Answer is : Mass/weight tied to the string = 0.032 kg. So tension is 0.032 kg weight. If we do rough and quick calculation using calculus, we get 0.045 kg weight.

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A stretched string oscillates in mechanical standing waves. Since on SOnometer the string is tightly fixed and not open, the length L is divided into an integral number of loops = n. The two ends of the string are nodes. Each loop is λ/2 long.

** L = n λ/2 => λ = 2 L / n ** where n = number of loops = 1 , 2, 3, 4, ....

Let the mass attached to the end of the string be M kg. The tension T = M g. Then μ = linear mass density of the string.

Velocity of a wave =** v = λ * f ** = wave length * frequency

Velocity of transverse waves on the string = v

** v = √(T/μ)**

=> M = v² μ / g = (f² μ / g) λ²

**∴ M ****= [ 4 f² L² μ / g ] / n²**

∴ M = K / n² for K = a constant.

* M = K / 5² *

*M + 0.018 = K / 4²*

=> 0.018 = K [1/16 - 1/25] => ** K = 0.8 kg**

So *M = 0.8 /5² = 0.032 Kg *

So the tension is 0.032 kg weight.