How do we differentiate between the sound from a guitar and sound from a flute given that all the parameters of the two instrumentmare are same I.e. frequency , wavelength and amplitude?


The differences which give you identifiable, signature recognition of instruments come from the waveform shape. A violin will have a jagged, spiky waveform which is different from the jagged spiky waveform of an harmonica, and a piano will have yet another different jagged waveform, and so on.

This waveform shape is largely the sum of the fundamental tone or note played by the instrument, plus the overtones which are added to the fundamental. Each kind of instrument favours different overtones to different degrees, and so the sum of fundemental overtones particular to a flute is fairly constant among all flutes, making that waveform recognizable as a flute. The waveform pattern of all cellos are similar enough be recognizable as a cello and different enough from a trombone or other instrument type to be distinguishable. 

Sometimes in the same family of instruments it is harder to distinguish between instruments because their construction results in similar waveforms. Violin, viola and cello have similar overtone sequences, and similar waveform, but they are not exactly identical and can be distinguished by careful listening.

Synthesizers try to produce the waveform of instruments they are copying, and are getting pretty good at doing so, but a really good listener can usually still recognize the differences in the waveform produced by a cheap synth, especially if the synth does not use purposely sampled sounds.

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