Question

In the formula V =E ^b d ^a, if V, E and d are the velocity longitudinal waves, bulk modulus of elasticity and density of the gaseous medium respectively, then calculate the values of a and b

Answer 1

Answer:

$b=\frac{1}{2}$ and $a=-\frac{1}{2}$

Explanation:

The velocity longitudinal waves depends on the bulk modulus and the density. It is given by the formula:

$V=\sqrt{\frac{\beta }{\rho} }$

Where V is the velocity , β is the bulk modulus and ρ is the density.

$V=\sqrt{\frac{\beta }{\rho} }\\V=\frac{\beta^\frac{1}{2} }{\rho^\frac{1}{2} } \\V=\beta^\frac{1}{2} \rho^-\frac{1}{2}$

Therefore comparing with $V =E ^b d ^a$, where V, E and d are the velocity longitudinal waves, bulk modulus of elasticity and density, the values of b and a can be gotten.

Therefore, $b=\frac{1}{2}$ and $a=-\frac{1}{2}$