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While using two-dimensional convolutional neural networks (2D-CNNs) in image processing, it is possible to manipulate domain information using channel statistics, and instance normalization has been a promising way to get domain-invariant features. Unlike image processing, we analyze that domain-relevant information in an audio feature is dominant in frequency statistics rather than channel statistics. Motivated by our analysis, we introduce Relaxed Instance Frequency-wise Normalization (RFN): a plug-and-play, explicit normalization module along the frequency axis which can eliminate instance-specific domain discrepancy in an audio feature while relaxing undesirable loss of useful discriminative information. Empirically, simply adding RFN to networks shows clear margins compared to previous domain generalization approaches on acoustic scene classification and yields improved robustness for multiple audio-devices. Especially, the proposed RFN won the DCASE2021 challenge TASK1A, low-complexity acoustic scene classification with multiple devices, with a clear margin, and this work is extended version of the work.