Can machines recording an audio-visual scene produce realistic, matching audio-visual experiences at novel positions and novel view directions? We answer it by studying a new task---real-world audio-visual scene synthesis---and a first-of-its-kind NeRF-based approach for multimodal learning. Concretely, given a video recording of an audio-visual scene, the task is to synthesize new videos with spatial audios along arbitrary novel camera trajectories in that scene. We propose an acoustic-aware audio generation module that integrates prior knowledge of audio propagation into NeRF, in which we implicitly associate audio generation with the 3D geometry and material properties of a visual environment. Furthermore, we present a coordinate transformation module that expresses a view direction relative to the sound source, enabling the model to learn sound source-centric acoustic fields. To facilitate the study of this new task, we collect a high-quality Real-World Audio-Visual Scene (RWAVS) dataset. We demonstrate the advantages of our method on this real-world dataset and the simulation-based SoundSpaces dataset. Notably, we refer readers to view our demo videos for convincing comparisons.