Answer :
To solve this problem we will apply the laws of Mersenne. Mersenne's laws are laws describing the frequency of oscillation of a stretched string or monochord, useful in musical tuning and musical instrument construction. This law tells us that the velocity in a string is directly proportional to the root of the applied tension, and inversely proportional to the root of the linear density, that is,
[tex]v = \sqrt{\frac{T}{\mu}}[/tex]
Here,
v = Velocity
[tex]\mu[/tex]= Linear density (Mass per unit length)
T = Tension
Rearranging to find the Period we have that
[tex]T = v^2 \mu[/tex]
[tex]T = v^2 (\frac{m}{L})[/tex]
As we know that speed is equivalent to displacement in a unit of time, we will have to
[tex]T = (\frac{L}{t}) ^2(\frac{m}{L})[/tex]
[tex]T = (\frac{7.8}{0.83})^2 (\frac{0.49}{7.8})[/tex]
[tex]T = 5.54N[/tex]
Therefore the tension is 5.54N