this is a simple rule of schooling:
there I was . . .
The guide book said . . .
"the first chime of Big Ben denotes the exact second of the hour and the subsequent 'gongs' come in two second intervals. The clapper for the bell is 400 cm long . . ."
my mind flashed back to EIU.
We determined that a pendulum about 25 cm long
makes a tic-tock ( over and back ) in one second.
Thus, it makes a "tic" ( from one side to the other ) in 1 / 2 second.
BUT . . . Big Ben makes its 'tic' in 2.0 seconds . . . four times slower.
Its clapper is much longer --- about 400 cm long, so a slower period would
be expected ( qualitative observation ).
now a quantitative observation:
WHY is the difference four to one? note that Big Ben's clapper is 16 x longer than our timer ( 400 cm vs 25 cm ).
That is, the square root of 16 ( sq. root of 16 ) vs. the square root of 1 ( sq. root of 1 ).
This is 4 : 1.
So . . . a 2 second tic-tock for Big Ben is 4x the 1 / 2 second tic-tock for our "1 second pendulum."