What is the speed of trasverse waves in a wire, when stretched by a weight of `25 kg`? The two metre length of the wire has a mass of `4.7 g`?

Answer

To find the speed of transverse waves in a wire stretched by a weight of 25 kg, we can follow these steps:

### Step 1: Calculate the Tension (T) in the Wire
The tension in the wire can be calculated using the formula:
\[ T = mg \]
where:
- \( m = 25 \, \text{kg} \) (mass)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the tension:
\[ T = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 245 \, \text{N} \]
(For simplicity, we can approximate \( g \) to \( 10 \, \text{m/s}^2 \) to get \( T \approx 250 \, \text{N} \))

### Step 2: Calculate the Mass per Unit Length (μ)
The mass per unit length \( \mu \) is given by:
\[ \mu = \frac{m}{L} \]
where:
- \( m = 4.7 \, \text{g} = 4.7 \times 10^{-3} \, \text{kg} \) (mass of the wire)
- \( L = 2 \, \text{m} \) (length of the wire)

Calculating \( \mu \):
\[ \mu = \frac{4.7 \times 10^{-3} \, \text{kg}}{2 \, \text{m}} = 2.35 \times 10^{-3} \, \text{kg/m} \]

### Step 3: Calculate the Speed of the Transverse Wave (v)
The speed of transverse waves in the wire can be calculated using the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]

Substituting the values we found:
\[ v = \sqrt{\frac{250 \, \text{N}}{2.35 \times 10^{-3} \, \text{kg/m}}} \]

Calculating:
\[ v = \sqrt{\frac{250}{2.35 \times 10^{-3}}} \]
\[ v = \sqrt{106383.0} \]
\[ v \approx 326.3 \, \text{m/s} \]

### Final Answer
The speed of the transverse wave in the wire is approximately:
\[ v \approx 326.3 \, \text{m/s} \]