The speed of the particle that can take discrete values is proportional to

As given in the question
Let the no. of loops in the wave be  $n$
Let wavelength be $\lambda$ 
Debroglie wavelength
$\lambda =\frac{h}{mv}$ ------------(1)
Also
$n\lambda =2\pi a$  --------------(2)
Substituting above
$v=\frac{nh}{2am}$
$v\propto n$

So, the answer is option (D).