The first step would be to check out About Mac computer startup tones and identify which one of these startup tones is the one you're experiencing with your Mid-2012 MBP.
Near enough is not good enough! If your startup tone does not match exactly one of the ones listed, please comment back and say so and describe which one it is closest to and what the difference is. Unfortunately, not all of the possible startup tones are listed on that page, but identifying the correct tone helps narrow down your problem!
A possibility?
There was a common problem with some MBP models, but this predominantly affected 13" pre-2012 models. Regardless, there was an issue with logic boards not being able to address the RAM. In many cases it was caused by pressure, over time, on the bottom of the MBP which in turn placed pressure on the logic board.
You could test for this by applying some pressure on the bottom case as you start up or wake the computer. Place the pressure as follows: facing the bottom case, apply the pressure to the centre of the case, but slightly to the right (but not all the way).
If it's slight physical damage such as this, then you'd need a new logic board. However, you could try and manage the situation by always using the MBP on an even surface (such as on a desk). Also, transporting it in your backpack sounds like some sort of trigger, so you may want to pack it in well so that the bottom case is not being 'bumped' by other items in your backpack, as this may affect how well the RAM is sitting in the slots. Finally, you may want to handle your MBP carefully (e.g. don't pick it up / carry it with only one hand).
[UPDATE]
Now that we've established it's definitely an issue concerning your RAM in some way, we need to try and get to the bottom of what's causing it. Please be patient as troubleshooting is often a process of elimination and can take some time. The next step is to do a general test of your hardware.
Run Apple Hardware Test
Your model MBP uses Apple Hardware Test. To use this, follow these steps:
- Shut down your MacBook Pro
- Insert your original 2 x 2GB memory modules
- 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, select the "Perform extended testing" checkbox and then click the Test button.
- Your test results will appear in the window in the bottom-right of the console
- Take a note of the results
- Shut down your MacBook Pro
- Now remove one of the 2GB memory modules and repeat steps 3 - 10
- Now reinsert the 2GB memory module and remove the other one and repeat steps 3 - 10
- Now remove the 2GB memory module and insert the 8GB model in the first memory slot and repeat steps 3 - 10
- Now remove the 8GB memory module and insert it instead into the second memory slot and repeat steps 3 - 10
- Now insert one of the original 2GB memory modules into the first memory slot and repeat steps 3 - 10
Note 1: These tests will take some time. At completion you should have run the Apple Hardware Test six times. Make sure you record the results clearly so you know what they were for each of the six memory configurations.
Note 2: If pressing and holding the D key at Step 4 doesn't work, start again at Step 3 and, at Step 4 press and hold both the OptionD keys instead. This will try and run Apple Hardware Test from the internet instead, so you will need to allow more time for it to complete.
