Answer:
b.
Explanation:
In case of Single Slit, diffraction will occur.
Then In Single slit Diffraction, width of central fringe is

where D= distance b/w screen and slit
a= slit width
\lambda = wavelength
Thus if Screen width increases keeping other factors same then width of central fringe becomes narrower as

On increasing the slit width the central bright fringe width The width of the central bright fringe becomes narrower.
Given that,
Frequency emitted by the bat, f = 47.6 kHz
The speed off sound in air, v = 413 m/s
We need to find the wavelength detected by the bat. The speed of a wave is given by formula as follows :

or

So, the bat can detect small objects such as an insect whose size is approximately equal to the wavelength of the sound the bat makes i.e. 8.67 mm.
This is a binary star system