Question

In a liquid with density $1300kg/m^3$, longitudinal waves with frequency 400 Hz are found to have wavelength 8.00 m. The bulk modulus of the liquid is $13.3\times {10}^{x}Pa$. Find x.

Answer 1

Given - $\rho =1300kg/m^3,n=400Hz,\lambda =8.00m$,

we have , velocity of wave $v=n\lambda$ ,

$v=400\times 8.00=3200m/s$

now the velocity of longitudinal wave in a liquid of density $\rho$ is given by ,

$v=\sqrt{K/\rho }$ , .....................eq1

where $K=$ bulk modulus of liquid ,

putting the value of $v$ and $\rho$ in eq1 , we get

$3200=\sqrt{K/1300}$ ,

or $3200\times 3200=K/1300$ ,

or $K=1.33\times {10}^{10}Pa$