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An electronic music enthusiast decides to use his electronic sound generator(synthesizer) to simulate the sound of a plucked guitar string. The guitar string, of length L, is playing the musical

note middle C (frequency f1= 256 Hz, nominally).He thinks that using his synthesizer to mimic the fundamental mode and first three overtones of the string will provide a satisfactory simulation. i) Briefly explain what this means – i.e. how can artificial electronic signals simulate a natural sound? (Hint: consider the shape of the plucked string and the combination of normal modes.) ii) Consider the fundamental resonance mode of the guitar string. Write down an equation describing how the displacement (y) of each point on the string (at position x) varies with time (t). Explain the meaning of each term.

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