Good intuition, that is what happens. Tap water is 5 times more viscous (thicker) than water at or near its boiling point. Thicker materials absorb higher frequencies. This is why low frequencies like bass will be hesrd through your walls, but higher frequencies will not. So you’ll hear the bass kick of that car nearby but not the lyrics.
So cold water will absorb more of the high pitch “clink” of the spoon against the glass leading to a lower pitched sound heard. While hot water will let more of that high pitched “clink” come through and lead to that higher pitched sound.
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