Sound notoriously is poorly transmitted in space; it’s a pressure wave, and there’s just not enough material floating around in space in order for that pressure to survive any distance in space. So anything that happens outside the confines of our little atmosphere is soundless to us. There are, of course, ways to reconstruct sounds from other information, but it’s usually not a reconstruction of what you would hear if you were there and had heard the noise through an atmosphere like our Earth’s.
But we know that the Moon should be constantly getting bombarded by small pieces of debris, because our own Earth gets hit by a considerable amount of small debris, and any dirty patches of the Earth’s orbit (such as those which are responsible for the meteor showers) are also going to be dirty patches for the Moon - it’s not really that far away from us, after all.
The main difference between a meteor shower on Earth and that same meteor shower on the Moon is that the Moon has no atmosphere. The atmosphere on Earth makes these meteors much easier to spot, because they leave a luminous trail across the sky. On the Moon, you’d expect these meteorites to make it all the way down to the surface of the Moon before there was any real observable trace of them.
Even then, they don’t make much of an announcement as to their arrival! Most impacts on the surface of the Moon are from relatively tiny pieces of grit, and so even though they hit the surface at incredible speeds, it can be hard to spot the aftermath on the surface. And even if you do spot a fresh crater, you won't know exactly how long it's been there, unless you can spot the moment of impact itself. There are a few observatories which do precisely this.
Any high speed impact is doing a lot of shifting around of energy, and even if a small fraction of that energy is converted into visible light, we can observe it. There are a few of these observatories, which look at the portion of the moon which falls in shadow, because the little blip of light will be more obvious there. NASA runs the Automated Lunar and Meteor Observatory (ALAMO) from Alabama, which is a multi-telescope setup and observes the shadowed part of the moon for small flashes of light. The multi-telescope nature of the facility means that any blip of light seen by all the telescopes isn’t very likely to be random noise.
A similar setup exists in Spain, with five telescopes working together to observe the shadowy Moon, called the Moon Impacts Detection and Analysis System (MIDAS). (Astronomers love a good acronym.) This system found a particularly bright impact flash, which was suggested to have come from a reasonably large object (a few feet across), and crashed into the surface at a whipping 38,000 miles per hour. These observatories are great for pinpointing exactly when new craters should be appearing on the Moon, and with satellites which map the Moon's surface, we can tie these flashes of light to brand new craters, and work backwards more accurately to determine what kind of object must have ended up smashing into the Moon.
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