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Yes, you would just get constructive and destructive interference. Where the wave forms meet. They would just pass though each other

You could see this by filling up your bath tub with some water and then poke your finger at opposite ends of the bath. When the two wave forms meet they will cross though each other, where the crescents meet it will be constructive interference and where the troughs meet it would be destructive interference

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Q: Can two wavefront cross each other's?
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