Two parts of sonometer wire, divided by a movable knife edge differ in length by 2 cm and produce 1 beat/s when sounded together. Assume fundamental frequencies. If the total length of the wire is 100 cm. The frequencies. If the total length of the wire is 100 cm. The frequencies of the two parts of the wire are

Options

A. `51Hz`.`50Hz`
B. `50.5Hz`,`49.5Hz`
C. `25Hz`,`24Hz`
D. `25.5Hz`,`24.5Hz`

Answer

D

Explanation

Let the two parts are `L_1` and `L_2` then `L_1=49cm` and `L_2=51cm`
For same tension `fprop(1)/(L)`
`impliesf_1L_1=f_2L_2`
`implies49f_1=51f_2` .(i)
Also `f_1-f_2=1` .(ii)
From (i) and (ii): `f_1=25.5Hz`
`f_2=24.5`