Was Sindarin more commonly spoken than the common tongue in Gondor?

Question

When Frodo is captured by the rangers of Ithilien he notices than two of them are speaking Sindarin, which may just be down to the fact they were southern Dúnedain. But it seems that a lot of the Gondor population would have been Dúnedain: Dol Amroth was ruled by a southern Dúnadan with a Sindarin name (Prince Imrahil), and we know that the Rangers of Ithilien spoke Sindarin.

They spoke together in soft voices, at first using the common speech, but after the manner of older days, and then changing to another language of their own. To his amazement, as he listened Frodo became aware that it was the elven-tongue that they spoke, or one but little different; and he looked at them with wonder, for he knew they must be Dunedain of the south, of the line of the lords of Westernesse.

That's two large populations of Gondor that most likely speak Sindarin.

So is Gondors most spoken language actually Sindarin or another form of elven-tongue?

Answer 1

It appears not, although the learned of them knew it:

The Dúnedain alone of all races of Men knew and spoke an Elvish tongue; for their forefathers had learned the Sindarin tongue, and this they handed on to their children as a matter of lore. ... In the days of the Númenorean kings this ennobled Westron speech [a variety of Westron with a number of Sindarin-based words added] spread far and wide, even among their enemies; and it became used more and more by the Dúnedain themselves, so that at the time of the War of the Ring the Elven-tongue was known to only a small part of the peoples of Gondor, and spoken daily by fewer. These dwelt mostly in Minas Tirith and the townlands adjacent, and in the land of the tributary princes of Dol Amroth.

(Lord of the Rings, Appendix F)

Thus, although the two groups of people you point out likely could speak Sindarin, they apparently didn't generally do so regularly. It's possible, though speculation on my part, that the Rangers Mablung and Damrod spoke in Sindarin in front of the hobbits in an attempt to keep their conversation secret.

Answer 2

Sindarin was a language spoken among Men who were Dúnedain and was hardly widely spoken in Gondor. In Gondor if you came across Men speaking Sindarin they are more likely than not Dúnedain. Everyone else spoke the Common Tongue. Most of the people of Gondor are NOT Dunedain, "the Dúnedain were thus from the beginning far fewer in number than the lesser men among whom they dwelt and whom they ruled" [The Languages and Peoples of the Third Age] and most of the people did NOT speak Sindarin. For example in Appendix F it is mentioned about the speech of the royalty in Rohan:

the lords of that people used the Common Speech freely, and spoke it nobly after the manner of their allies in Gondor, for in Gondor whence it came the Westron kept still a more gracious and antique style. [Appendix F]

This Common Speech was in large part derived from the native tongue of the Dúnedain which was Adûnaic. They brought it with them to Middle-earth as they interacted with the people there from their various havens. The Dúnedain "used therefore the Common Speech in their dealings with other folk and in the government of their wide realms." [Appendix F] As you can see not only was it used throughout Gondor, it was also spoken by and with non-Gondorians.

In Letter # 347 from The Letters of J.R.R. Tolkien he says:

In Gondor the generally used language was 'Westron', a lang. about as mixed as mod. English, but basically derived from the native lang. of the Numenoreans; but Sindarin was an acquired polite language and used by those of more pure N[umenorean] descent, esp. in Minas Tirith, if they wished to be polite. [First Houghton Mifflin paperback edition 2000]

In Gondor, Westron or the Common Tongue was used by everyone. Sindarin was used by the few, that is, the Dúnedain.