Two sonometer wires of the same material and cross - section are of lengths `50 cm and 60 cm` and are stretched by tensions of `4.5 kg and 5.12 kg`, respectively . If the number of beats heard ( when the two wires are vibrating ) be ` 2 per second ` , find the mass per unit length of the wires . Take `g = 10 m//s^(2)`.

Explanation

To solve the problem step by step, we will follow the principles of wave mechanics and the properties of sonometer wires.

### Step 1: Understand the given data
We have two wires:
- Wire 1: Length \( L_1 = 50 \, \text{cm} = 0.5 \, \text{m} \), Tension \( T_1 = 4.5 \, \text{kg} \)
- Wire 2: Length \( L_2 = 60 \, \text{cm} = 0.6 \, \text{m} \), Tension \( T_2 = 5.12 \, \text{kg} \)
- Number of beats heard = 2 beats per second
- Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \)
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