Question

Two identical strings of length 'l' and '2l' vibrate with fundamental frequencies 'N' hertz and '1.5 N' hertz, respectively. The ratio of tensions for smaller length to larger ______.

Options

• 1 : 9

• 9 : 1

• 1 : 3

• 3 : 1

Answer 1

Two identical strings of length 'l' and '2l' vibrate with fundamental frequencies 'N' hertz and '1.5 N' hertz, respectively. The ratio of tensions for smaller length to larger 1 : 9.

Explanation:

N = `1/(2l) sqrt("T"_1/"m")`

`1.5 "N" = 1/(4l) sqrt("T"_2/"m")`

`therefore sqrt("T"_1/"T"_2) = ("N" xx 2l)/(1.5 "N" xx 4l) = 1/3`

`"T"_1/"T"_2 = 1/9`