Not only that, but the way to turn off sounds (if possible) is usually clearly marked in the settings for the specific app. You either see it in the section for that app when you launch "Settings" on your iPhone, or in a section in within the app marked "settings."
For example, the official Twitter app for iPhone has very little sounds, but it has some sound "effects" that occur like when you pull down to "refresh" it makes a little "pop" sound. To disable those sound effects, you tap the little " " button in the bottom right corner of the app, then tap on "Accounts & Settings" and then tap on the "Settings" button at the bottom left of the screen. Then under the "Advanced" tab you will find the option to disable sound effects.
Okay now that I think about it, that is more than just a few taps away, but it follows the pretty typical procedure for a lot of apps. It should still only take a few seconds of looking around to find it.