‘And in that day you will say,
I will give thanks to you, O Yahweh,
For although you were angry with me,
Your anger is turned away,
And you comfort me.
Behold, God is my salvation,
I will trust and will not be afraid,
For Yah Yahweh is my strength and my song,
And he is become my salvation.'
The hymn is first of all a song of thanksgiving that Yahweh's anger has been turned away from them, even though they recognise that they have deserved it. Thus instead of visiting them in anger and judgment as they deserved He has visited them in comfort and strengthening. That indeed is why they, those who are left, are now in a position to sing the hymn. But note that the hymn is in the singular. Each one is able to echo the sentiments behind the words. It is an individual experience for them all.
It then goes on to declare that their whole confidence is in God. The God Who should have been the source of their punishment has instead been the source of their deliverance. It is to Him that they owe everything. And because of this they know that they can rest on Him in total confidence, and not be afraid. Indeed ‘Yah Yahweh' has been, and is, their strength and their song, even in the midst of trial. But now He has also become their deliverance.
These last phrases come from Exodus 15:2. Thus they are related to the Exodus deliverance, re-emphasising that Isaiah sees their future deliverance as being a new Exodus.
Yah Yahweh is a dual repetition of the Name Yahweh. Yah is the shortened form often found in names (compare also Hallel-u-Yah - ‘praise to Yahweh'), and is found in Exodus 15:2. Thus here there is especial stress on the covenant relationship and on the uniqueness of their God, coming from hearts full of praise and worship.