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Question: If \(x = a\sin\left( \omega t + \frac{\pi}{6} \right)\) and \(x^{'} = a\cos\omega t\), then what is ...

If x=asin⁡(ωt+π6)x = a\sin\left( \omega t + \frac{\pi}{6} \right) and x′=acos⁡ωtx^{'} = a\cos\omega t, then what is the phase difference between the two waves

A

π / 3

B

π / 6

C

π / 2

D

π

Answer

π / 3

Explanation

Solution

x=asin⁡(ωt+π6)x = a\sin\left( \omega t + \frac{\pi}{6} \right)and x′=acos⁡ωt=asin⁡(ωt+π2)x' = a\cos\omega t = a\sin\left( \omega t + \frac{\pi}{2} \right)

∴\therefore Δφ=(ωt+π2)−(ωt+π6)=π3\Delta\varphi = \left( \omega t + \frac{\pi}{2} \right) - \left( \omega t + \frac{\pi}{6} \right) = \frac{\pi}{3}