Please help me finding the exact meaning of beats
What is the length of 1 beat or 2 beat…… ?

In the recitation of the Qur'an, the length of one vowel should be consistent, meaning a fath should equal a dhammah in lengthen and a kasrah should be equal to both the fath and the dhammah.  They should be equal and consistent during the reading.  The timing of a vowel is called a "harakah" in Arabic; in English this is translated as a vowel count.  Some may have translated it as a beat, but the correct term is a vowel count.
 A lengthened letter, such as an alif with no hamzah or sukoon following it is lengthened two vowel counts.  So whatever timing you use in your reading, fast, slow, or medium, you can measure out the time it takes you to say one letter with a vowel, and multiply it by two to find the time of an alif, which is two vowel counts.  Two vowel counts for you may be longer than two vowel counts for another person depending on your speed of reading.  Also, one time you maybe reading slowly and another time quickly, and you will base your lengthening each time on your speed and how long it takes you to say one letter with a vowel.  You cannot judge it in seconds or by counting on your fingers since your fingers maybe quicker or slower than the vowel counts in your reading.
The same measure is used for longer medds which are lengthened four, or five, or six counts.  Four vowel counts is the length it takes you to say a letter with a vowel multiplied by four.