Question

In a liquid with density $1300\frac{kg}{m^3}$, longitudinal waves with frequency 400 Hz are found to have wavelength 8.00 m. Calculate the bulk modulus of the liquid.

• A. $1.33\times {10}^{10}\frac{N}{m^2}$
• B. $3.33\frac{N}{m^2}$
• C. $3.33\times {10}^{10}\frac{N}{m^2}$
• D. $1.33\frac{N}{m^2}$

Answer 1

The correct option is A

$1.33\times {10}^{10}\frac{N}{m^2}$

Given $\rho =1300\frac{kg}{m^3}$

F = 400 $H_z$

$\lambda$ = 8 m

To find B Okay if nothing is coming to head then just try to write down a formula with the Bulk modulus.

Aah!$v=\sqrt{\frac{B}{\rho }}$

Velocity of sound in a medium

Hmm!!! But I don't know velocity also.

Is there any other way to find that out.

Yes, of course!

V = $\lambda$f

= $8\times 400$

V = 3200

Now go back to the first equation

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

B =$v^2\times \rho$

B =$(3200{)}^2\times 1300$

= $13312\times {10}^6$

B = $1.33\times {10}^{10}\frac{N}{m^2}$