First of all, we need to find the fundamental frequency of the string.
The fundamental frequency of a string is given by:
[tex]f_1 = \frac{1}{2L} \sqrt{ \frac{T}{\mu} } [/tex]
where L is the length of the string, T the tension and [tex]\mu [/tex] the linear density.
Using the information given in the exercise: L=0.660 m, T=56.7 N and [tex]\mu =8.30 \cdot 10^{-4} kg/m[/tex], we find
[tex]f_1 = \frac{1}{2\cdot 0.660 m} \sqrt{ \frac{56.7 N}{8.30 \cdot 10^{-4}kg/m} }=198 Hz [/tex]
The beat frequency is given by the difference in frequency between the fundamental frequency of the string and the tuning fork (196 Hz), so it is:
[tex]f_b = 198 Hz - 196 Hz = 2 Hz[/tex]
