A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N . When t

Question

A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N . When the tension in the wire is changed to 54 N , the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is $\qquad$ Hz .\

Professor PC Thomas Classes · Answer

(6) : $l=1 \mathrm{~m}, T=6 \mathrm{~N}, T^{\prime}=54 \mathrm{~N}, b=12$ Let the frequency be $f$. $$ \begin{aligned} & \quad f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}} \ & 	ext { so, } \quad f_{1}=\frac{1}{2 	imes 1} \sqrt{\frac{6}{\mu}} \Rightarrow f_{2}=\frac{1}{2 	imes 1} \sqrt{\frac{54}{\mu}} \ & \frac{f_{2}}{f_{1}}=3 \Rightarrow f_{2}=3 f_{1} \ & 	ext { And, } f_{2}-f_{1}=12 \Rightarrow 3 f_{1}-f_{1}=12 \ & f_{1}=6 \mathrm{~Hz} \end{aligned} $$