Answer:
658 Hz
Explanation:
Third harmonic is given by
[tex]f_A=3\times 440\\\Rightarrow f_A=1320\ Hz[/tex]
Second harmonic is given by
[tex]f_E=2\times 659\\\Rightarrow f_E=1318\ Hz[/tex]
The difference between the two frequencies is 1320-1318 = 2 Hz
Now, [tex]\Delta f=4\ Hz[/tex]
The beat frequency is given by
[tex]\Delta f=3f_A-2f_E'\\\Rightarrow f_E'=\dfrac{3f_A-\Delta f}{2}\\\Rightarrow f_E'=\dfrac{1320-4}{2}\\\Rightarrow f_E'=658\ Hz[/tex]
The frequency of the E string when she hears four beats per second is 658 Hz