To fix this problem, go to line 176 of audio-player.php (/wp-content/plugins/audio-player/audio-player.php).
The line looks like this:
$pageName = add_options_page("Audio player options", "Audio Player", 8, $this->optionsPageName, array(&$this, "outputOptionsSubpanel"));
Change the 8 (a numeric user level) to ‘activate_plugins’ (single quotes included), so that the line looks like this:
$pageName = add_options_page("Audio player options", "Audio Player", 'activate_plugins', $this->optionsPageName, array(&$this, "outputOptionsSubpanel"));
