Aside from analyzing the BGM and looking cool, the HUD Sound Waves chip serves one other purpose. According to posts like the one in this thread, it helps you find a specific Pod in the desert:
There's an item in the desert (pod C) that emits a high-pitched sound when you're close to it so it's easier to find. The sound display detects this noise, giving a hint to people who can't hear it (or hear poorly in general, or people like me who thought my speakers were dying instead of thinking it was an actual game sound).
This is backed up in this thread, as well:
I believe it's meant to help those who have a handicap with their hearing.
There is an thing (a pod) in the desert that can be found through a sound it makes. Not everyone can hear it.
If you've already found this Pod or are confident in your hearing abilities, there appears to be no other purpose to this chip other than being a BGM analyzer.
Most of the music is without lyrics. However, some tracks do include lyrics, but not all are in real languages. The ones that include lyrics in actual languages have lyrics sung in your chosen language for dialogue. (The main example I'm thinking of is "Birth of a Wish", which, depending on your language setting, will have the robots chant "This Cannot Continue" or "Kono Mama Ja Dame")
That is, if you chose Japanese audio, the lyrics will be in Japanese, whereas if you chose English, the lyrics will be in English.
The sole exception would be the "Weight of the World Medley" featured in the [E]nd of YoRHa ending, which features the Japanese, French, and English singers of the soundtrack together.
The rest of the music with lyrics, however, appears to be in a made-up language, similar to the dialogue in Gravity Rush. See this thread:
The composer said the language is based on old gaelic and what he believes Japanese could sound like in 1000 years.
So there is likely some root words and rules that are real.
Another thread discussing this can be seen here:
Its an invented language, same with the OST of NieR 1.
Follows the same route as shadow of the colossus. Mix of english, japanese, spanish, french etc.
Take a few languages like French, English, etc, try to imagine how they transform over centuries. Make some lyrics for a song.
Best Answer
That's technically an attack, as I discovered recently. It doesn't do very much damage and it's quite difficult to aim, so it's not very useful. Most weapons can close the gap between you and an enemy pretty well as it is.
Here is a video of me partially attempting an arena with only pod kicks. If it looks like its powerful, it's because these enemies are 19 levels lower. It doesn't actually do much damage.