A wave with no frequency and no wavelength is not a well-defined concept in the context of classical wave phenomena. Frequency and wavelength are fundamental properties of waves, and they are intricately linked through the wave equation.
However, in some specialized areas of physics, such as quantum mechanics, there is a concept known as a "wave packet" that can exhibit certain properties that might resemble a wave with no frequency and no well-defined wavelength. A wave packet is a localized disturbance that consists of a superposition of waves with different frequencies and wavelengths. The superposition can result in an overall shape that appears to have no definite frequency or wavelength.
It's important to note that this concept is not a traditional wave in the classical sense, but rather a description used in quantum mechanics to represent the wave-like behavior of particles. In this context, a wave packet represents the probability distribution of finding a particle at a particular position and time.