A compass needle oscillates \( 20 \) times per minute at a place where the dip is \( 30^{\circ} \) and \( 30 \) times per minute where the dip is \( 60^{\circ} \). The ratio of total magnetic field due to the earth at two places respectively is \( \dfrac{4}{\sqrt{x}} \). The value of \( x \) is:
