It is very unlikely that your hearing can be damaged by a smoke detector. A smoke detector gives a signal of around 85 decibels.Even if we assume the detector emits a sound of 90 decibels, even then you're only at risk after an hour.
The sound of a smoke detector seems much louder than it is, and that's of course its purpose.
These are the rules of thumb for exposure to noise:
- Noises below 75 dB are safe.
- With stronger sounds, make sure you don't expose your ears for too long. For example, with sounds of 85 dB, you reach the safety limit after eight hours.
- For every 3 dB added, the sound pressure approximately doubles on your eardrum. So you can be exposed to that noise for only half as long without risk, e.g. 88 dB is only safe for four hours, 91 dB for two hours.