Mathematics

Problem

Two sound sources

S_{1}

and

S_{2}

are placed on the

x

-axis at

x = -13\,\text{m}

and

x = 13\,\text{m}

respectively. They emit signals in phase. A microphone moves along a path such that the time difference between receiving signals from

S_{1}

and

S_{2}

is constant, corresponding to a path difference of

10\,\text{m}

. This path is a branch of a hyperbola. Calculate the distance between the directrices of this hyperbola.