Why is my MacBook Air is making ticking sounds?
You don't specify the exact model of MacBook Air, but if it's one of the first models, or one of the Late 2008 or mid 2009 models, then it's possible you have a HDD for storage instead of a SSD. 

A hard drive starting to have problems could certainly explain the ticking sound (although you seem to provide very precise and regular intervals). Otherwise it could be a fan.

Regardless, I would strongly recommend you testing your hardware. How you do this will depend on your model, so choose the appropriate option below.

Run Apple Hardware Test for all MacBook Airs up to and including the Mid-2012 models

Your model uses Apple Hardware Test. To use this, follow these steps:


Shut down your MacBook Pro 
Restart your MacBook Pro
Press and hold the D key before the gray startup screen appears.
After a while, Apple Hardware Test (AHT) will start.
When prompted, select your language and click the right arrow. 
When the AHT console appears, you can choose to run Basic tests by clicking the Test button. However, I suggest you select the "Perform extended testing" checkbox before you click the Test button.
Your test results will appear in the window in the bottom-right of the console.


Note 1: that the extended test will take some time. Take a note of the results and report back. 

Note 2: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete.

Run Apple Diagnostics for all MacBook Airs from Mid-2013 onwards

Your model uses Apple Diagnostics. To use this, follow these steps:


Fully shut down your Mac
Restart your Mac
Immediately press the D key and keep it down until you see the Diagnostics screen appear
Wait for Diagnostics to finish (this typically only takes a few minutes)
Once complete, one of two things will appear on the screen:


a No issues found message
a brief description of any errors found plus further instructions

If the diagnostics test does find errors, take a note of what they are


Note: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete. 

Regardless, take a note of what happens and let me know how you went.