Why did the Ju-87 Stuka have a siren?
Wikipedia:


  The B-1 [variant] was also fitted with "Jericho trumpets", essentially propeller-driven sirens with a diameter of 0.7 m (2.3 ft) mounted on the wing's leading edge directly forward of the landing gear, or on the front edge of the fixed main gear fairing. This was used to weaken enemy morale and enhance the intimidation of dive-bombing. After the enemy became used to it, however, they were withdrawn. The devices caused a loss of some 20–25 km/h (10-20 mph) through drag. Instead, some bombs were fitted with whistles on the fin to produce the noise after release.


So, yes, it was purely psychological and actually hindered the pilot by reducing air speed in ordinary flight and they were removed when they stopped having the psychological effect.