I believe it's understood what type of voice I'm refering to, but for context I'm linking this youtube video where that type of voice is clearly heard:
Why do people in general find such type of voice funny?
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Two things come to mind for me.. First, at a very basic level, things that are perceptually salient capture our attention (Corbetta & Shulman, 2002), and this is obviously important for understanding our environment and assessing changes for threats (e.g.). In the video you linked, you have that perceptual salience and it's also in an animated and clearly exaggerated fashion.
The second thing that comes to mind is the voices that older children and adults make when communicating with infants. This sort of speech seems to serve an attentional/affective function (Gauthier & Shi, 2011), and research suggests that this sort of speech is actually a reflection of the infant's own communication styles (Smith & Trainor, 2008). Obviously, we might use such a voice because it sounds funny to them and we might get the infant to laugh. Who knows whether we intrinsically find it funny (if so, why?), or whether we learn to laugh at it as infants. It could well be that we simply come hardwired to interpret a perceptually salient and non-threatening social stimulus like that to be amusing.
Gauthier, B., & Shi, R. (2011). A connectionist study on the role of pitch in infant-directed speech. The Journal of the Acoustical Society of America, 130(6), EL380-EL386.
DOI: 10.1121/1.3653546 PMID: 22225130
Smith, N. A., & Trainor, L. J. (2008). Infant-directed speech is modulated by infant feedback. Infancy, 13(4), 410-420.