Answer:
∴ The unit of B is =[tex]\frac{kg}{m \times s^{2} }[/tex]
Step-by-step explanation:
Here question is given,
The speed of sound in a fluid
[tex]v=\sqrt{\frac{B}{\rho} }[/tex] (equation 1)
Where,
v = speed of sound in [tex]\frac{m}{s}[/tex]
B = bulk modulus
And [tex]\rho[/tex] = fluid density in [tex]\frac{kg}{m^{3} }[/tex]
Square on both side in equation 1 and we get;
[tex]v^{2} =\sqrt{\frac{B}{\rho} }^{2}[/tex]
[tex]v^{2} =\frac{B}{\rho}[/tex]
[tex]B=v^{2} \times \rho[/tex] (equation 2)
Plug the unit value of v and [tex]\rho[/tex] in equation 2;
[tex]B=\frac{ \frac{m^{2} }{s^{2} } }{\frac{kg}{m^{3} } }[/tex]
[tex]B=\frac{kg}{m \times s^{2} }[/tex]
∴ The unit of B is =[tex]\frac{kg}{m \times s^{2} }[/tex]
