A person standing at a distance of 6 m from a source of sound receives sound wave in two ways, one directly from the source and the other after reflection from a rigid boundary as shown in figure . Find the maximum wavelength (in m) for which the person will receive maximum sound intensity.

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answer is 4.

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Detailed Solution

Path length of the reflected wave reaching the person is $x_{1} = 5 + 5 = 10 m$
Path a length of the direct wave is x₂ = 6m
Path difference , $Δx = 10 m - 6 m = 4 m$
For destructive interference :
$Δx = λ, 2 λ, 3 λ \dots \dots . . [Δx = 0 is not possible]$
$or 4 = λ, 2 λ, 3 λ \dots \dots λ = 4, \frac{4}{2}, \frac{4}{3} \dots \dots ∴ λ_{max} = 4 m$

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