Conversation so far:
how did Lee de Forest amplify the audio frequency?
he came up with the idea of strengthening the audio frequency output from a grid Audion by feeding it into a second tube for additional amplification.
did Lee de Forest have any problems with amplifying audio frequency?
de Forest's gassy version of the Audion could not handle even the relatively low voltages used by telephone lines.
how did Lee de Forest fix the problems with amplifying audio frequency?
By improving the tube's design, it could be more fully evacuated, and the high vacuum allowed it to successfully operate at telephone line voltages.
Are there any other interesting aspects about the Lee de Forest article?
AT&T, through a third party who disguised his link to the telephone company, purchased the wire rights to seven Audion patents.

Question: how much did they purchase it for?
Self-contained rewrite: how much did At&T purchase seven Audion patents for?