While large audio-language models (LALMs) have demonstrated state-of-the-art audio understanding, their reasoning capability in complex soundscapes still falls behind large vision-language models (LVLMs). Compared to the visual domain, one bottleneck is the lack of large-scale chain-of-thought audio data to teach LALM stepwise reasoning. To circumvent this data and modality gap, we present SightSound-R1, a cross-modal distillation framework that transfers advanced reasoning from a stronger LVLM teacher to a weaker LALM student on the same audio-visual question answering (AVQA) dataset. SightSound-R1 consists of three core steps: (i) test-time scaling to generate audio-focused chains of thought (CoT) from an LVLM teacher, (ii) audio-grounded validation to filter hallucinations, and (iii) a distillation pipeline with supervised fine-tuning (SFT) followed by Group Relative Policy Optimization (GRPO) for the LALM student. Results show that SightSound-R1 improves LALM reasoning performance both in the in-domain AVQA test set as well as in unseen auditory scenes and questions, outperforming both pretrained and label-only distilled baselines. Thus, we conclude that vision reasoning can be effectively transferred to audio models and scaled with abundant audio-visual data.