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

As given in the question
Let the no. of loops in the wave ben
Let wavelength be λ
Debroglie wavelength λ=h/mv —————(1)
Also nλ=2πa ——————(2)
Substituting above
v=nh/2amv
∝n
So, the answer is option (D).