I thought I'd share a circuit for generating pulse trains that repeat for a certain duration and frequency. The example is shown in an online circuit simulator and uses two timers. One controls the burst width and burst frequency and the other controls the individual pulses that make up the burst.
You can tinker with the circuit using the links below:
Removed superfluous AND gate and added a NOR gate to fix error on reset. The extra NOR gate may not be needed for the real circuit. The 555 controlling burst width and frequency was replaced with a square wave source to better illustrate that any square wave source can be used to control the burst width and frequency.
First version. Had some redundant components that were not needed.