  Observations and 3D MHD simulations of the transverse MHD waves in the solar
corona have established that true wave energies hide in the nonthermal line
widths of the optically thin emission lines. This displays the need for a
relation between the nonthermal line widths and transverse wave amplitudes for
estimating the true wave energies. In the past decade, several studies have
assumed that the root mean square (rms) wave amplitudes are larger than
nonthermal line widths by a factor of $\sqrt{2}$. However, a few studies have
ignored this factor while estimating rms wave amplitudes. Thus there appears to
exist a discrepancy in this relation. In this study, we investigate the
dependence of nonthermal line widths on wave amplitudes by constructing a
simple mathematical model followed by 3D MHD simulations. We derive this
relation for the linearly polarised, circularly polarised oscillations, and
oscillations excited by multiple velocity drivers. We note a fairly good match
between mathematical models and numerical simulations. We conclude that the rms
wave amplitudes are never greater than the nonthermal line widths which raises
questions about earlier studies claiming transverse waves carry enough energy
to heat the solar corona.
