Final answer:
The stage of sleep characterized by brain waves with a fast frequency and low amplitude is Stage 1 sleep. Option A.
Step-by-step explanation:
The stage of sleep characterized by brain waves with a fast frequency and low amplitude, similar to beta waves, is Stage 1 sleep.
Stage 1 sleep is a transitional phase that occurs between wakefulness and sleep. During this stage, brain wave activity shows a decrease in frequency and an increase in amplitude compared to wakefulness.
The brain waves during Stage 1 sleep are known as alpha and theta waves, with alpha waves being more synchronized and relatively higher in frequency (8-12 Hz) and lower in amplitude compared to beta waves. So Option A.