If $A$ is the area of the coil, there are $N$ turns in the coil, $\omega$ being the angular velocity of the armature, then the flux through each turn in time $t$ is given by
$\phi=B A \,\cos \, \omega \, t$
Using Faraday's Law, the emf induced in each turn of the coil is
$-\frac{d \phi}{d t}=B A \,\omega \,\sin \,\omega t$
The total induced emf in the coil
$\varepsilon=N B A \,\omega \, \sin \, \omega t$
Now if we double $\omega, \varepsilon$ will be doubled.