What is relationship between entropy and frequency in image
If I understand correctly, you are taking the entropy in the image from the distribution of black and white pixels. In image (a) you have 50% black, 50% white, so the entropy is 1 bit. In image (b) you have 85% black, 15% white, so the entropy is 0.6 bits.

If you make another image (c) with black and white stripes equal in width to the black stripes in image (a), you will have 50% black, 50% white again, i.e. entropy 1. But the frequency will be less than image (a).

So for this notion of entropy, the answer is: No, in general there is no relation between entropy and frequency in an arbitrary image.

However, in real world images energy is more concentrated in low frequencies than in high frequencies. So if you define entropy in terms of the distribution of such images, you will find a relationship between frequency and entropy.