# The velocity of sound depends upon elastic density of medium and coefficient of elasticity .derive expression by dimensional analysis.

1
Log in to add a comment

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Elastic density of medium = d = mass / length = M L⁻³

Coefficient of elasticity E = stress / strain

= [ M L⁻¹ T⁻² ]

let velocity v be = d^n E^m

so L¹ T⁻¹ = M^(n+m) L^(- 3 n - m ) T^(- 2m)

equating the powers of corresponding dimensions

n + m = 0 so n = -m.

3 n + m = -1 => n = -1/2 and m = 1/2

SO the formula is : v = K √ (E / d) where K is a constant

Coefficient of elasticity E = stress / strain

= [ M L⁻¹ T⁻² ]

let velocity v be = d^n E^m

so L¹ T⁻¹ = M^(n+m) L^(- 3 n - m ) T^(- 2m)

equating the powers of corresponding dimensions

n + m = 0 so n = -m.

3 n + m = -1 => n = -1/2 and m = 1/2

SO the formula is : v = K √ (E / d) where K is a constant