A tuning fork A of unknown frequency produces $\text{5\hspace{0.17em}beats}/\text{s}$ with a fork of frequency 340Hz. When fork A is filed, the beat frequency decreases to $\text{2\hspace{0.17em}beats}/\text{s}$/ What is the initial frequency of fork A before filing ?

Initially beat frequency = 5 Hz
so, ${\rho }_{\text{A}}=340\pm 5=345\text{\hspace{0.17em}Hz}$, or 335 Hz
After filing frequency increases slightly
so, new value of frequency of  $\text{A}>{\text{ρ}}_{\text{A}}$
Now, beat frequency = 2 Hz
⇒ new ${\rho }_{\text{A}}=340\pm 2=342\text{\hspace{0.17em}Hz}$ , or 335Hz
hence, original frequency of A is ${\rho }_{\text{A}}=335\text{\hspace{0.17em}Hz}$