Question

For an increase in the bulk modulus of a material but without any change in the density, what happens to the speed of sound in that material?

Answer 1

The speed of sound, c, is given by the Newton-Laplace formula
$c = \sqrt{ \frac{K}{\rho} }$
where
K = bulk modulus
ρ =  density

Because the density is constant, the speed of sound is proportional to the square root of the bulk modulus.

Therefore when the bulk modulus increases, the speed of sound increases by the square root of the bulk modulus.

For example, if K is doubled, then
$c = \sqrt{2K} = \sqrt{2} \sqrt{K}$

Answer:
If the bulk modulus increases by a factor of n, then c increases by a factor of √n.