Explain repression of the tryptophan operon. how does it work when tryptophan is present and when tryptophan is not present

Trp operon is controlled by both repression and attenuation. If we just look at repression, then:

Present of Tryptophan: you don't need the biosynthetic genes to be expressed (think being lazy and only doing what you absolutely have to do - why spend energy when you don't have to!).

So, when tryptophan is present it binds the trp repressor (they are dimers) which changes the conformation of the dimer so it can now bind and repress transcription for the operon.

No Tryptophan, the repressor proteins still dimerize but without tryptophan binding to them, the shape is wrong and the dimer cannot bind and inhibit transcription of the operon.

Attenuation is also important ... not sure if you need this but;

There is a leader peptide that is transcribed upstream of the trp operon. Within this leader sequence are two back-to-back trp codons - pretty unusual

If there's lots of tryptophan the ribosome that comes along isn't slowed down because there are lots of charged tRNA-TRP. When the ribosome isn't slowed down, then the mRNA hairloop structure that forms is called 3-4 and is a termination signal for the RNA polymerase - the ribosome pops off and the operon is not transcribed.

When there's little tryptophan, the ribosome comes across those two TRP codons and stalls. This then forms a 2-3 hairloop structure which allows the RNA polymerase to continue transcription of operon.