A sound source, detector and a cardboard are arranged as shown in figure. The wave is reflected from the cardboard at the line of symmetry of source and detector. Initially the path difference between the reflected wave and the direct wave is one third of the wavelength of sound. Find the minimum distance by which the cardboard should be moved upwards so that both waves are in phase.
Text Solution
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(4 cm)
Initially path difference 2S 1 – 24 = λ/3 ...(i)
⇒ where λ = 6
If shifting is x for bring waves in phase 2S 1 ' – 24 = λ...(ii)
subtract (ii) and (i)
2S 1' – 2S 1 = 
S 1 ’ – S 1 = 
S 1 ' – S 1 = 
– 
= 2
on solving x = 4 cm
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