Two side$-$by$-$side loudspeakers at the origin emit $684$ HzHz sound waves on a day when the speed of sound is $342$ m$/$sm$/$s$.$ A microphone $2\mathrm{.}00$ mm away on the xx$-$axis detects a maximum in the sound intensity. Then one of the speakers is moved slowly along the yy$-$axis.

Part A

How far does it move before the microphone first detects a minimum in the sound intensity?

Express your answer with the appropriate units.

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yy $=$

$\mathrm{.}25$m