Determine which of the following statements is/are FALSE:(i) Harmonic frequencies are integer multiples of the fundamental frequency.(ii) Harmonics share the same tone when being heard as audio.(iii) Linear combinations of harmonics may result in aperiodic signals.a.(i) and (iii) onlyb.(i), (ii) and (iii)c.(i) and (ii) onlyd.(ii) and (iii) only
Question
Determine which of the following statements is/are FALSE:(i) Harmonic frequencies are integer multiples of the fundamental frequency.(ii) Harmonics share the same tone when being heard as audio.(iii) Linear combinations of harmonics may result in aperiodic signals.a.(i) and (iii) onlyb.(i), (ii) and (iii)c.(i) and (ii) onlyd.(ii) and (iii) only
Solution
To answer this question, let's analyze each statement:
(i) Harmonic frequencies are integer multiples of the fundamental frequency. This statement is TRUE. By definition, a harmonic frequency is a frequency that is an integer multiple of a base frequency.
(ii) Harmonics share the same tone when being heard as audio. This statement is FALSE. While harmonics are related to the fundamental frequency, they do not share the same tone. They contribute to the overall timbre or quality of the sound, but they are not perceived as the same tone as the fundamental frequency.
(iii) Linear combinations of harmonics may result in aperiodic signals. This statement is TRUE. When harmonics (which are periodic signals) are combined linearly, the resulting signal can be aperiodic, depending on the phase and amplitude of the individual harmonics.
So, the false statement is (ii). Therefore, the correct answer is d. (ii) and (iii) only.
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