We need to stop treating developers like precious children. You do not need ABSOLUTE SILENCE to be able to do your work. 99% of us are not writing the next PageRank or inventing the next Djkstra's Algorithm. And even when we are 99% of the time is spent on build environments and configuration and plumbing.
This does not require absolute uninterrupted focus surrounded by silence. Making a mistake does not cause a bomb to go off or a plane to fall out of the sky.
Put on a pair of comfortable headphones and do not plug them into anything and 75% of the noise around you is gone. Turn on some white noise or some gentle ambient music of dozens of lyrics-free genres and it goes up to 95%. If the only way you can work is if you can't hear any other noise outside of your own head, you have failed as a human being because no other profession requires that.
No, most people don't need to work in an anechoic chamber.
But any distracting noise adds to cognitive load, and since you're being paid to use your cognitive abilities, productivity suffers.
If you're paying people to do something and then making it harder for them to do it, the problem is not with the people.
I'm sorry I don't have empathy for bullshit rare disorders like https://en.wikipedia.org/wiki/Misophonia
There's a lot of evidence that open offices destroy productivity, and almost no evidence that they increase it.
So whatever your reasoning hiring people, paying them a lot of money, and then making it harder for them to do their jobs is an irrational position.
[1] By cancel out, I mean make it impossible to understand the conversation, while the headphones are silent or playing in low volume.
(NB. This reply entirely useless if you can't tolerate in-ear buds.)
http://productivity.stackexchange.com/questions/7213/do-nois...
Managers who deliberately create environments where headphones are mandatory should be brought up on charges.
Basic rule of thumb: If your headphones are loud enough to block out ambient conversation, they're damaging your ears. In 20 years, deafness is going to be associated with programmers in the same way we associate black lung with coal miners.
Also, I'm happy for you that your brain is only derailed by particularly loud ringtones or people tapping you on the shoulder, you lucked out on that one! But my brain is different: https://en.wikipedia.org/wiki/Misophonia