Question

lf the length of a stretched string is shortened by 40 % and the tension is increased by 44%, then the ratio of the final and initial fundamental frequencies are ____________.

Options

• 1 : 3

• 3 : 4

• 4 : 3

• 2 : 1

Answer 1

lf the length of a stretched string is shortened by 40 % and the tension is increased by 44%, then the ratio of the final and initial fundamental frequencies are 2 : 1.

Explanation:

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

`therefore "n"_2/"n"_1 = l_1/l_1 sqrt("T"_2/"T"_1)`

`therefore "n"_2/"n"_1 = l_1/((l_1 - 40/100l_1))  sqrt((("T"_1 + 44/100"T"_1))/"T"_1)`

`= 100/60 xx 12/10 = 2`

`therefore "n"_2 : "n"_1 = 2 : 1`