[javascript] Javascript array declaration: new Array(), new Array(3), ['a', 'b', 'c'] create arrays that behave differently

Consider this example Javascript code:

a = new Array();
a['a1']='foo';
a['a2']='bar';

b = new Array(2);
b['b1']='foo';
b['b2']='bar';

c=['c1','c2','c3'];

console.log(a);
console.log(b);
console.log(c);

Results in the Firebug console are as follows:

For a (the '[]' had to be expanded by clicking on the '+' button):

[]      
a1  "foo"   
a2  "bar"

For b:

[undefined, undefined]

For c:

["c1", "c2", "c3"]

My questions are:

1. Am I using the array['key']='value' syntax correctly?
2. Why isn't array b working as expected?
3. Why are arrays a and c displayed differently in the console? It also seems that jQuery is unable to iterate through the array a with it's .each() method.
4. Could you reccomend any good tutorials on Javascript array behaviour?

NOTE: Google Chrome's Firebug displays only [] for array 'a', without the option to expand it.

EDIT: Alright, it seems that arrays in Javascript have only numerical keys, so adding a string as a key name makes an object out of an array. But why doesn't jQuery's .each work with it?

$.each(a, function ()
    {
    alert ('derp');
    })

This code, appended to the script, produces no alerts.

Arrays in JS have two types of properties:

Regular elements and associative properties (which are nothing but objects)

When you define a = new Array(), you are defining an empty array. Note that there are no associative objects yet

When you define b = new Array(2), you are defining an array with two undefined locations.

In both your examples of 'a' and 'b', you are adding associative properties i.e. objects to these arrays.

console.log (a) or console.log(b) prints the array elements i.e. [] and [undefined, undefined] respectively. But since a1/a2 and b1/b2 are associative objects inside their arrays, they can be logged only by console.log(a.a1, a.a2) kind of syntax