A Level Physics Practice Exam

What is the wavelength expressed in radians for one complete cycle?

1. π

2. 2π

3. 4π

4. 3π

The correct answer is: 2π

In the context of wave mechanics, one complete cycle of a wave corresponds to a full oscillation, which can be described in terms of radians. A complete cycle is represented by a phase change of \(2\pi\) radians. When considering the wave function, it typically starts at zero amplitude, rises to a maximum, returns to zero, decreases to a minimum negative amplitude, and returns back to zero, completing one full oscillation or cycle. This entire process encompasses a range of \(0\) to \(2\pi\) radians. Consequently, the wavelength expressed in radians for one complete cycle is indeed \(2\pi\), reflecting the total angular displacement over one complete cycle of the sinusoidal function, such as a sine or cosine wave.