No, a wave cannot have a frequency if it has zero amplitude, and vice versa.
Frequency refers to the number of cycles or oscillations of a wave that occur per unit of time. It represents how many times the wave repeats its pattern in a given time interval. Without any oscillations or cycles, there is no frequency.
Amplitude, on the other hand, refers to the maximum displacement or intensity of a wave from its equilibrium position. It represents the magnitude or strength of the wave. If the amplitude is zero, it means there is no displacement or intensity, and the wave essentially reduces to a flat line or zero signal.
In order for a wave to have a frequency, it must have oscillations or cycles. And to have an amplitude, the wave must have some magnitude or intensity. Therefore, a wave with zero amplitude cannot have a frequency, and a wave with zero frequency cannot have an amplitude.