Calculate the velocity of sound in steel given Young's modulus of steel `=2xx10^(11) N m^(-2)` and density of steel `=7800 kg m^(-3)`.

Answer

To calculate the velocity of sound in steel, we can use the formula that relates the velocity of sound (v) to Young's modulus (Y) and density (d) of the material:

\[ v = \sqrt{\frac{Y}{d}} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Young's modulus of steel, \( Y = 2 \times 10^{11} \, \text{N/m}^2 \)
- Density of steel, \( d = 7800 \, \text{kg/m}^3 \)

2. **Substitute the values into the formula:**
\[ v = \sqrt{\frac{2 \times 10^{11} \, \text{N/m}^2}{7800 \, \text{kg/m}^3}} \]

3. **Calculate the division inside the square root:**
\[ \frac{2 \times 10^{11}}{7800} = 2.5641 \times 10^{7} \, \text{m}^2/\text{s}^2 \]

4. **Take the square root of the result:**
\[ v = \sqrt{2.5641 \times 10^{7}} \approx 5064 \, \text{m/s} \]

5. **Final Result:**
The velocity of sound in steel is approximately \( 5064 \, \text{m/s} \).