This app was mentioned in 4 comments, with an average of 1.00 upvote
Förderschullehrer hier: damit meine SuS sich über Lärm zunächst erstmal bewusst werden und ihn dann vermeiden können nutze ich die Noise-Meter App.
Man kann verschiedene Einstellungen wählen und die App hat den Lärmpegel im Klassenzimmer merklich verändert.
https://play.google.com/store/apps/details?id=com.pjw.noisemeter&hl=de
Would a visualisation help?
https://play.google.com/store/apps/details?id=com.pjw.noisemeter
I haven't tried this app for your purposes, so I'm not sure if it will be suitable. It supposedly has logging.
https://play.google.com/store/apps/details?id=com.pjw.noisemeter
> I wonder if you could get away with a smartphone app. I mean I'm sure there are decibel metering apps, but I wonder if they have any accuracy.
Well apparently someone actually tested this, and the paper suggests you can get accuracy within ±2 dB if you get a properly implemented app (and also the hardware plays a huge role, iPhones seem to be more reliable/uniform in this respect).
Edit: For Android, this app is free, works, and doesn't seem to contain spyware/doesn't want any suspicious permissions. No idea about accuracy (paper says hardware variance between phone models was too great), but should probably give you a ballpark idea. For iOS the linked paper has some app suggestions.
FWIW, I'm getting values in the 50s at my usual listening volume (fusion jazz played on the HD202 at a level that does a fair job of drowning ambient noise).