Category and sub-category list

Hi all,

Just have a question as to how to use php queries. Hopefully this will make sense.

On my website I am putting together a page that displays a list of categories (with category images, enabled through a category image plugin).

This is my code at the moment:

<?php foreach (get_categories() as $cat) : ?>
<div id="show_onair_box">
 <img src="<?php echo z_taxonomy_image_url($cat->term_id); ?>" />
<div id="show_onair_title">
<a href="<?php echo get_category_link($cat->term_id); ?>"> <?php echo $cat->cat_name; ?></a>
</div>
</div>
 <?php endforeach; ?>

The only problem is that at the moment all categories on the site are being displayed. I only want to show categories under a particular parent category. Say my parent category had the ID 4, how would I go about specifying this in the code?

If someone could help it would be much appreciated!

Thanks