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.

The speed of sound in a medium is given by:
[tex]c= \sqrt{ \frac{K_s}{\rho} } [/tex]
where
Ks is the bulk modulus
[tex]\rho[/tex] is the medium density

In our problem, [tex]c=1533 m/s[/tex] and [tex]\rho =1025 \cdot 10^3 kg/m^3[/tex], so if we re-arrange the previous equation we can find the bulk modulus of sea water:
[tex]K_s = \rho c^2 = (1025 kg/m^3)(1533 m/s)^2=2.41 \cdot 10^9 N/m^2[/tex]

Answer Link

aachen aachen · Answer 2 · 2019-09-09T16:19:39+02:00

Answer:

Bulk modulus, [tex]B=2.40\times 10^9\ N/m^2[/tex]

Explanation:

Given that,

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

Density of water, [tex]\rho=1.025\times 10^3\ kg/m^3[/tex]

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 :

[tex]v=\sqrt{\dfrac{B}{\rho}}[/tex]

[tex]B=v^2\times \rho[/tex]

[tex]B=(1533\ m/s)^2\times 1.025\times 10^3\ kg/m^3[/tex]

[tex]B=2.40\times 10^9\ N/m^2[/tex]

So, the bulk modulus of the sea water is [tex]2.40\times 10^9\ N/m^2[/tex]. Hence, this is the required solution.