Fall detection for the elderly is a well-researched problem with several proposed solutions, including wearable and non-wearable techniques. While the existing techniques have excellent detection rates, their adoption by the target population is lacking due to the need for wearing devices and user privacy concerns. Our paper provides a novel, non-wearable, non-intrusive, and scalable solution for fall detection, deployed on an autonomous mobile robot equipped with a microphone. The proposed method uses ambient sound input recorded in people's homes. We specifically target the bathroom environment as it is highly prone to falls and where existing techniques cannot be deployed without jeopardizing user privacy. The present work develops a solution based on a Transformer architecture that takes noisy sound input from bathrooms and classifies it into fall/no-fall class with an accuracy of 0.8673. Further, the proposed approach is extendable to other indoor environments, besides bathrooms and is suitable for deploying in elderly homes, hospitals, and rehabilitation facilities without requiring the user to wear any device or be constantly "watched" by the sensors.