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    Question: Why can't BBC Radio 1 be broadcast on 98.9 FM over the whole country, using a large number of local transmitters all tuned to the same frequency?

    (Hint - think about superposition, and constructive and destructive interference).

    This was a sample question given by my teacher.

    I thought that different waves from different transmitters would out of of phase from one - another so the waves would interfere destructively in certain regions so the resultant waves are smaller, and in certain regions where the phase different is 180º, this would mean that a shadow would be created where no one can tune into the radio station.

    Is this right?
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    That seems good, but the last bit is not completely right. For example if there are 3 waves coming to a point and lets call them A, B and C. If A=1m, B=2m and C=-3m, then at that point the A+B+C=0, the waves A,B,C aren't in phase, but they aren't in antiphase either. So it might better to say, some regions the waves will cancel out completely leaving a "shadow", as you mentioned.

    Also, if this was an exam question and worth more than a couple marks, I would add another line describing the superposition principle. E.g. When two or more waves superimpose at a point the resultant displacement is the sum of the individual waves.
 
 
 
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