The bulk modulus of mercury is `2.8 xx 10^(10)" N/m"^2` and the density is 13600 kg/m`""^2.` What is the speed of sound in mercury ?

Answer

To find the speed of sound in mercury, we can use the formula:

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

Where:
- \( V \) is the speed of sound,
- \( B \) is the bulk modulus of the medium,
- \( \rho \) is the density of the medium.

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Bulk modulus of mercury, \( B = 2.8 \times 10^{10} \, \text{N/m}^2 \)
- Density of mercury, \( \rho = 13600 \, \text{kg/m}^3 \)

**Step 2: Substitute the values into the formula.**
Using the formula for the speed of sound:

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

Substituting the values we have:

\[ V = \sqrt{\frac{2.8 \times 10^{10}}{13600}} \]

**Step 3: Calculate the value inside the square root.**
First, calculate the division:

\[ \frac{2.8 \times 10^{10}}{13600} = \frac{2.8 \times 10^{10}}{1.36 \times 10^4} \]

This simplifies to:

\[ = 2.058823529 \times 10^6 \]

**Step 4: Take the square root.**
Now, we take the square root of the result:

\[ V = \sqrt{2.058823529 \times 10^6} \]

Calculating this gives:

\[ V \approx 1430 \, \text{m/s} \]

### Final Answer:
The speed of sound in mercury is approximately \( 1430 \, \text{m/s} \).

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