The phrase "waves spread" is correct and usable in written English.
You could use it in a sentence such as: "The sound of laughter spread through the room in waves".
Waves spread out as they propagate.
The Bay Area may be the epicenter, but the shock waves spread everywhere.
Radio waves spread out and become relatively weak as they travel long distances.
Following the initial disturbance to the sea surface, water waves spread in all directions.
Those waves spread out through the cosmos, stretching and compressing space and time like the ripples on a pond.
Of all seismic waves, Rayleigh waves spread out most in time, producing a long wave duration on seismographs.
As with chickenpox, they tend to appear in waves, spreading over one side of the body or face.
The energy of Love waves, like that of other surface waves, spreads from the source in two directions rather than in three, and so these waves produce a strong record at seismic stations even when originating from distant earthquakes.
"In the old days," he said, leaning over to whisper in his Boston accent, "Erroll Garner and Art Tatum would play, and the music would just roll over the audience like waves, spreading joy all over the place.
The snapshots show the tsunami waves spreading isotropically from the initial height given by Eq. 20.
Cosmologists had theorized that the big bang sent sound waves spreading through the early universe like ripples from a pebble thrown into a pond.
