The wake potential and wake phenomena for swift proton in an amorphous carbon target were studied by utilising various dielectric function formalisms, including the Drude dielectric function, the Drude–Lorentz dielectric function and quantum dielectric function. The Drude model results exhibited a damped oscillatory behaviour in the longitudinal direction behind the projectile; the pattern of these oscillations decreases exponentially in the transverse direction. In addition, the wake potential extends slightly ahead of the projectile which also depends on the proton coordinate and velocity. The effect of electron binding on the wake potential, characterised by the ratio to 0.1, has been studied alongside the Drude–Lorentz dielectric function and quantum dielectric function formalisms; the results evidently show that the wake potential dip depth decreases with more oscillations when the electron density ratio decreases from 10 to 0.1. One of the primary objectives of the present work is to construct a reasonably realistic procedure for simulating the response of target to swift ions by combining an expression for the induced wake potential along with several important dielectric function models; the aim of this research is to reduce computational complexity without sacrificing accuracy. This is regarded as being an efficient strategy in that it creates suitable computer simulation procedures which are relevant to actual solids. After comparing this method with other models, the main differences and similarities have been noted while the end results have proved encouraging.