If the bulk modulus of water is 2100 Mpa, then speed of sound in water is (take density of water, `rho=1000 kg//m^(3))`

Options

A. `1320 m//s`
B. `1450 m//s`
C. `1580 m//s`
D. `1630 m//s`

Explanation

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

### Step 1: Understand the formula
The speed of sound \( v \) in a medium is given by the formula:
\[ v = \sqrt{\frac{B}{\rho}} \]
where:
- \( B \) is the bulk modulus of the medium,
- \( \rho \) is the density of the medium.

### Step 2: Convert the bulk modulus to standard units
The bulk modulus of water is given as \( 2100 \, \text{MPa} \). We need to convert this to Pascals (Pa):
\[ B = 2100 \, \text{MPa} = 2100 \times 10^6 \, \text{Pa} = 2.1 \times 10^9 \, \text{Pa} \]

### Step 3: Use the density of water
The density of water is given as:
\[ \rho = 1000 \, \text{kg/m}^3 \]

### Step 4: Substitute the values into the formula
Now we can substitute the values of \( B \) and \( \rho \) into the formula for the speed of sound:
\[ v = \sqrt{\frac{2.1 \times 10^9}{1000}} \]

### Step 5: Simplify the expression
Calculating the fraction:
\[ \frac{2.1 \times 10^9}{1000} = 2.1 \times 10^6 \]
Now, we take the square root:
\[ v = \sqrt{2.1 \times 10^6} \]

### Step 6: Calculate the square root
We can separate the square root:
\[ v = \sqrt{2.1} \times \sqrt{10^6} = \sqrt{2.1} \times 1000 \]
Calculating \( \sqrt{2.1} \):
\[ \sqrt{2.1} \approx 1.45 \]
Thus,
\[ v \approx 1.45 \times 1000 = 1450 \, \text{m/s} \]

### Final Answer
The speed of sound in water is approximately:
\[ \boxed{1450 \, \text{m/s}} \]