Question

The fundamental frequency of a string stretched with a weight 'M' kg is 'n' hertz. Keeping the vibrating length constant, the weight required to produce its octave is ______.

Options

• M

• 4M

• 2M

• 8M

Answer 1

The fundamental frequency of a string stretched with a weight 'M' kg is 'n' hertz. Keeping the vibrating length constant, the weight required to produce its octave is 4M.

Explanation:

`"n" prop sqrt"T", "n"_2 = 2"n"_1`

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

`2 = sqrt("T"_2/"T"_1)`

`therefore "T"_2/"T"_1` = 4

∴ T₂ = 4T₁

∴ M₂ = 4M