When the sirens sing they are creating sound waves. A sound wave is a mechanical wave and therefore requires a medium to pass through. Lucky for the sailors air and water can act as this medium. So even while drowning you can still appreciate the enchantingly deadly song of the sirens. But what makes a siren song deadly? Using the idea of resonance as evidence we can assume that its the frequency at which the sirens sing their songs which give it its deadly touch. Resonance occurs when one object emitting a sound wave with a specific frequency cause another object to vibrate with the same frequency. So here's my theory. Sirens sing at a particular natural frequency. This frequency then vibrates our eardrums. Our eardrums send this wave to our brains to interpret. Our brains do so by creating chemical paths in our brains. This is true of all sound. Now I'll attempt to explain they mythological part. The natural frequency at which the sirens sing is stored in a chemical path similar to the path where we store our natural euphoria's. Therefore when the sound is translated and stored in our brain it is confused with this natural drug and has a hypnotizing effect.
Cool side note: In physics the Greek symbol landau is used to represent wave length. here are some sirens names who have the landau symbol in them
Greek Name
Transliteration
Translation
Θελξιοπη
Thelxiopê
Charming Voice
Θελξινοη
Thelxinoê
Charming-the-Mind
Θελξιεπεια
Thelxiepeia
Charming
Μολπη
Molpê
Song
Αγλαοφωνος
Aglaophônos
Splendid Sounding
Αγλαοπη
Aglaopê
Splendid Voice
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