No, he wouldn't necessarily be a viscount at all. Not every family with an earldom also holds a viscounty; some (like the earldom of Shaftesbury) have baronies as subsidiary titles.
If he were a viscount, he'd be Viscount {Placename} or the Viscount of {Placename}, depending on usage (mostly Viscounts "of" somewhere are of somewhere in Scotland). But he'd be styled "Viscount Whatever", not "Lord Whatever" even though he'd be addressed as "Lord Whatever".
Let me give an example:
"Ms. Smith, let me introduce David Armstrong-Jones, Viscount Linley."
"Delighted to meet you, Lord Linley."
Of course Linley is an odd case, because he actually uses his title as his professional name, so many people know him as "David Linley"...
In any case, here are the key elements:
A) What is the family's surname? (The Earl of Snowdon's family surname is Armstrong-Jones; the Earl Spencer's family surname is Spencer; the Earl of Shaftesbury's family surname is Ashley-Cooper; and so on.)
B) What are the subsidiary titles? (An earldom usually has a viscounty and/or a barony or baronies as subsidiary titles.)
So if the father is Henry Hare, Earl of Cottenham (who'd be addressed as "Lord Cottenham"), then his eldest son might be styled as follows: Hartley Hare, Viscount Hare (if there's a viscounty of Hare); Hartley Hare, Viscount Somewhereelse (if the viscounty is attached to a place); Hartley Baron Hare (if there's a barony of Hare); or Hartley Hare, Baron Somewhereelse (if there's a barony attached to another place).
Whether he's Viscount Hare or Baron Hare, he'd be addressed as "Lord Hare"; if he was Viscount Somewhereelse or Baron Somewhereelse, he'd be addressed as "Lord Somewhereelse".
He'd certainly NOT be "Viscount Cottenham" because an earldom and a viscounty are almost never the same.
