  The paper presents a new analysis and a new interpretation of oscillations
observed in the experiments of near wakes of cylinders at Mach 4 and Mach 6 and
Reynolds number range 2 $\times$ 10$^4$ to 5 $\times$ 10$^5$ by
\cite{schmidt2015oscillations} and \cite{thasu2022strouhal}. It is shown that
the presence of such oscillations is strongly Reynolds number dependent. It is
further shown that there is a threshold Reynolds number below which wake
unsteadiness and oscillations do not appear. Attention is drawn to the earlier
experimental investigation of supersonic wakes behind cylinders and spheres by
\cite{kendall1962exp} which discusses cylinder oscillations and confirms the
concept of threshold Reynolds number. Following the earlier work of
\cite{goldburg1965strouhal} on hypersonic wakes of spheres and cones, a
Strouhal number($St_\theta$) based on total wake momentum thickness ($\theta$)
is shown to be the relevant similarity parameter for correlating the hypersonic
and high supersonic wakes of spheres, cones, as well as cylinders. In this
limited sense, $St_\theta$ can be said to be `universal'. A universal Strouhal
number based on only one geometry (\textit{i.e.,} a circular cylinder) and over
a limited Reynolds number range as proposed by \cite{schmidt2015oscillations}
is much too restrictive.
