Free/Libre Open Source Software
“A shot timer is a shot activated timer used in shooting sports, which starts the competitor by an audible signal and also records the competitor’s time electronically by detecting the sound of each shot together with the time from the start signal. When the competitor is finished the timer will show the time from the start signal until the last shot. The time is usually recorded to hundredths of a second, which is required by competitions…” (Thanks Wikipedia)
Edit: Typically one pushes a button to make a loud “beep” noise and start the timer. Then loud “bangs” cause a display to show the elapsed time.
They are often dedicated hand-held devices, but Android devices should also be able to do it, and there are proprietary apps in play store: