Question

The bulk modulus and the density of water are greater than those of air. With this much of information, we can say that velocity of sound in air
(a) is larger than its value in water
(b) is smaller than its value in water
(c) is equal to its value in water
(d) cannot be compared with its value in water.

Answer 1

Cannot be compared with its value in water

Explanation:

The speed of sound $c$ is given by the Newton–Laplace equation:-

$c = \sqrt{\frac{K}{\rho}}$

where, $K =$ bulk modulus  

$\rho =$ density of the fluid

According to Newton–Laplace equation, It is clear that if bulk modulus (K) increases then velocity of sound (c) also increases but when density of fluid increases then velocity of sound (c) decreases. Bulk modulus and density of fluid (ρ) for water are greater than those of air is given in question. So the ratio (K/ρ) is different for water and air and it can not be compared, so the answer is (d).  

Answer 2

The Answer is option d)  

Explanation:

We know that,  

With B = Bulk Modulus

$\rho$ = Density of Fluid

then, V = $\sqrt \frac {B}{\rho}$,  where V is Velocity

And it is far clear that V is directly proportional to B

but

V is inversely proportional to $\rho$

On comparing the densities and bulk modulus between Air and Water,

Air has both values greater than Water.

But, In case of Water, Bulk Modulus increases Velocity and Density decreases Velocity.

Hence, As a result we are not able to compare the sound velocity in both the mediums

but we could have done that if the ratio of Bulk Modulus and Density could have been there for both water and air.

Answer = Option (d)