Re: When we have REM sleep what type brain waves(alpha or beta)we have?

Dear Arun,
 Thank you for your interesting question about brainwave activity 
during sleep. Brainwave activity has been widely investigated both in 
awake and asleep individuals and the different activity patterns have 
been well characterized. Before I answer your specific question about 
REM sleep, allow me to briefly review what is known about brainwave 
activity as measured by electroencephalography (EEG).
 When we are awake and involved in active thinking or speaking or 
when we are emotionally aroused or excited, EEG records very 
low-amplitude (small), high-frequency (fast) brain waves. This pattern 
is called Beta activity. When an awake person is resting quietly, 
brainwaves become a little bit bigger and slower and that is known 
as Alpha activity, or in case of deep rest, as in meditation for example, 
Theta activity.
 Alpha and Theta activity are also observed during the first stages of 
sleep (1 and 2), which are short, transitory phases between 
wakefulness and real, "deep" sleep. As sleep becomes deeper, 
brainwave activity becomes much more synchronized and its shows 
an higher-amplitude, lower-frequency pattern that is called Delta 
activity. These activities define the later stages of sleep (3 and 4), 
which are called slow-wave sleep and which provide the most 
benificial rest to the sleeper.
 Aserinsky and Kleitman (1955) were the first to notice that about 90 
minutes after the beginning of sleep, many abrupt physiological 
changes could be seen. More specifically, the eyes start to make 
"rapid eye movements" (REM), muscle tonus disseapears and the 
EEG reveals brainwave activity similar to that of an awake, alert 
individual (Beta, Alpha and/or Theta activity). This latter observation 
brought about the name "paradoxical sleep", as the brain seems 
awake while the person sleeps. This period, in which all dreams 
occur, lasts between 20 and 30 minutes and usually comes 4 or 5 
times a night.
 To know more about the mechanisms that control our different sleep 
patterns, or about the possible roles of REM sleep, have a look at a 
good physiology textbook like Carlson’s Physiology and Behavior 
(2001), or at a specialized sleep textbook like Empson’s Sleep and 
Dreaming (1993).
 I hope this helps,
 Cheers
 Benoit  

References:
Aserinsky, N.E. & Kleitman, N. (1955). Regularly occuring periods of 
     eye motility and concomitant phenomena during sleep. Science, 
     118, 273-274.
Carlson, N.R. (2001) Physiology of Behavior (7th Ed.). Boston: Allyn 
     and Bacon.
Empson, J. (1993). Sleep and Dreaming. New York: Simon and 
     Shuster.