Standing waves are set up on two strings fixed at each end, as shown in the drawing. The two strings have the same tension and mass per unit length, but they differ in length by $0\mathrm{.}51$ cm $.$ The waves on the shorter string propagate with a speed of $\backslash (42\mathrm{.}1\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ and the fundamental frequency of the shorter string is $232$ Hz $.$ Determine the beat frequency produced by the two standing waves.

Problem $38$

Beat frequency $=$