Explanation

(a) The frequency, when a sonometer wire of vibrating length is 48 cm.
$v_{1} = \frac{c}{2 \times \iota_{1}} = \frac{c}{2 \times 0.48} = \frac{c}{0.96}$
The frequency, when a sonometer wire of vibrating length is 50 cm.
$v_{2} = \frac{c}{2 \times \iota_{2}} = \frac{c}{2 \times 0.50} = \frac{c}{1.00}$
$v_{1} - v_{2} = 8$ $v_{1}$
[table] $v_{2}$ | 4 ; $v_{3}$ | 4 [/table]
$\therefore\frac{v_{1}}{v_{2}} = \frac{1.00}{096} \Longrightarrow \delta$
$v_{1} = \frac{1.00}{0.96}v_{2}$
$\because v_{2} + 8v_{2} \times \frac{100}{96}$
$v_{2} = 192\ Hz.$
The frequency of the tuning fork.
$v = v_{2} + 4 = 192 + 4 = 196\ Hz$