It is easy.
A piano can also be an analog computer.
We hold with out foot the right pedal depressed. So all strings are free to vibrate in all their permissible modes of vibration.
Then we clap our hands and we hear the reverb of the clap from the piano.
Then we can close our ears. Let someone sing loudly a vowel note towards the piano. We uncover our ears and we can hear the piano repeating vowels, notes, even words.
A pulse having a short duration of time has a high bandwidth (Heisenberg uncertainty principle). We clap our hands. It lasts for a short time. All strings will vibrate sympathetically. All strings are pushed. The blast of air is short in time. If not the strings vibrating back would be decelerated. A short pulse therefore contains a large frequency spectrum making notes of all frequencies to vibrate.
Further reading:
Waves - Berkeley Physics Course - Frank S. Crawford Jr. - McGraw Hill
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