According to those numbers for a ~10cm bar you'd need ~1 microsecond resolution, or more depending on your tolerance of the tungsten mixture (for 1% tungsten-platinum alloy substitution you'll need ~10ns resolution).
I'm not sure this is easy to achieve! A best case commercial speaker/microphone will have a ~100khz bandwidth, which gives ~10 microsecond resolution. If you're aiming for high accuracy you also need to account for thermal variations in speed of sound, which would require a some precise thermometers.
I suppose don't use a speaker/microphone then. Use a laser reflected at an angle off the bar to an optical transducer and strike the bar. Watch for the initial strike and the reflection. The time domain is nothing for a dedicated CPU such as the 64MHz one I use in my projects. If the only issue is sensing the phenomenon, I'm sure something could be devised.
I'm not sure this is easy to achieve! A best case commercial speaker/microphone will have a ~100khz bandwidth, which gives ~10 microsecond resolution. If you're aiming for high accuracy you also need to account for thermal variations in speed of sound, which would require a some precise thermometers.