Here's how the frequency of a simple pendulum changes when its length is doubled:

The frequency will decrease by a factor of the square root of 2.

Explanation:

The frequency (f) of a simple pendulum is determined by the following equation:

* f = 1 / (2π) * √(g/L)

Where:

* f is the frequency in Hertz (Hz)

* g is the acceleration due to gravity (approximately 9.8 m/s²)

* L is the length of the pendulum in meters

Let's analyze the effect of doubling the length (L):

1. New length: 2L

2. New frequency: 1 / (2π) * √(g / (2L))

Notice that the only change is the length in the denominator of the square root. We can rewrite the new frequency expression:

* New frequency = (1 / √2) * [1 / (2π) * √(g/L)]

The term in brackets is the original frequency (f). Therefore:

* New frequency = (1 / √2) * f

Conclusion:

Doubling the length of a simple pendulum reduces its frequency by a factor of the square root of 2 (approximately 0.707). This means the pendulum will swing back and forth slower.