If the bulk modulus of water is 2100 M Pa, what is the speed of sound in water ?

Options

A. `1450ms^(-1)`
B. `2100ms^(-1)`
C. `1400ms^(-1)`
D. `1200ms^(-1)`

Explanation

To find the speed of sound in water given the bulk modulus, we can use the formula:

\[ v = \sqrt{\frac{B}{\rho}} \]

where:
- \( v \) is the speed of sound,
- \( B \) is the bulk modulus,
- \( \rho \) is the density of the medium (water in this case).

### Step-by-Step Solution:

1. **Identify the given values**:
- Bulk modulus of water, \( B = 2100 \, \text{MPa} = 2100 \times 10^6 \, \text{Pa} \) (since 1 MPa = \( 10^6 \, \text{Pa} \))
- Density of water, \( \rho = 1000 \, \text{kg/m}^3 \)

2. **Substitute the values into the formula**:
\[ v = \sqrt{\frac{2100 \times 10^6 \, \text{Pa}}{1000 \, \text{kg/m}^3}} \]

3. **Calculate the fraction inside the square root**:
\[ \frac{2100 \times 10^6}{1000} = 2100 \times 10^3 = 2.1 \times 10^6 \]

4. **Take the square root**:
\[ v = \sqrt{2.1 \times 10^6} \]

5. **Calculate the square root**:
\[ v \approx 1450 \, \text{m/s} \]

6. **Final answer**:
The speed of sound in water is approximately \( 1450 \, \text{m/s} \).