Speed of sound waves in a fluid depends

Options

A. directly proportional to the square root of bulk modulus of the medium.
B. inversely proportional to the bulk modulus of the medium.
C. directly proportional to the density of the medium
D. inversely proportional to the density of the medium

Explanation

To determine how the speed of sound waves in a fluid depends on various properties of the medium, we can analyze the relationship using the formula for the speed of sound in a fluid.

### Step-by-Step Solution:

1. **Understanding the Formula**: The speed of sound \( v \) in a fluid is given by the equation:
\[ v = \sqrt{\frac{B}{\rho}} \]
where \( B \) is the bulk modulus of the medium and \( \rho \) is the density of the medium.

2. **Analyzing the Bulk Modulus**: The bulk modulus \( B \) measures a material's resistance to uniform compression. A higher bulk modulus indicates that the medium is less compressible, which allows sound waves to travel faster.

3. **Analyzing the Density**: The density \( \rho \) of the medium is the mass per unit volume. A higher density means that the medium has more mass, which can slow down the propagation of sound waves.

4. **Proportional Relationships**:
- The speed of sound is **directly proportional** to the square root of the bulk modulus \( B \). This means that if the bulk modulus increases, the speed of sound increases.
- The speed of sound is **inversely proportional** to the square root of the density \( \rho \). This means that if the density increases, the speed of sound decreases.

5. **Conclusion**: Based on the analysis:
- The correct answer to the question is that the speed of sound waves in a fluid is **directly proportional to the square root of the bulk modulus** and **inversely proportional to the square root of the density**.

### Final Answer:
The speed of sound waves in a fluid depends **directly on the square root of the bulk modulus** and **inversely on the density** of the medium.

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