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The expression for the dynamical spectral structure of the density fluctuation near the QCD critical point has been derived using linear response theory within the purview of Israel–Stewart relativistic viscous hydrodynamics. The change in the spectral structure of the system as it approaches the critical point has been studied. The effects of the critical point have been introduced in the system through a realistic equation of state and the scaling behaviour of various transport coefficients and thermodynamic response functions. We have found that the Rayleigh and Brillouin peaks are distinctly visible when the system is away from the critical point but the peaks tend to merge near the critical point. The sensitivity of the structure of the spectral function on wave vector (k) of the sound wave has been demonstrated. It has been shown that the Brillouin peaks get merged with the Rayleigh peak because of the absorption of sound waves in the vicinity of the critical point. [ABSTRACT FROM AUTHOR]