If the bulk modulus of water is 4000 MPa, what is the speed of sound in water ?

Explanation

To find the speed of sound in water using the bulk modulus, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The speed of sound in a fluid can be calculated using the formula:
\[ v = \sqrt{\frac{B}{\rho}} \]
where \( v \) is the speed of sound, \( B \) is the bulk modulus, and \( \rho \) is the density of the fluid.

2. **Identify Given Values**:
- Bulk modulus of water, \( B = 4000 \, \text{MPa} \)
- Density of water, \( \rho = 1000 \, \text{kg/m}^3 \)

3. **Convert Units**: Convert the bulk modulus from MPa to N/m² (Pascals):
\[ 4000 \, \text{MPa} = 4000 \times 10^6 \, \text{N/m}^2 = 4 \times 10^9 \, \text{N/m}^2 \]

4. **Substitute Values into the Formula**:
\[ v = \sqrt{\frac{4 \times 10^9 \, \text{N/m}^2}{1000 \, \text{kg/m}^3}} \]

5. **Simplify the Expression**:
\[ v = \sqrt{4 \times 10^6 \, \text{m}^2/\text{s}^2} \]

6. **Calculate the Square Root**:
\[ v = \sqrt{4} \times \sqrt{10^6} = 2 \times 10^3 = 2000 \, \text{m/s} \]

7. **Conclusion**: The speed of sound in water is:
\[ v = 2000 \, \text{m/s} \]