Answer
The depth of the ocean floor is 1.7 km
Work Step by Step
We can find the speed of the wave in sea water using the formula:
$v = \sqrt{\frac{B}{\rho}}$
where
$B$ is the Bulk modulus
$\rho$ is the density
Substituting the values and solving:
$v = \sqrt{\frac{B}{\rho}}$
$v = \sqrt{\frac{2.0\times 10^9~N/m^2}{1.025\times 10^3~kg/m^3}}$
$v = 1.4\times 10^3~m/s$
Next, we find the distance the wave travels in 2.4 seconds:
$d = v~t$
$d = (1.4\times 10^3~m/s)(2.4~s)$
$d = 3.4\times 10^3~m$
Since this distance $d$ is the total distance that the wave traveled, the depth of the ocean floor is half of this distance.
$\frac{d}{2} = 1.7\times 10^3~m = 1.7~km$
The depth of the ocean floor is 1.7 km.
