Question

Two identical strings X and Z made of same material have tension T_x and T_z in them If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio `"T"_x/"T"_"z"` is ______.

Options

• 1.25

• 0.44

• 1.5

• 2.25

Answer 1

Two identical strings X and Z made of same material have tension T_x and T_z in them If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio `"T"_x/"T"_"z"` is 2.25.

Explanation:

Given: Tension on string X is T_x tension on string Z is T_z, both the strings are made of same material, fundamental frequency for string X is f_x = 450 Hz, fundamental frequency for string Z is f_z = 300 Hz.

To find: `"T"_x/"T"_"z"`

Let the length of the two strings be L and the mass per unit length of the strings be µ.

Fundamental frequency of string X :

`f_x = 1/(2"L") sqrt("T"_x/mu)`        ...(i)

Fundamental frequency of string Z :

`f_z = 1/(2"L") sqrt("T"_"z"/mu)`      ...(ii)

From equations (i) and (ii) :

 `"T"_x/"T"_"z" = f_x^2/f_"z"^2`

= 2.25