In the second speed, two swaras are sung for one unit of a talam.  
eg.  
Sari gama padha nisa l Sani dapa maga risall  
Sari gama padha nisa l Sani dapa maga risall  

In the third speed four swaras are sung for one unit of a talam.  
eg.  
Sarigama padhanisa Sanidhapa magarisa l Sarigama padhanisa Sanidhapa magarisa ll  
Sarigama padhanisa Sanidhapa magarisa l Sarigama padhanisa Sanidhapa magarisa ll  

Increase in speed means doubling the swaras from the previous speed. Likewise, various combinations are practised.  

Jantai Varisai  
The next exercise consists of repeating the same swara twice with stress on the second swara. Here also, different combinations in three speeds are practised.  
eg.  
sasa riri gaga mama l papa dhadha nini sasa ll  
sasa nini dhadha papa l mama gaga riri sasa ll  

Dhatu Varisai  
This next exercise has swaras which jump from one to another skipping the swaras in between. The swaras instead of coming in the usual order of Sa ri ga ma, are sung - sama gama. This helps one to have good control over swarasthanas. This exercise is also practised in three speeds.  

Melsthyai Varisai  
The swara exercises are practised in the higher octave so as to enable one to sing in higher range.  

All the above exercies are meant to strengthen the swarasthanam, voice of the vocalist.The above exercises introduce the basic concept of Carnatic music - sruti & Layam to the student. They provide a good training to the voice. 
 
 

Learning Carnatic Music  Introduction Stages in Abhyasaganam -  Alankaram, Gitam & Swarajathis, Varnams Tala Tala - Structure   Tala - Angams & Jaathis Tala - Maarga Thalams Gamakas