Final answer:
The simplest wave without harmonics is a sinusoidal wave, described by a single sine or cosine function. Its frequency is independent of the amplitude, and for mechanical waves like a mass on a spring, it's determined by the object's intrinsic properties. Light is an example of an electromagnetic wave that doesn't require a medium.
Step-by-step explanation:
The simplest form of a wave that contains no harmonics is a sinusoidal wave, which can be described by a single sine or cosine function. An example of a simple harmonic oscillator is a mass on a spring, where the frequency of the oscillation is determined by the mass and the spring constant and is independent of the amplitude of the oscillation. The wave equation, y (x, t) = A sin (kx - ωt), clearly illustrates how you can obtain the wave's amplitude, wave number, and angular frequency directly from its form. In this case, the amplitude (A) represents the maximum displacement from the equilibrium position.
In the context of waves, like in surface water waves, the oscillation of the medium (e.g., water) is up and down, while the wave disturbance propagates horizontally. The frequency of the wave (f) is the number of complete cycles that pass a point per unit time, and it is calculated as f = 1/T, where T is the period of the wave. It's important to note that even if the amplitude were to change, the frequency would remain constant because it's determined by the wave's intrinsic properties, like tension and mass density, in the case of a string.
An example that a wave does not require a medium to propagate is an electromagnetic wave, such as light, which can travel through the vacuum of space.