While mixing clips with different audio Sample Rates is generally infrequent, it can occur (for example, when borrowing a clip from another project). This recipe will alert you to this issue before you've edited a mismatched clip into your sequence.
Go to Project Window | Settings tab | Double-click the Audio Project settings.
The Audio Project settings dialog window will open.
Set Convert Sample Rates When Playing to Never.
Close the Audio Project settings dialog window.
By default, Media Composer is set to play audio that is not at the Project Sample Rate (Project Window | Settings tab | Audio Project | Convert Sample Rates When Playing | Always). By turning this feature off, if/when you load a clip into your Source Window with a mismatched sample rate, then you will not be able to hear the audio play. That's a pretty good sign that something is not as it should be. This will cause you to...