The speed of sound in a liquid is `1500 ms^(-1)`.The density of the liquid is `1.0xx10^(3) kg m^(-3)`.Determine the bulk modulus of elasticity of the liquid.

Answer

To determine the bulk modulus of elasticity of the liquid, we can use the relationship between the speed of sound in a medium, its density, and its bulk modulus. The formula is given by:

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

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

### Step 1: Write down the known values
- Speed of sound, \( v = 1500 \, \text{m/s} \)
- Density of the liquid, \( \rho = 1.0 \times 10^3 \, \text{kg/m}^3 \)

### Step 2: Rearrange the formula to solve for bulk modulus \( B \)
To find \( B \), we can rearrange the formula:

\[ B = v^2 \cdot \rho \]

### Step 3: Substitute the known values into the equation
Now, substitute the values of \( v \) and \( \rho \):

\[ B = (1500 \, \text{m/s})^2 \cdot (1.0 \times 10^3 \, \text{kg/m}^3) \]

### Step 4: Calculate \( (1500 \, \text{m/s})^2 \)
Calculate the square of the speed of sound:

\[ (1500)^2 = 2250000 \, \text{m}^2/\text{s}^2 \]

### Step 5: Multiply by the density
Now, multiply this result by the density:

\[ B = 2250000 \cdot (1.0 \times 10^3) = 2250000000 \, \text{N/m}^2 \]

### Step 6: Express in scientific notation
Convert this result into scientific notation:

\[ B = 2.25 \times 10^9 \, \text{N/m}^2 \]

### Final Answer
The bulk modulus of elasticity of the liquid is:

\[ B = 2.25 \times 10^9 \, \text{N/m}^2 \]

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