Tuning fork A of frequency 258Hz gives 8 beats with a tuning fork B. When the tuning fork A is filed and again A and B are sounded, the number of beats heard decreases. The frequency of B is …….Hz

When filed, frequency of a tuning fork decreases. 

It is given that the number of beats produced is decreased when fork B is filed. 

$\left|{\mathrm{f}}_{\mathrm{A}}-{\mathrm{f}}_{\mathrm{B}}\right|$decreases with decrease in ${\mathrm{f}}_{\mathrm{B}}$ means 

${\mathrm{f}}_{\mathrm{B}}>{\mathrm{f}}_{\mathrm{A}}$

$\because {\mathrm{f}}_{\mathrm{B}}-{\mathrm{f}}_{\mathrm{A}}=8\Rightarrow {\mathrm{f}}_{\mathrm{B}}={\mathrm{f}}_{\mathrm{A}}+8$

$\therefore {\mathrm{f}}_{\mathrm{B}}=266\mathrm{Hz}$