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Examine the following equations and test whether interference, beats or stationary waves will arise from the superposition of (i) 1 and 2 (ii) 1 and 3 (iii) 1 and 4 (iv) 2 and 3 (v) 2 and 4 (vi) 3 and 4 ? `1. xi_(1)=acos2pi((t)/(T)+(x)/(lambda))` `2. xi_(2)=acos2pi((t)/(T)-(x)/(lambda))` `3. xi_(3)=acos2pi((t)/(T)+(x+P)/(lambda)+phi)` `4. xi_(4)=acos2pi((t)/(T+alpha)+(x)/(lambda)),alphaltT` |
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Answer» (i) 1 and 2 represent two waves of same amplitude and frequency travelling in opposite directions. Their superposition will produce stationary waves. (ii) 1 and 3 represent two waves of same frequency and amplitude with a phase difference and travelling in the same direction . their supereposition will produce interference. (iii) 1 and 4 represent two waves two waves of same amplitude travelling in same direction, but having slightly different frequencies. their superposition will produce beats. (iv) Similarly, superposition of 2 and 3 will produce stationary waves. (v) Superposition of 2 and 4 will produce interference. (vi) Superposition of 3 and 4 will give rise to beats. |
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