嗖 is an onomatopoeic word used to describe the sound of something moving very fast through the air. It often appears in the pattern 嗖地 or 嗖的一声 (with a whoosh). Reduplication 嗖嗖 suggests repeated or continuous fast movement.
Left mouth radical — used across nearly every onomatopoeia in the language to flag 'this character represents a sound.' Same role in 嗡, 哗, 嘎, 嘟, 啾. Without it, 叟 is just 'old man'; with it, the character names the whoosh of something flying past.
Right 叟 supplies the sound — sǒu → sōu, tone change only. The 'old man' meaning is irrelevant; pure phonetic borrowing. Same phonetic appears in 馊 (spoiled), 飕 (rustling wind), 艘 (boat measure word) — a small but consistent sōu/sǒu family.
