A sine wave in the time waveform will produce what type of line in the spectrum?

A sine wave in the time waveform will produce what type of line in the spectrum?

• A. Sidebands
• B. Harmonics that are not evenly spaced
• C. Harmonics that are evenly spaced
• D. A single peak

Answer: (D)

A sine wave in the time domain is characterized by its pure frequency and continuous nature, producing a very specific representation in the frequency spectrum. When a pure sine wave is present, its transformation into the frequency domain results in a distinct single peak at its fundamental frequency. This is due to the fact that a sine wave contains only one frequency component and does not include any harmonics or additional frequency content. Unlike complex waveforms, which may produce sidebands or a series of harmonic frequencies, a pure sine wave does not introduce any additional frequencies, leading to this clear and singular representation in the spectrum. The absence of harmonics or sidebands confirms that all the energy is concentrated at that single frequency, producing the clean peak that is indicative of a sine wave's perfect periodic nature. In contrast, other waveforms, particularly those with sharp transitions or multiple frequencies, would produce more complicated spectral representations, such as evenly or unevenly spaced harmonics.

A sine wave in the time domain is characterized by its pure frequency and continuous nature, producing a very specific representation in the frequency spectrum. When a pure sine wave is present, its transformation into the frequency domain results in a distinct single peak at its fundamental frequency. This is due to the fact that a sine wave contains only one frequency component and does not include any harmonics or additional frequency content.

Unlike complex waveforms, which may produce sidebands or a series of harmonic frequencies, a pure sine wave does not introduce any additional frequencies, leading to this clear and singular representation in the spectrum. The absence of harmonics or sidebands confirms that all the energy is concentrated at that single frequency, producing the clean peak that is indicative of a sine wave's perfect periodic nature.

In contrast, other waveforms, particularly those with sharp transitions or multiple frequencies, would produce more complicated spectral representations, such as evenly or unevenly spaced harmonics.