Two waves are represented by: x1=Asinωt+π6 and x2=Acosωt. Then the phase difference between them is

AP EAMCET · PHYSICS · Waves and Sound

Two waves are represented by: $x_{1} = A \sin (ω t + \frac{π}{6})$ and $x_{2} = A \cos ω t$ . Then the phase difference between them is

A $\frac{π}{6}$
B $\frac{π}{3}$
C $\frac{π}{2}$
D $π$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{π}{2}$

Step-by-step Solution

Detailed explanation

Given, x1=Asinωt+π6 and x2=Acosωt x1 can be written as x1=Acosπ2-ωt-π6 x1=Acosπ3-ωt The phase difference between them =π2

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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