A tuning fork A of unknown frequency produces 5beats s ^ - 1 with a...

Initially beat frequency $= 5Hz$

so, ${ρ}_{A} = 340 \pm 5 = 345Hz,$ or $335Hz$

after filing frequency increases slightly so, new value of frequency of $A > {ρ}_{A}$

Now, beat frequency $= 2Hz$

$⇒$ new ${ρ}_{A} = 340 \pm 2 = 342Hz,$ or $338Hz$

hence, original frequency of $A$ is ${ρ}_{A} = 335Hz$