An effect which was common on amplifiers in the fifties is called Tremolo. The amps also might have had reverb or an echo effect built into the amplifier with its own knob adjuster. Some British amplifiers back then had this effect built in.

Tremolo – Quick repetition of one note, or rapid alternation between two notes.

Now is a Tremolo effect possible with a whammy bar? A whammy bar on a guitar is a pitch shifter to my understanding.

Therefore, it has been said that Leo Fender misnamed his Stratocaster's whammy bar when he called it a "Tremolo" bar. The misunderstanding has continued to this very day as guitarists have ultimate faith in the godfather of guitar makers when he made an honest mistake.

The whammy bar does not produce a rapid alternation between 2 notes. What the whammy bar does do is to change the pitch of the notes being played. A pitch involves frequency.

Back to the definition of tremolo -- a pitch shift is not the same as a quick repetition of one note or the rapid alternation between two notes.

Vibrato is another similarly confused term in with pitch shifting and tremolo but again, tremolo is as different from vibrato as reverb is different from delay effects.