Is 10,000 images for one class of spectrograms good enough for music classification model?
Agreed with Emre. One thing that can be helpful when asking the question is to look at comparable datasets since there's usually some around. For spectrograms for example, there are 150,000 samples w/ 12 labels here, 2890 samples here, and 1 million samples with various labels here. 

Find a few examples and gauge a rough order of magnitude of samples per class given how close the tasks are to yours. That should give you at-least a starting point. Then, if lets say one set is very large, usually someone will have written a paper using that set, and that can help start both the architecture and size jumping off point (and maybe a baseline for transfer learning) of your task.