The in-universe reason (from the original teleplay) is that he was "grinning with relief" at having discovered that the source of the strange noise was nothing more than an exotic plant.
16 EXT, TALOS XV RAVINE - LIMITED ANGLE DOWN
Revealing little or nothing but the ravine floor where we see a sudden
eddy of dust as if the surface here is being blasted by an invisible
force. Then, Winter and his landing party materialize, CAMERA IS
EMPHASIZING Winter, allowing us to share his reaction at this first
look at a strange new world. We HOLD an instant while Winter and the
landing party look, registering some surprise, then:
17 ANOTHER ANGLE
Revealing the weird violet sky, twin suns, around them is multi-hued
jagged rocks, here and there orangish vegetation not too dissimilar
from Earth desert plants. Suddenly, a MUSICAL FLUTE-LIKE SOUND. The
landing party reacts, then Mister Spock moves forward, grins in relief
as he points out the source — a plant with paper-thin rigid leaves
which vibrate in the breeze. He blows on it, produces new MUSICAL
NOTES. (These wind-plant SOUNDS will identify and set mood for all our
scenes on the surface of Talos IV).
We learn (in subsequent episodes of Trek) that Vulcans gain additional emotional control as they age. It creates a nice counterpoint to show a discernible difference in attitude between the younger/less experienced Spock, aged 24 years and pretty fresh from the Academy and the older Spock, aged 37 who's seen more than his fair share of death and destruction.