What happens to the frequency of a pendulum if its length is doubled?

When the length of a pendulum is doubled, the frequency of the pendulum actually decreases. The frequency of a simple pendulum is inversely related to the square root of its length, as described by the formula:

[ f = \frac{1}{2\pi} \sqrt{\frac{g}{L}} ]

where ( f ) is the frequency, ( g ) is the acceleration due to gravity, and ( L ) is the length of the pendulum. When you double the length ( L ), the equation becomes:

[ f' = \frac{1}{2\pi} \sqrt{\frac{g}{2L}} ]

This shows that the new frequency ( f' ) will be lesser than the original frequency ( f ). Specifically, by doubling ( L ), the frequency is halved because the square root of 2 in the denominator means it takes longer for the pendulum to complete each oscillation. Thus, the frequency changes in such a way that it will be half its original value.

In summary, the correct response to what happens to the frequency of a pendulum when its length is doubled is that the frequency is halved.