How do you say "in all directions" in a single word?

You could use omnidirectionally, though it might sound a bit too technical.

Alternatively, "everywhere" could also be used.

Note 1: Just in case the link above stops working, according to Oxford Dictionaries (https://en.oxforddictionaries.com/definition/omnidirectionally) "omnidirectionally" means, precisely, "in all directions".

Note 2: Where I said above that the word might sound too technical, I was speaking from a linguistic point of view, in full agreement with some members' view of the word provided as "awful". However, this is ELU, not an engineering site, and if there is a mistake, it lies with the original sentence which refers to the sound travelling in all directions. I'm not interested in engineering here but in providing an answer to the question which, I remind you, is how to say in all directions in a single word. The prefix omni- means "all", just like the original sentence: therefore, I merely answered what was asked.

A common everyday adverb is radially

From Cambridge Dictionary "in a way that spreads out from a central point"
Example: Gravitational field lines spread out radially from the centre of the Earth.

Whilst it is most often applied in a planar 2D fashion, it can equally be applied to describe travel to or from a point in 3D.

Sound is a form of energy that travels radially.

see Radially Propagating Sound Waves note that since the web is not yet 3D this sample will look like its seen by a flat earth observer. and for the record here is an image of an omnidirectional radially quaquaversal sound wave.

Technically for radio an Omnidirectional antenna radiates toroidally about one axis. I have also seen omnidirectional also applied to microphones that pick up and speakers that emanate, sound from all around at one level.
"What is meant by omnidirectional when it comes to sound? ... sound from all directions around it.... Although claiming to be omnidirectional, none of them are really spherical."