A wave with changing frequency is known as a chirp or a frequency-modulated (FM) wave. The equation for a chirp waveform can be represented as:
A(t) = A0 * sin[2π(f0 * t + β * t^2/2)]
In this equation:
- A(t) represents the instantaneous amplitude of the wave at time t.
- A0 is the initial amplitude or peak amplitude of the wave.
- f0 is the initial frequency of the wave.
- β is the rate of change of frequency with time (also known as the chirp rate).
To graph a chirp waveform, you can plot the amplitude A(t) on the y-axis and the time t on the x-axis. The amplitude at each point in time can be calculated using the above equation. By varying the chirp rate β, you can control the rate at which the frequency of the wave changes. A positive β value corresponds to an increasing frequency chirp, while a negative β value corresponds to a decreasing frequency chirp.
The resulting graph will show the variation of the wave's amplitude as it evolves over time, with the frequency changing according to the specified chirp rate. The shape of the graph will depend on the specific values of A0, f0, and β chosen for the chirp waveform.