Question

Two interfering waves(having intensities 9 i and 4i) path difference between them is 11 lambda.The resultant intensity at this point will be

Answer 1

hence, resultant intensity at the point will be 25i .

two waves having intensities 9i and 4i are given. path difference between them is 11λ.

so, phase difference , Φ = 2π/λ

= 2π/λ × 11λ

= 22π

now resultant intensity , I = i1 + I2 + 2√(I1.I2)cosΦ

= 9i + 4i + 2√(9i × 4i) cos(22π)

= 13i + 2 × 6i cos(11 × 2π +0)

= 13i + 2 × 6i cos0° [ as we know, cos(2nπ + x) = cosx]

= 13i + 12i

= 25i

hence, resultant intensity at the point will be 25i

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Answer 2

$\huge\bold\purple{Answer:-}$

two waves having intensities 9i and 4i are given. path difference between them is 11λ.

so, phase difference , Φ = 2π/λ

= 2π/λ × 11λ

= 22π

now resultant intensity , I = i1 + I2 + 2√(I1.I2)cosΦ

= 9i + 4i + 2√(9i × 4i) cos(22π)

= 13i + 2 × 6i cos(11 × 2π +0)

= 13i + 2 × 6i cos0° [ as we know, cos(2nπ + x) = cosx]

= 13i + 12i

= 25i

hence, resultant intensity at the point will be 25i