Short, rhythmic bursts of brainwave activity that appear during stage 2 sleep are called

These brain activity during stage 2 of sleep are called sleep spindles. These are sudden bursts of brain activity from the reticular nucleus of the thalamus. In an EEG tracing, these look like fluctuations of voltage (see attached image). Sleep spindles do represent time periods wherein the thalamus inhibits conscious processing hence keeping the person in the asleep state. 

Short, rhythmic bursts of brainwave activity that appear during stage 2 sleep are called Sleep spindle.
The stage two of sleep is characterized by sleep spindles and also the K-complexes. Sleep spindle are sudden bursts of oscillatory brain activity generated in the reticulated nucleus of the thalamus that occur during the second stage. They are called sleep spindles because of how they look when printed out on the ECG reading.

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