Answer:  

Dr. Todo Mitsugu kindly answered the question above. 
  
  
When a balloon is fully blown, it is extremely stretched and its shape becomes very different from the original form. At this stage, the balloon holds a very high level of elastic energy (the energy for the balloon to resume its original shape). 
  

When we poke a fully blown balloon with a needle, it pops and instantly breaks into a piece of rubber although the original puncture made by the needle is very tiny. This phenomenon is caused by the edge of the puncture which is very sharp and easily stretches into a long slit.    A balloon pops when the tiny puncture stretches into a long slit consuming a small portion of the elastic energy that has been stored in the balloon. The rest (probably the most part) of the elastic energy is converted to sound and heat. The smaller the energy for popping the balloon (or expanding the puncture into a slit), the higher the sound and heat become.

The moment of balloon burst   from HiViz.com, with permission

  
Now a sound is a vibration. When the puncture expands, it creates vibration, which spreads into the air as sound waves and then reaches our ears. (Although I am not certain about how the vibrations are created.) 
  
  
Acknowledgement 
Dr. Todo Mitsugu
He is studying the breakdown behaviour of polymeric materials.
  
 

This article is translated by Chemistryquestion.com from the original article in Chemistryquestion.jp.  Please let us know if you find any errors.