The potential energy of a string $E_{pot}$ is given by $$E_{pot}=T \times L\tag{1}$$ where $T$ is the string tension and $L$ is the length of the string.
The internal kinetic energy $E_{kin}$ of a string at rest, with no translational velocity, is due to quantum zero-point fluctuations
$$E_{kin} \times \frac{L}{c} \approx \hbar,$$
$$E_{kin} \times L \approx 1.\tag{2}$$
where we use natural units with $\hbar=c=1$. (I have no evidence for this statement - I just guessed it - see comment below by ACuriousMind).
As the string is a bound object (using the virial theorem with $n=1$) we must have
$$E_{kin} \approx E_{pot}.\tag{3}$$ Therefore substituting Eqn.$(1)$ and Eqn.$(2)$ into Eqn.$(3)$ we obtain $$T\approx\frac{1}{L^2}.\tag{4}$$
If we assume that the rest mass energy $M$ of the string is given by its total energy then we have
$$M = E_{kin} + E_{pot} \approx 1/L\tag{5}$$
so that by substituting Eqn.$(5)$ into Eqn.$(4)$ we obtain
$$T \approx M^2.\tag{6}$$
It seems perfectly reasonable physically that a string of rest mass $M \approx T \times L$ should have a tension $T \approx M^2$ and a length $L \approx 1/M$.
However, as I understand it, string theory implies that strings have a length of the order of the Planck length $l_{Pl}=1/M_{Pl}$ and a tension $M^2_{Pl}$.
Does my crude semi-classical picture of a particle, represented as a string fluctuating with zero-point energy held together with string tension, give no physical understanding at all?
