Question

The Fourier series of an odd periodic function, contains only?

• A. Sine Terms
• B. Cosine Terms
• C. Odd Harmonics
• D. Even Harmonics

Answer 1

The correct option is A

Sine Terms

The explanation for the correct option:

Option(A):Sine Terms

1. A Fourier series represents a periodic function as a sum of sine and cosine functions (possibly infinite).
2. A function $\mathrm{y}=\mathrm{f}\left(\mathrm{t}\right)$ is basically said to be odd if $\mathrm{f}(-\mathrm{t})=-\mathrm{f}\left(\mathrm{t}\right)$holds good for all values of $t$ .
3. The graph of an odd function is always said to be symmetrical about the origin.
4. Let the odd function be $\mathrm{f}\left(\mathrm{t}\right)=\sin \mathrm{t}$, for which the graph can be represented as:

5. From the above graph, we can conclude that the Fourier series of an odd periodic function contains only sine terms.

Explanation for the incorrect option:

Option(B):Cosine Terms

1. The Fourier series of an odd periodic function contains only the Cosine Terms.
2. Hence, the given option does not coincide with the correct concept.

Option(C):Odd Harmonics

1. Odd Harmonics are not the only function that the Fourier series of an odd periodic function contains.
2. Thus, the given option is the incorrect one.

Option(D): Even Harmonics

1. The Fourier series of an odd periodic function contains only the Cosine Terms.
2. Hence, the given option does not correspond to the correct concept.

Hence, the Fourier series of an odd periodic function contains only Sine Terms.