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The bulk modulus of a liquid of density $8000\,kg{m^{ - 3}}$ is $2 \times {10^9}N{m^{ - 2}}$. The speed of sound in that liquid is (in $m{s^{ - 1}}$ ):
A) $200$
B) $250$
C) $100$
D) $350$
E) $500$

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Last updated date: 13th Jun 2024
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Answer
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Hint: To solve this question, you simply need to recall the various formulae of velocity of sound in fluids, i.e. liquids and gases. The formula that is required in this question is the one which relates the velocity of sound in the liquid with the ratio of its bulk modulus and density raised to a power.

Complete step by step answer:
As explained in the hint section of the solution to the asked question, the main and only thing that is needed to know to solve the asked question is nothing but the formula of velocity of sound which relates the bulk modulus of the liquid, density of the liquid and the velocity of sound in that particular liquid. Since the question has already given us the values of the density of the liquid and the bulk modulus respectively, all we need to do is to substitute the values of the density of the liquid and the bulk modulus of the liquid in the formula and get the answer which can be ticked as the correct option.
To solve the question, we need to know the following formula:
$v = \sqrt {\dfrac{B}{\rho }} $
Where, $B$ is the bulk modulus of the liquid
$\rho $ is the density of the liquid and,
$v$ is the velocity of sound in the particular liquid, or fluid
The question has already told us that the density of the liquid is $\rho = 8000\,kg{m^{ - 3}}$
Similarly, it has also been told to us that the bulk modulus of the liquid is $B = 2 \times {10^9}N{m^{ - 2}}$
Substituting the given values in the formula, we get:
$v = \sqrt {\dfrac{{2 \times {{10}^9}}}{{8000}}} \,m/s$
Upon solving, we get:
$v = 500\,m/s$
This value of the velocity of sound matches the value given in the option (E).
Hence, the correct answer is the option (E).

Note: In the given question, we don’t need to use the corrected formula of the velocity of sound since nothing is hinted about it in the question. The formula we used is Newton's formula, which assumes an isothermal condition which was later corrected by Laplace assuming adiabatic process.