Final answer:
The period of a pendulum decreases when it is shortened, due to the direct proportionality between the pendulum's period and the square root of its length. Amplitude has little effect on the period unless it is very large. Moreover, as a wave's period increases, its frequency decreases.
Step-by-step explanation:
If a pendulum is shortened, its period decreases. The period, T, of a simple pendulum can be calculated using the formula T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. This indicates that the period of a pendulum is directly proportional to the square root of its length. Therefore, if the length of the pendulum is shortened, the period will become smaller because the square root of a smaller length is less. This relationship is independent of the amplitude of the pendulum as long as the amplitude is not extremely large, typically less than about 15°.
Regarding your reference question, when the period of a wave increases, its frequency decreases. This is because frequency (f) is the reciprocal of the period (T), so if T becomes larger, f must become smaller, and vice versa.