Standing+Waves+and+Speed+of+Sound

On the one hand, the speed of sound in a metal is: math {v_c} = \sqrt {\frac{E}{\rho }} math

where E is the Young’s or tensile modulus (elasticity) of the metal and is math \rho math the density of the metal. On the other hand, the speed of sound in a metal is: math {v_c} = {\lambda _n}\,{f_n} math

i.e. the product of the wavelength math {\lambda _n} = \frac{n} math where n is the number of nodes and the length l of the rod and the frequency math {f_n} math (of standing waves generated in a rod or bar of the metal).