Declare this for P/Invoke:
private const int APPCOMMAND_VOLUME_MUTE = 0x80000;
private const int WM_APPCOMMAND = 0x319;
[DllImport("user32.dll")]
public static extern IntPtr SendMessageW(IntPtr hWnd, int Msg, IntPtr wParam, IntPtr lParam);
And then use this line to mute/unmute the sound.
SendMessageW(this.Handle, WM_APPCOMMAND, this.Handle, (IntPtr) APPCOMMAND_VOLUME_MUTE);