The fundamental frequency of a sonometer wire is 100 Hz for a certain length and tension. If only the length of the wire is increased by 25% , when will be the percentage change in the frequencies of second harmonics in the first and second case ?

Options

A. Increase by 30%
B. Decrease by 30%
C. Decrease by 20 %
D. Increase by 20%

Answer

C

Explanation

`n_(1) = 100 ` Hz, second harmonic = `200 ` Hz
` n_(2)/n_(1) = l_(1)/l_(2) = 4/5 :. N_(2) = 100 xx 4/5 = 80 ` Hz
Its second harmonic ` = 160 ` Hz
` :. ` For 200 Hz, the change si 40
` :. ` For 100 Hz, the change is 20
Percentage change ` = 20%` decrease