Along with the 5 genes (trpE, trpD, trpC, trpB and trpA) coded by the trp operon there is a short protein-coding region at the 5' end of the operon called trpL. This does not code for a functional product but the very process of transcribing and then translating this sequence is the basis of another level of regulation of the operon (besides negative control by TrpR). This is regulation by attenuation. The basic idea is that even if transcription initiates when trp levels are high (which can happen since TrpR will occasionally come free from the Operator sequence) transcription will be terminated early (attenuated).
The process is fairly complicated and I will not give a diagram here but you can watch the video below. The basis of attenuation is as follows:
The RNA within the trpL region can form two different structures. One is a transcription-termination signal, the other is not.
Whether the termination signal is formed or whether the alternate structure forms depends on the position of the ribosome that is translating just behind RNA Polymerase.
If the ribosome gets stalled and is farther behind RNAP then the termination signal does NOT form. This is because the stretch of RNA just behind the RNAP is not covered by the ribosome and so it is free to H-bond other stretches of RNA. This leads to the formation of the second structure and prevents formation of the termination structure. Therefore, transcription does not terminate (attenuate)
If the ribosome does not get stalled then it is right behind RNAP and covers the region of RNA necessary for the formation of the non-termination structure. Since the structure is not formed, the transcription termination structure can form and transcription terminates (attenuates).
So, it all comes down to ribosome stalling. The important feature here is that the TrpL sequence contains two consecutive Trp codons. If trp levels in the cell are low then when the ribosome reaches these codons it will have to wait a longer time for a charged trp-tRNA to enter. Therefore, if trp levels are low the ribosome will stall at these codons. As we have seen, if it stalls then transcription DOES NOT terminate.
Therefore:
Low Trp = Ribosome Stalling = No termination structure = No Attenuation = EXPRESSION
High Trp = NO Ribosome Stalling = Termination structure = Attenuation = NO EXPRESSION