Multimodal content, such as mixing text with images, presents significant challenges to rumor detection in social media. Existing multimodal rumor detection has focused on mixing tokens among spatial and sequential locations for unimodal representation or fusing clues of rumor veracity across modalities. However, they suffer from less discriminative unimodal representation and are vulnerable to intricate location dependencies in the time-consuming fusion of spatial and sequential tokens. This work makes the first attempt at multimodal rumor detection in the frequency domain, which efficiently transforms spatial features into the frequency spectrum and obtains highly discriminative spectrum features for multimodal representation and fusion. A novel Frequency Spectrum Representation and fUsion network (FSRU) with dual contrastive learning reveals the frequency spectrum is more effective for multimodal representation and fusion, extracting the informative components for rumor detection. FSRU involves three novel mechanisms: utilizing the Fourier transform to convert features in the spatial domain to the frequency domain, the unimodal spectrum compression, and the cross-modal spectrum co-selection module in the frequency domain. Substantial experiments show that FSRU achieves satisfactory multimodal rumor detection performance.