The two parts of a sonometer wire divided by a movable knife edge , differ in length by `2 mm` and produce `1 beat//s` , when sounded together . Find their frequencies if the whole length of wire is `1.00 m`.

Explanation

Let `l_(1), l_(2)` be the lengths of the two parts of sonometer wire. Therefore, `l_(1)+l_(2)=100cm` and `(l_(1)-l_(2))=0.2cm.`
`:. l_(1)=50.1cm and l_(2)=49.9cm`
As `m=v_(2)-v_(1):. 1=v_(2)-v_(1)` …(i)
Also `(v_(2))/(v_(1))=(l_(1))/(l_(2))=(50.1)/(49.9)`
From (i), `(50.1)/(49.9) v_(1)-v_(1)=1 or (0.2)/(49.9)v_(1)=1`
`v_(1)=(49.9)/(0.2)=249.5Hz`
Again, from (i),
`v_(2)=1+v_(1)=1+249.5=250.5Hz`