In a sine wave function, one cycle corresponds to a complete oscillation of the wave from its starting position, through its maximum displacement in one direction, back to its starting position, and then through its maximum displacement in the opposite direction, and finally back to its starting position again.
The number of wavelengths in one cycle is determined by the frequency of the sine wave. The wavelength of a sine wave is the distance between two consecutive points that are in phase, meaning they have the same displacement and velocity at the same point in time. It is usually denoted by the symbol λ (lambda).
The relationship between wavelength (λ) and frequency (f) is given by the equation:
λ = c / f
where c is the speed of light (or any other wave propagation speed). This equation shows that wavelength is inversely proportional to frequency. As frequency increases, the wavelength decreases, and vice versa.
To calculate the number of wavelengths in one cycle, we need to consider the relationship between wavelength and the length of the cycle. In one cycle, the wave completes a full oscillation, which corresponds to a distance equal to one wavelength (λ). Therefore, the number of wavelengths in one cycle is:
Number of wavelengths = 1 / λ
So, if you know the wavelength of a sine wave, you can determine the number of wavelengths in one cycle using the equation above.