give the definition of the frequency of a wave
Frequency For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter   ν  {\displaystyle \nu }  or ν (nu) (see e.g. Planck's formula).
Quantum mechanics Quantum mechanics gradually arose from the necessity of discrete energy values in Max Planck's solution in 1900 to the black-body radiation problem, and from the necessary correspondence between energy and frequency in Albert Einstein's 1905 paper which offered a quantum-based theory to explain the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle.