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(B) The frequency of a sonometer wire is given by $f_w = \frac{v}{2L}$.Since the tuning fork produces $5 \ beats/sec$ in both cases,the frequency of t

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$195$

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(B) The frequency of a sonometer wire is given by $f_w = \frac{v}{2L}$.Since the tuning fork produces $5 \ beats/sec$ in both cases,the frequency of the wire $f_w$ is either $(f + 5)$ or $(f - 5)$.For the shorter length $(95 \ cm)$,the frequency is higher: $f_1 = \frac{v}{2 	imes 0.95} = f + 5 \dots (1)$For the longer length $(100 \ cm)$,the frequency is lower: $f_2 = \frac{v}{2 	imes 1.00} = f - 5 \dots (2)$Dividing $(1)$ by $(2)$:$\frac{f+5}{f-5} = \frac{1.00}{0.95} = \frac{100}{95} = \frac{20}{19}$$19(f + 5) = 20(f - 5)$$19f + 95 = 20f - 100$$f = 195 \ Hz$.

Length of a sonometer wire is either $95 \ cm$ or $100 \ cm$. In both the cases,a tuning fork produces $5 \ beats/sec$ with the wire. The frequency of the tuning fork is- (in $Hz$)

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