The theory of superposition of waves has been widely deployed in many engineering applications such as medical imaging, engineering measurements, and wave propagation in structures. However, these applications are prone to the interference of unwanted waves. The root cause of the weakness could be ascribable to the wave propagation pattern, which is not actively controlled. A new concept of imposing a time-lagging effect on the source of the wave as an active wave emission strategy is introduced and discussed in this paper. A numerical solver has been developed based on the finite volume Euler explicit method to investigate the wave propagation pattern when there is a time-lagged effect and frequency difference at the source of the wave. Our results reveal that time-lagged wave propagation will be more immune to the disturbance of other waves. The larger the time lag, the more resilient the wave is to resist the interference of other waves, even at a higher frequency. Time-lagged waves can be regarded as a promising active wave emission method that has many potential and robust engineering applications to be explored in the future.