In robotics, understanding human interaction with autonomous systems is crucial for enhancing collaborative technologies. We focus on human-swarm interaction (HSI), exploring how differently sized groups of active robots affect operators' cognitive and perceptual reactions over different durations. We analyze the impact of different numbers of active robots within a 15-robot swarm on operators' time perception, emotional state, flow experience, and task difficulty perception. Our findings indicate that managing multiple active robots when compared to one active robot significantly alters time perception and flow experience, leading to a faster passage of time and increased flow. More active robots and extended durations cause increased emotional arousal and perceived task difficulty, highlighting the interaction between robot the number of active robots and human cognitive processes. These insights inform the creation of intuitive human-swarm interfaces and aid in developing swarm robotic systems aligned with human cognitive structures, enhancing human-robot collaboration.