To solve this problem it is necessary to apply the related concepts to string vibration. This concept shows the fundamental frequency of a string due to speed and length, that is,
[tex]f = \frac{v}{2L}[/tex]
Where
v = Velocity
L = Length
Directly if the speed is maintained the frequency is inversely proportional to the Length:
[tex]f \propto \frac{1}{L}[/tex]
Therefore the relationship between two frequencies can be described as
[tex]\frac{f_2}{f_1}=\frac{l_1}{l_2}[/tex]
[tex]f_2 = \frac{l_1}{l_2}(f_1)[/tex]
Our values are given as,
[tex]l_1 = 24"\\f_1 = 247Hz\\l_2 = 18"[/tex]
Therefore the second frequency is
[tex]f_2 = \frac{l_1}{l_2}(f_1)\\f_2 = \frac{24}{18}(247)\\f_2 = 329.33Hz[/tex]
The frequency allocation of 329Hz is note E.
