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Why do the different musical instruments producing note of same frequency, same amplitude have different quality?

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Question

Why do the different musical instruments producing note of same frequency, same amplitude have different quality?

Very Short Answer
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Solution

Different instruments produce different subsidiary vibrations, or overtones, along with the main vibration. The combination of these vibrations gives each instrument a distinct waveform, so the notes have different quality.

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Chapter 6: Sound - EXERCISE-3 [Page 137]

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