of frequency–independence for the detector response for the wave coming from the direction determined by ${{\boldsymbol \Omega}}\cdot{\bf n}_{ED}={\rm v}$ since both antenna patterns $F^{st}$ and $F^{sl}$ do. But interestingly for the particular combination of the scalar modes which is motivated on the theoretical ground by the massive scalar tensor theories the net sensitivity is null for ${{\boldsymbol \Omega}}\cdot{\bf n}_{ED}={\rm v}$, (see Eq. (\[eq:null:s\]) and Fig. \[f:s\]).

Similarly one can obtain the detector response for the scalar wave that in the conformal gauge has the form $$\begin{aligned}
{\rm h}_{s}(t,{\bf x}) & = &
h_{s}^{0}\,{{\boldsymbol \epsilon}}^{p}\cos{\left[\omega\left(t - \frac{{{\boldsymbol \Omega}}\cdot{\bf x}}{{\rm v}}\right) + \phi_{0}\right]};\end{aligned}$$ it is given by (the real part of Eq.(\[eq:sED1\])) $$\begin{aligned}
\label{eq:sED2}
s_{ED}(t) & = &
\text{sinc}\left[ \frac{x(1-c_{ED})}{2} \right]\,F^{s}({\bf n}_{ED})\,
h_{s}^{0}\,\cos{\left[ \omega\left(t - \frac{{{\boldsymbol \Omega}}\cdot{\bf x}_{E}}{{\rm v}}\right) - \frac{x}{2}\left( 1+c_{ED} \right) + \phi_{0}\right]}.\end{aligned}$$ We see that due to the relation (\[eq:hsl:hst:rel\]) between the scalar transversal and longitudinal modes the initial phase $\phi_{0}$ of the $h^{st}$ and $h^{sl}$ signals is the same. From the one–arm response one can construct in a standard way other responses, e.g. the Michelson interferometer based on ${\bf n}_{ED_1}$ and ${\bf n}_{ED_2}$ is defined as $$\begin{aligned}
\label{eq:M}
M(t) & = & s_{ED_1}(t-L) + s_{D_1E}(t) - s_{ED_2}(t-L) - 