Psychological Weapon
This is the argument the sound would trigger a fear response in the brain. This would make the enemy shit his pants at first exposure and for every exposure -- think of Hermann Grids and the sort; even if you know what's going on, you can't do a goddamn thing about it. However, a white noise generator would cancel the effect (basically, create a noise that cancels out the leo's sine). This would also require considerable trials -- I realize the Nazis would have had no qualms in piling a bunch of Jews into a trench and exposing them to a bunch of noises to see which produces the greates fear, but I still giggle at the thought of a bunch of soldiers being given a questionaire and being asked, "Which scares you more?" Vrooooooom!
Even if the Nazi's did that, the similiarities between the 4F responses is so minute that getting the *exact* one would be extremely difficult. There's no way to guarantee that it would elicit "fight" in friendly and "flight" in enemy as both sides are facing an inevitable battle. Sure, friendlies could be told that "this sound will terrrify your enemies and render them useless" to strengthen their fight instincts, but enemies could be told "these idiots are armed with speakers" to lessen their flight instincts.
That's how I can dismiss it as an intended physiopsychological weapon and attribute it more to:
Conditioned Responses to Specific Stimuli
Fairly sure I've beat this one about the head and neck. It's entirely likely the exhaust was designed around this, but the reality is *every* vehicle on the battlefield is going to have this affect on combatants. To make it more pronounced and directly attributable to the Leopard (distinguishable), it's highly likely it was given a distinct noise. This can generalize to every diesel or specify to the Leo at 1200 RPM (and only at 1200 RPM).
The down side to this is extinction. Unpaired matchings (leopard sound - effects of battle) will cause the fear response to lessen. Every time a leopard is heard, be it starting up to charge the batteries to just moving around, and it doesn't engage a conditioned enemy, the fear will lessen. And since tanks can be heard so far off, the unpaired matchings would be very common.
Most militaries counter these types of pairings with conditioning of their own. As I previously mentioned, taste is the easiest thing to condition people to. Matching the effects of battle with positive stimuli will provoke desirable responses. Japanese did this with their Kamikaze pilots (big meals and video broadcasts).
I suppose this would classifiy it as a psychological weapon, albeit a pretty flakey one given we want no-one to survive their first encounter with the Leopard, which leads me to my next point.
The Effects of Expectancy on Combat
In the same way the Pipes announced the inevitable approach of combat, so too can the Leo's exhaust. Properly progandized or rumour milled, this can produce expectancy. If you expect something to scare the pants off you, it'll scare the pants off you. However, without really knowing what the leopard sounds like, the enemy would just be afraid of anything they thought was a leopard. This would not require any particular engineering genius, just a distinct sound. Imagine the en dreading the approach of a tank that has no echo hearing the Mallard Mk 1's dreaded "Quaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaack!"
But that leads me to my next point...
The Exhaust Manipulating Psychoperception
Given the knowledge of the time (and our present knowledge), this is another highly probably design. A low-pitched sound is going to travel a considerable distance further than a high-pitched one. A low-pitched sound will penetrate further than high-pitched. This means the mean, low-pitched rumble is going to go further and be negatively affected less by terrain. It's also why it has a high-pitched horns, because that spread is easily defeated by terrain and won't travel as far; this is probably another reason for the selection of turbine engines in "stealthier" tanks. Since low-pitch travels so well and so far, it's very difficult to locate the sound-generator. Several of these spread out over 1km is going to make locating and distancing any specific one very difficult -- the stealth George spoke of, possibly in a manner of teaching you how to suck eggs.
However, *every* low-pitched vehicle is going to produce sound with these properties, which is why I think it's important to...
Address and Debunk these Myths
It's not unlikely that we're going to face armour equipped enemies in the future. Hell, given the way weapons proliferation goes, it's not unlikely we won't face Leopards on the field of battle. A careful analysis of all the sources can circumvent any undue fears blue forces will face in dealing with armour that stem entirely from personal cognitions.
