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The physics behind the transmission of sound waves and the transmission of EM waves are quite different. With that said, the theory behind your idea of pi shifting a sound wave into destructive interference is solid. Noise cancelling headphones use this principle. I suspect any device you could build would share more in common with noise cancelling headphones than the jammer above. One of the greatest difficulties will be that the human voice is an incredibly intricate wave. You would need sophisticated recording equipment to achieve a strong effect.I have to agree with rlogan, if you are hearing whispers from an unkown source, that is a sure sign of a health condition. You should seek medical advice.
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