1.

Sound of wavelength λ passes through a Quincke’s tube, which is adjusted to give a maximum intensity I0. Through what distance should the sliding tube be moved to give an intensity I0/2? (a) λ/2 (b) λ/3 (c) λ/4 (d) λ/8

Answer»

Correct Answer is: (d) λ/8

Let a = amplitude due to each wave.

I0 = k(2a)2 = 4ka2

Let ϕ = phase difference to obtain the intensity I0 /2.

Amplitude = a' = (a2 + a2 + 2a2 cos ϕ) =2acos (ϕ/2).

∴ I0 /2 = k[4a2cos2(ϕ/2)] = I0cos(ϕ/2).

or (ϕ/2) = 1/

or ϕ/2 = π/4

or ϕ = π/2 = 2π/λ Δ, where Δ = path difference.

∴ Δ = λ/4 = 2x, where x = displacement of the sliding tube.

∴ x = λ/8.



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