You can adjust the volume of Siri the same way you adjust the volume on your iOS device while playing a game, using an app or listening to music. The trick is to have Siri enabled while using the volume buttons on the side of your device to raise or lower his/her volume bar. Here's how:
1) activate Siri (press and hold the home button)
2) use the volume control buttons on the side of your iPad or iPhone
To test the volume just tell Siri "I'm testing your volume" and he/she will reply "is this thing on".