The evolution of the properties of short-scale electrostatic waves across collisionless shocks remains an open question. We use a method based on the interferometry of the electric field measured aboard the magnetospheric multiscale spacecraft to analyze the evolution of the properties of electrostatic waves across four quasi-perpendicular shocks, with 1.4 <= MA <= 4.2 $1.4\le {M}_{A}\le 4.2$ and 66 degrees <=theta Bn <= 87 degrees $66{}<^>{\circ}\le {\theta }_{Bn}\le 87{}<^>{\circ}$. Most of the analyzed wave bursts across all four shocks have a frequency in the plasma frame fpl ${f}_{pl}$ lower than the ion plasma frequency fpi ${f}_{pi}$ and a wavelength on the order of 20 Debye lengths lambda D ${\lambda }_{D}$. Their direction of propagation is predominantly field-aligned upstream and downstream of the bow shock, while it is highly oblique within the shock transition region, which might indicate a shift in their generation mechanism. The similarity in wave properties between the analyzed shocks, despite their different shock parameters, indicates the fundamental nature of electrostatic waves for the dynamics of collisionless shocks.