Fourier Sine Series Calculator – Step by Step Online Tool
Looking for an easy way to calculate the Fourier sine series of a function? Our Fourier Sine Series Calculator helps you expand periodic functions into their sine components quickly and accurately. This tool is especially useful for students, teachers, and engineers dealing with waveforms, signal processing, or boundary value problems.
Fourier Sine Series Calculator
Output:
Fourier Sine Coefficients bn
| Term (n) | Coefficient bn | Sine Term |
|---|
Partial sum expansion
Fourier Sine Series Graph
This chart shows how the Fourier sine series approximation converges to the original function as the number of terms increases.
How the Fourier Sine Series Calculator Works
- Input function: Type your function f(x).
- Set interval: Enter the interval [0,L].
- Choose number of terms: Select how many sine terms to compute.
- Click calculate: The calculator computes the sine coefficients bn.
- View results: Get a table, series expression, and an interactive plot.
Mathematically, the Fourier sine series is:
f(x) ≈ Σn=1∞ bn sin(nπx/L)
where bn = (2/L) ∫0L f(x) sin(nπx/L) dx
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Frequently Asked Questions (FAQs)
- Q1: What is the Fourier sine series used for?
- A: It’s used to represent functions defined on [0,L] using only sine terms, especially for solving PDEs with boundary conditions.
- Q2: How many terms should I use?
- A: Start with 5–10 terms for a basic approximation. For higher accuracy, use 20+ terms.
- Q3: Can I use this calculator for any function?
- A: Yes, but the function should be piecewise continuous on the interval [0,L].
- Q4: What’s the difference between Fourier sine and Fourier cosine series?
- A: The sine series is used when boundary conditions require the function to vanish at x=0, while the cosine series is used when the function is symmetric about the y-axis.
- Q5: Does this calculator show graphs?
- A: Yes, it provides a visual plot comparing your original function and its Fourier sine series approximation.