Question

A segment of wire vibrates with a fundamental frequency of 450 Hz under a tension of 9 kg weight. The tension at which the fundamental frequency of the same wire becomes 900 Hz is ____________.

Options

• 36 kg-weight

• 27 kg-weight

• 18 kg-weight

• 72 kg-weight

Answer 1

A segment of wire vibrates with a fundamental frequency of 450 Hz under a tension of 9 kg weight. The tension at which the fundamental frequency of the same wire becomes 900 Hz is 36 kg-weight.

Explanation:

`"n"_1 = "k" sqrt"T"_1`

`"n"_2 = "k" sqrt"T"_2`

`Rightarrow "n"_1/ "n" _2 = sqrt("T"_1/"T"_2) Rightarrow ("n"_1/"n"_2)^2 = "T"_1/"T"_2`

`Rightarrow "T"_2 = "T"_1 xx ("n"_2/"n"_1)^2`

` = 9 xx (900/450)^2`

`= 9 xx 4 = 36  "kg weight".`