A square of elastic sheet of dimension (`axxa`) has a mas `125gm`. A force of `2.5N` is applied to each of the four edges. What is the velocity of waves on the sheet? `a=0.75m`

Explanation

To find the velocity of waves on the elastic sheet, we can follow these steps:

### Step 1: Identify the given values
- Mass of the sheet, \( m = 125 \, \text{g} = 0.125 \, \text{kg} \) (since 1 g = 0.001 kg)
- Side length of the square sheet, \( a = 0.75 \, \text{m} \)
- Force applied on each edge, \( F = 2.5 \, \text{N} \)

### Step 2: Calculate the mass per unit length (\( \mu \))
The mass per unit length (\( \mu \)) can be calculated using the formula:
\[ \mu = \frac{m}{L} \]
where \( L \) is the length of one edge of the square sheet. Since the sheet is square, the length \( L = a = 0.75 \, \text{m} \).

Substituting the values:
\[ \mu = \frac{0.125 \, \text{kg}}{0.75 \, \text{m}} = \frac{0.125}{0.75} \approx 0.1667 \, \text{kg/m} \]

### Step 3: Calculate the wave velocity (\( v \))
The velocity of waves on the sheet can be calculated using the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
where \( T \) is the tension (force applied) and \( \mu \) is the mass per unit length.

Substituting the values:
\[ v = \sqrt{\frac{2.5 \, \text{N}}{0.1667 \, \text{kg/m}}} \]

### Step 4: Perform the calculation
Calculating the right-hand side:
\[ v = \sqrt{2.5 \times 6} = \sqrt{15} \approx 3.872 \, \text{m/s} \]

### Step 5: Round off the answer
Rounding off \( 3.872 \, \text{m/s} \) gives approximately:
\[ v \approx 4 \, \text{m/s} \]

### Final Answer
The velocity of waves on the sheet is approximately \( 4 \, \text{m/s} \).

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