Searching for free relaxing music in Google brings up about 1.5 million results. So there have to be ways of narrowing that down!
Some of the sites you will find allow you to become your own DJ and let you slide controls up and down to mix your own track. Which is a good idea so long as you're not too stressed to be able to make the selections. The other snag I found with the site that allowed me to mix my own track was that there didn't appear to be a way of saving the track I'd "composed". But I could always buy some tracks instead.
And thereby hangs the problem with searching for free relaxing music. Either it's free because it's been pirated or it's free because it is the "sprat to catch a mackerel" and they really want you to buy something.
You can usually tell pirated tracks a mile off. They typically come with free software that allows you to search out music tracks and comes with dire warnings that it must not under any circumstances be used for illegal music downloading. Yeah, right. If you believe that no-one puts up illegal music on these file sharing services, you're not from this planet.
Assuming you want legal relaxing music tracks to download, you're often then stuck with samplers (maybe 30 seconds or so) or splashing out money to stay on the right side of the law. You might strike lucky and find some music to download that's to your taste and where the copyright notice allows you to do so. Or you could spend fruitless hours in your quest for free music. If you value your time, it may be cheaper to spend a few dollars and get straight to the downloads.