Question #43056

A standard Young's Double Slit Experiment setup has two slits $S_1$ and $S_2$ separated by a distance $d = 0.5 \text{ mm}$, placed symmetrically on the y-axis at $x=0$. The slits are illuminated by coherent light of wavelength $\lambda = 600 \text{ nm}$. The observation screen is replaced by a uniform circular disc of mass $M = 2.0 \text{ kg}$ and radius $R = 0.3 \text{ m}$, lying in the plane $x = D = 0.4 \text{ m}$. The disc is mounted on a frictionless axle along the x-axis passing through its center $(D, 0, 0)$, and is initially at rest. A small sticky particle of mass $m = 0.5 \text{ kg}$ moving with velocity $\vec{v} = v_0 \hat{k}$ where $v_0 = 15 \text{ m/s}$, strikes the edge of the disc at the point $(D, y_0, z_0)$ where $y_0 = 0.18 \text{ m}$ and $z_0 = 0.24 \text{ m}$, and embeds itself. Due to the rotation of the disc, the effective path length from $S_1$ and $S_2$ to any point on the disc changes continuously, causing the observed intensity to oscillate with a beat frequency $\Delta f$. Assuming $d \ll D$ and $d \ll R$, find the maximum beat frequency $\Delta f_{\text{max}}$ observed anywhere on the disc after the collision.