Fading color using frequency and amplitude

I have a program that fades two RGB colors. Since the fading of color can be interpreted as a wave, i want to know how do i change my update color function so that i can define a frequency and amplitude. I want to make the fading go fast if i increase the frequency and get bigger circles when i increase the amplitude.Can you provide me the mathematical formula.How do i change the code below to incorporate that. Any help, thanks.

bool updateColorValue(float &currentValue, uchar goalValue, 
          float deltaValue, Lights::MSecs dtime)
{
  if (deltaValue == 0) return true;
    currentValue += deltaValue * dtime; 
if ((deltaValue < 0 && currentValue <= goalValue) || 
   (deltaValue > 0 && currentValue >=   goalValue)) {

     currentValue = goalValue;
     return true;
 } else return false;
}

void setCurrentGoal (uint goalNum) {
_currentGoal = goalNum;
RGB color = _goalColors[_currentGoal];
_deltaColor.R = (color.R - _currentColor.R)/(double)_period;
_deltaColor.G = (color.G - _currentColor.G)/(double)_period;
_deltaColor.B = (color.B - _currentColor.B)/>/(double)_period;
}