Question

In a liquid with a density of 1400 kg/m3, longitudinal waves with a frequency of 390 Hz are found to have a wavelength of 7.60 m. Calculate the bulk modulus of the liquid. Express your answer in pascals.

Answer 1

Answer:

The bulk modulus of the liquid is 1.229 x 10¹⁰ Pa

Explanation:

Given;

density of liquid, ρ = 1400 kg/m³

frequency of the wave, f = 390 Hz

wavelength, λ = 7.60 m

The speed of the sound is given by;

v = fλ

v = 390 x 7.6

v = 2964 m/s

The bulk modulus of the liquid is given by;

$v = \sqrt{\frac{B}{\rho}}\\\\v^2 = \frac{B}{\rho}\\\\B = \rho v^2$

where;

B is bulk modulus

B = (1400)(2964)²

B = 1.229 x 10¹⁰ N/m²

B = 1.229 x 10¹⁰ Pa

Therefore, the bulk modulus of the liquid is 1.229 x 10¹⁰ Pa