Must a creature be able to hear the caster’s whisper to be targeted by the Dissonant Whispers spell?

Dissonant whispers says:

You whisper a discordant melody that only one creature of your choice within range can hear, wracking it with terrible pain. The target must make a Wisdom saving throw.

I initially took the first sentence to mean that the creature must be able to hear the caster’s whisper to be targeted by dissonant whispers, but now I’m not so sure.

Perhaps I’ve read it one too many times… although only one creature can hear the whisper, the spell doesn’t require that the creature must hear the whisper. Am I reading too much into this?