The velocity of sound is ___ to the density of the medium

Options

A. directly proportional to
B. inversely proportional to
C. directly proportional to the square root of
D. inversely proportional to the square root of

Explanation

To solve the question "The velocity of sound is ___ to the density of the medium," we need to establish the relationship between the velocity of sound (V) and the density of the medium (ρ).

### Step-by-Step Solution:

1. **Identify the Relevant Formula**:
The speed of sound in a medium can be expressed using the formula derived from Laplace's equation:
\[ V = \sqrt{\frac{\gamma P}{\rho}} \]
where:
- \( V \) = velocity of sound,
- \( \gamma \) = adiabatic index (a constant for a given gas),
- \( P \) = pressure of the medium,
- \( \rho \) = density of the medium.

2. **Analyze the Formula**:
In the formula, we can see that the velocity of sound \( V \) is dependent on the density \( \rho \). The formula shows that \( V \) is proportional to the square root of the pressure and inversely proportional to the square root of the density.

3. **Establish the Relationship**:
From the formula, we can deduce that:
\[ V \propto \frac{1}{\sqrt{\rho}} \]
This indicates that the velocity of sound is inversely proportional to the square root of the density of the medium.

4. **Conclusion**:
Therefore, we can conclude that "The velocity of sound is inversely proportional to the square root of the density of the medium."

### Final Answer:
The velocity of sound is **inversely proportional to the square root of the density of the medium**.