The density of the material of a wire used in sonometer is `75xx10^(-2) kg //m^(3)`. If the stress on the wire is `3.0xx10^(4) N//m^(2)`, the speed of transverse wave in the wire will be

Options

A. 100 m/s
B. 200 m/s
C. 300 m/s
D. 400 m/s

Explanation

To find the speed of transverse waves in the wire, we can use the formula derived from Newton's laws:

\[ v = \sqrt{\frac{\text{stress}}{\text{density}}} \]

### Step 1: Identify the given values
- Density of the material of the wire, \( \rho = 75 \times 10^{-2} \, \text{kg/m}^3 \)
- Stress on the wire, \( \sigma = 3.0 \times 10^{4} \, \text{N/m}^2 \)

### Step 2: Substitute the values into the formula
Now, we substitute the values of stress and density into the formula:

\[ v = \sqrt{\frac{3.0 \times 10^{4}}{75 \times 10^{-2}}} \]

### Step 3: Simplify the expression
First, we need to simplify the denominator:

\[ 75 \times 10^{-2} = 0.75 \, \text{kg/m}^3 \]

Now, substituting this back into the equation:

\[ v = \sqrt{\frac{3.0 \times 10^{4}}{0.75}} \]

### Step 4: Calculate the division
Calculating the division:

\[ \frac{3.0 \times 10^{4}}{0.75} = 4.0 \times 10^{5} \]

### Step 5: Take the square root
Now, we take the square root:

\[ v = \sqrt{4.0 \times 10^{5}} = 2000 \, \text{m/s} \]

### Final Answer
Thus, the speed of the transverse wave in the wire is:

\[ v = 2000 \, \text{m/s} \]

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