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Over the last few decades, different types of plasma waves (e.g., the ion acoustic waves (IAWs), electrostatic solitary waves (ESWs), upper/lower hybrid waves, the Langmuir waves etc.) have been observed in the upstream, downstream and ramp regions of the collisionless interplanetary (IP) shocks. These waves appear as short duration (only a few milliseconds at 1 au) electric field signatures in the in-situ measurements, with typical frequencies $\sim1-10$ kHz. A number of IAW features at the IP shocks seem to be unexplained by kinetic models and requires a new modeling effort. Thus, this paper is dedicated to bridge this gap. In this paper, we model the linear IAWs inside the shock ramp, by devising a novel linearization method of the two-fluid magnetohydrodynamic equations with spatially dependent shock parameters. It is found that, for parallel propagating waves, the linear dispersion relation leads to a finite growth rate dependent on the the shock density compression ratio, as Wind data suggest. Further analysis reveals that the wave frequency grows towards the downstream within the shock ramp, and the wave growth rate is independent of the electron-to-ion temperature ratio, as Magnetospheric Multiscale (MMS) in-situ measurements suggest, and uniform within the shock ramp. Thus, this study help understand the characteristics of the IAWs at the collisionless IP shocks.