In Y.D.S.E.,the separation between the two sl | vedclass

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(B) The path difference at the central point $O$ on the screen due to the source $S$ being at a distance $y$ from the central axis is given by $\Delta

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$\frac{v a}{\lambda h}$

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(B) The path difference at the central point $O$ on the screen due to the source $S$ being at a distance $y$ from the central axis is given by $\Delta x = \frac{a y}{h}$.For constructive interference (maximum brightness) at the central point,the path difference must be an integer multiple of the wavelength: $\Delta x = n \lambda$,where $n = 0, 1, 2, \dots$.Thus,$\frac{a y}{h} = n \lambda \Rightarrow y = \frac{n \lambda h}{a}$.The velocity of the source is $v = \frac{dy}{dt}$.The rate of change of the order $n$ is given by $\frac{dn}{dt} = \frac{a}{h \lambda} \frac{dy}{dt} = \frac{a v}{h \lambda}$.This represents the frequency of the fringes passing through the central point,which corresponds to the frequency of change in brightness.

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