The equation of wave is $y=60 \sin (1200 t-6 x)$, where ' $y$ ' is in micron, ' t ' is in second and ' x ' is in metre. The ratio of maximum particle velocity to the wave velocity of wave propagation is

The wave equation $y = 60 \sin(1200t - 6x)$ has amplitude $A = 60 \times 10^{-6}$ m, angular frequency $\omega = 1200$ rad/s, and wave number $k = 6$ rad/m.

Maximum particle velocity is $v_{p,\text{max}} = A\omega = (60 \times 10^{-6})(1200) = 0.072$ m/s.

Wave velocity is $v_w = \omega / k = 1200 / 6 = 200$ m/s.

The ratio $v_{p,\text{max}} / v_w = A\omega / (\omega / k) = Ak = (60 \times 10^{-6})(6) = 3.6 \times 10^{-4}$, matching option C.