share the property of having frequency–independent one-arm response functions, $F^{p}({\bf n}_{ED})\,{\cal T}(x;c_{ED})$, in the directions determined by ${{\boldsymbol \Omega}}\cdot{\bf n}_{ED}={\rm v}$ (see Figs.\[f:st\], \[f:sl\]).

In fact this feature for the $+$ and $\times$ tensorial modes was explored in [@BPPP08] and used in putting the limits on the speed of gravitational waves from pulsar timing and providing a bound on the graviton mass $m_{g}\leq 8.5\times 10^{-24}$eV. Here however we restrict ourselves from the beginning to the theories in which the standard $+$ and $\times$ modes travel with the speed of light unlike the scalar modes whose amplitudes as was shown in the previous chapter are related. Thus the detector response for the scalar wave having in the conformal gauge the form $\left[(1 + {\rm h}_{s}(t,{\bf x})\right]\eta_{\mu\nu}$ with the amplitude ${\rm h}_{s}(t,{\bf x})=h_{s}^{0}e^{i\,\omega(t-{{\boldsymbol \Omega}}\cdot{\bf x}/{\rm v})}$ is given by the Eq. (\[eq:sED1\]) with the antenna pattern function that reads $$\begin{aligned}
\label{eq:null:s}
F^{s}({\bf n}_{ED}) & = & F^{st}({\bf n}_{ED}) + \left(1 - \frac{1}{{\rm v}^2}\right)\,F^{sl}({\bf n}_{ED}) \\
& = &
\frac12-\frac{1}{{\rm v}^2}\,F^{sl}({\bf n}_{ED}) =
\frac{{\rm v}^2 - ({{\boldsymbol \Omega}}\cdot{\bf n}_{ED})^2}{2\,{\rm v}^2},\nonumber\end{aligned}$$ if we use $F^{st} + F^{sl} = \frac12$, $F^{sl}=\frac12({{\boldsymbol \Omega}}\cdot{\bf n}_{ED})^2$. We notice that the antenna pattern function $F^{s}$ must preserve the property 