Answer:
4 Hz
Explanation:
The frequency of a string is given by
[tex]f =\dfrac{k}{2l}\sqrt{\dfrac{T}{\mu}}[/tex]
where k is a constant that determines the mode of the vibration,
l is the length of the string,
T is the tension in the string,
[tex]\mu[/tex] is the linear density or mass per unit length of the string
It follows that f is directly proportional to [tex]\sqrt{T}[/tex] provided other factors are constant.
This relation is expressed as
[tex]\dfrac{f_1}{\sqrt{T_1}}=\dfrac{f_2}{\sqrt{T_2}}[/tex]
[tex]f_1[/tex] is the frequency when tension is [tex]T_1[/tex] and [tex]f_2[/tex] is the frequency when tension is [tex]T_2[/tex].
[tex]f_2=f_1\sqrt{\dfrac{T_2}{T_1}}[/tex]
[tex]f_2=523\sqrt{\dfrac{610}{620}} =519[/tex]
The beat frequency is the difference in the frequencies. Hence,
f = 523 - 519 = 4 Hz
