Complex sentence: The image formed by the sand, in turn, is influenced by the frequency spectrum of the vibration only because each vibration mode is characterized by a specific frequency: therefore, the spectrum of the signal that excites the vibration determines which patterns are actually nodally displayed.
Split into simpler sentences: The image formed by the sand, in turn, is influenced by the frequency spectrum of the vibration only because each vibration mode is characterized by a specific frequency. Therefore, the spectrum of the signal that excites the vibration determines which patterns are actually nodally displayed.