The long tube with slots on the sides visually distinguishes the shotgun microphone from others. Designed to be more directional than conventional microphones, how does that long cylinder with notches increase the ratio of on-axis to off-axis sound?
In the 1950s Harry Olson (of RCA 44 mic fame) created a microphone system that used a series of parallel tubes to improve directionality. The operating principle is frequency cancellation by difference in timing. Any time you take the same signal, delay and recombine it, there is a cancellation. The greater the timing delay, the lower the frequency that is cancelled.
Below we see a simple illustration with only two tubes, one longer than the other. The sound arriving at a common mic element ON axis will have the same path length. In other words sound arrives at the element through both tubes at the same time. But at an angle the tube length delays sound through the longer tube. When they combine, there is a cancellation at a certain frequency. So the path length difference cancels some off-axis sound but the on-axis arrives intact. Olsen used a series of tubes to cancel a significant portion of the spectrum, which made his system more directional than it would have been otherwise.