$$
begin{align*}
f_{1} & = 252 mathrm{Hz} \
f_{2} & = 256 mathrm{Hz} \
f_{3} & = 259 mathrm{Hz}
end{align*}
$$

$$
textbf{Definition of Beat Frequency:}
$$

$$
begin{align*}
text{beat frequency} & = text{absolute value of the difference in frequency} \
f_{beat} & = big|f_A – f_B big|
end{align*}
$$

Therefore, the beat frequency between $f_1$ and $f_2$ is

$$
begin{align*}
f_{12} & = big|f_1 – f_2 big| \
& = big|(252 – 256) big| \
& = 4 mathrm{Hz}
end{align*}
$$

Similarly, the beat frequency between $f_2$ and $f_3$ is

$$
begin{align*}
f_{23} & = big|f_2 – f_3 big| \
& = big|(256 – 259) big| \
& = 3 mathrm{Hz}
end{align*}
$$

Similarly, the beat frequency between $f_1$ and $f_3$ is

$$
begin{align*}
f_{13} & = big|f_1 – f_3 big| \
& = big|(252 – 259) big| \
& = 7 mathrm{Hz}
end{align*}
$$

Hence, the beat frequencies are

$$
begin{align*}
f_{beat} & = 3 mathrm{Hz} , 4 mathrm{Hz} text{and} 7 mathrm{Hz}
end{align*}
$$

$$
f_2=f_1+f_{beat}=441;Hz+dfrac{8.00;beats}{2.00;s}=445;Hz
$$