Physics

Problem

The speed

v

of longitudinal waves in a thin, uniform rod is thought to depend only on the Young’s modulus

Y

of the material and its density

\rho

. Which of the following relations is compatible with dimensional analysis? (Here

C

is a dimensionless constant.) a)

v = C\sqrt{Y\rho}

v = C\sqrt{\dfrac{Y}{\rho}}

v = C\,(Y\rho)^{1/4}

v = C\,\dfrac{Y}{\rho}