Question

The velocity of sound in sea water is 1533 m/s. find the bulk modulus (in n/m2) of sea water if its density is 1.025 ´ 103 kg/m3.

Answer 1

Bulk modulus,
`B=2.40* 10^9\ N/m^2`

Step-by-step explanation:

Given that,

The velocity of sound in sea water, v = 1533 m/s

Density of water,
`\rho=1.025* 10^3\ kg/m^3`

We need to find the bulk modulus. The speed of sound also depends on the bulk modulus of the material. The relationship is given by :

`v=\sqrt{(B)/(\rho)}`

`B=v^2* \rho`

`B=(1533\ m/s)^2* 1.025* 10^3\ kg/m^3`

`B=2.40* 10^9\ N/m^2`

So, the bulk modulus of the sea water is
`2.40* 10^9\ N/m^2`. Hence, this is the required solution.

Answer 2

The speed of sound in a medium is given by:

`c= \sqrt{ (K_s)/(\rho) }`
where
Ks is the bulk modulus

`\rho` is the medium density

In our problem,
`c=1533 m/s` and
`\rho =1025 \cdot 10^3 kg/m^3`, so if we re-arrange the previous equation we can find the bulk modulus of sea water:

`K_s = \rho c^2 = (1025 kg/m^3)(1533 m/s)^2=2.41 \cdot 10^9 N/m^2`