Radio presenter Paul Griffiths, of Tadcaster, captured the blasts on his CCTV camera and shared them on his Twitter feed @GriffoRadio.
They were caused when aircraft from RAF Coningsby in Lincolnshire were launched on Monday night to identify an unresponsive civilian aircraft.
People reported hearing what sounded like two loud explosions which were later confirmed to have been sonic booms.
Air France confirmed that the unresponsive plane had been one of their aircraft but it later landed safely guided by the Typhoon jets.
Typhoon pilots are on standby 24 hours a day to defend UK airspace.
Squadrons are based at RAF Coningsby, covering the south of the country, and RAF Lossiemouth in Moray, to cover the north.
The Quick Reaction Alert (QRA) crews can take off within minutes to intercept aircraft which have caused concern.
This can be because they are Russian military aircraft, or civilian planes which have stopped communicating with air traffic control, are not following their flight plan or have sent an emergency signal.
On some occasions pilots are given permission to fly at supersonic speeds - which may results in a sonic boom - to reach the aircraft as soon as possible.
Ministry of Defence figures show that QRA were launched on 12 days last year - eight in response to Russian aircraft and four to investigate other planes.
In January 2015 Typhoons were scrambled when two Russian Tu-95 Bear planes were flying close to UK airspace.
The Foreign Office said the incident was part of an “increasing pattern of out-of-area operations by Russian aircraft”.
The Russian ambassador was summoned to account for what had happened.
Typhoons are under the direction of controllers at RAF Boulmer in Northumberland and RAF Scampton in Lincolnshire, although any decision to shoot down an aircraft could only be taken at a high political level.
Aviation expert Dr Stephen Wright said it was understandable for people to be concerned because it was such an unusual event.
He said: “I live in Far Headingley and at first I thought a car must have ploughed into the front of the house. Then I heard the sounds of the jets and realised what it was.
“My neighbours had all come out so I put their minds at rest, but these things are incredibly rare because it’s illegal to break the sound barrier in the UK.
“Anyone who does it has to explain themselves to the Civil Aviation Authority and faces a hefty fine and possible imprisonment. But protecting the realm, as these guys were, is a pretty good excuse.”
Anything travelling faster than the speed of sound – which is around 760mph – could cause a sonic boom.
Dr Wright, an aviation lecturer at Leeds University, expects the jets were travelling in excess of Mach 2, which is around twice that speed.
“These guys were really going for it. When you’re travelling at that speed there’s a constant boom that resonates.
“This is because the air in advance of the plane can’t get out of the way in time, creating a shockwave.
“It can’t be heard on the plane itself but those of us on the ground hear it as a boom when the aircraft passes close to us. The strength of the noise is determined by how high and how fast the plane is travelling.”
Dr Wright added: “It’s very unusual but it demonstrates how seriously the UK takes its security, with aviation safety being paramount after 9/11.”