The density of a solid is `8930 kgm^(-3)` and its young's modulus is 117GPa. What is the velocity of sound in the solid?

Answer

To find the velocity of sound in the solid, we can use the formula:

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

where:
- \( V \) is the velocity of sound,
- \( E \) is the Young's modulus,
- \( \rho \) is the density of the solid.

### Step 1: Identify the given values
- Density (\( \rho \)) = \( 8930 \, \text{kg/m}^3 \)
- Young's modulus (\( E \)) = \( 117 \, \text{GPa} = 117 \times 10^9 \, \text{N/m}^2 \)

### Step 2: Substitute the values into the formula
We substitute the values of Young's modulus and density into the formula for the velocity of sound:

\[ V = \sqrt{\frac{117 \times 10^9 \, \text{N/m}^2}{8930 \, \text{kg/m}^3}} \]

### Step 3: Calculate the value inside the square root
First, calculate the fraction:

\[ \frac{117 \times 10^9}{8930} \approx 13140.5 \, \text{m}^2/\text{s}^2 \]

### Step 4: Take the square root
Now, take the square root of the result from Step 3:

\[ V \approx \sqrt{13140.5} \approx 114.7 \times 10 \approx 3619.65 \, \text{m/s} \]

### Final Answer
The velocity of sound in the solid is approximately:

\[ V \approx 3619.65 \, \text{m/s} \]

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