The Right to Remain Silent

The law is complicated.

On the one hand, I think it should be OK if a couple wants to dance quietly at a national monument.  On the other hand, I think there's a legitimate case to be made for designating quiet areas in a park - places free from the ambient sounds and noises that are otherwise inescapable in a big city.
Several musicians who work in the 840-acre park and do not use electronic sound systems said parks enforcement officers had recently ordered them to cease playing or leave certain areas, including Bethesda Fountain, Strawberry Fields and the Boathouse. John Boyd, a singer, said he had refused and received six summonses. 
On Sunday afternoon, the civil liberties lawyer Norman Siegel and Geoffrey Croft, the founder of NYC Park Advocates, a nonpartisan group that supports city parks, joined some of those musicians in a passageway next to Bethesda Fountain. 
Mr. Siegel called the establishment and expansion of the Quiet Zones “antithetical to the principles, values and spirit of the First Amendment.” 
He said he and Mr. Croft would speak with lawyers for the city and ask that the parks officers stop enforcing the rules against people who were not using amplified sound and were not unreasonably loud or causing concern among onlookers. 
“Civil liberties are not details or niceties or technicalities,” said Arlen Oleson, 56, a hammer dulcimer player who frequents the park. “Civil liberties are the basis of our society.”
I ain't a lawyer, but I know a li'l bit, and it seems to me that one person's "right" to play un-amplified, "not unreasonably loud" dulcimer music in a public place violates everyone else's "right" to enjoy some peace and quiet nearby.  Competing interests, scarce resources, alternative uses...if only there were a social science designed to address problems like this.

We already make it a practice to put limits on speech (like in the security line at an airport, or when there's not a FIRE! in a crowded theater), so I think we're left just trying to figure out where these limits should should be drawn.

New York has laws that limit honking your car's horn.  The laws aren't very easy to enforce, but they exist. Are these not limits on "speech" as we've come to view that term through the emanations and penumbras of the constitution?  If not, why not?