depends on the tension T , its length l and its mass per unit length μ . Using dimensional analysis, the relation is ( k dimensionless)

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[ T − 1 ] = ( [ M L T − 2 ] ) a ([ L ] ) b ( [ M L − 1 ] ) c − 2 a = − 1 ⇒ a = 2 1 ​ ; a + c = 0 ⇒ c = − 2 1 ​ ; a + b − c = 0 ⇒ b = − 1 . So n = l k ​ μ T ​ ​ .

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