In this study, a minimal mathematical model of the cardiovascular system is used to study the effects of changes in arterial compliance and cardiac contractility on the onset time of Korotkoff sounds during an auscultatory procedure. The model provides blood pressure waveforms in the ventricle, the aorta and the brachial artery. From these waveforms, pre-ejection time, pulse propagation time and rise time of the blood pressure at the brachial artery can be computed. The time delay between onset time of ECG Q wave and onset time of Korotkoff sound is the sum of these three times. Rise time is zero and the time delay is minimal when the cuff pressure is slightly above the diastolic pressure. This minimum time delay is represented by QKD. Simulation results suggest that during the Bruce exercise protocol QKD decreases to one-third of its pre-exercise value if the cardiac contractility increases threefold. The effect of arterial compliance is not as significant as that of the cardiac contractility. From data recorded during an exercise test, it is observed that QKD decreases considerably as the test load is increased. We show in this study that the amount of decrease in QKD can be used as an index of the amount of increase in cardiac contractility during an exercise ECG test. Use of signal averaging for reducing the effect of motion artifacts during an exercise test is also shown to be very instrumental for making accurate QKD measurements.