Question

Two identical strings X and Z made of the 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 $\frac{T_x}{T_z}$ is:

• A. 2.25
• B. 1.25
• C. 0.44
• D. 1.50

Answer 1

The correct option is A

2.25

Given data:

Fundamental frequencies of $T_x=$450 Hz

Fundamental frequencies of $T_z=$300 Hz

$T_x/T_z$ = ?

Calculation:

The string is given by the velocity of the wave

$\nu =\sqrt{\frac{T}{\mu }}$

So,

$f=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$

For identical string l and $\mu$ will be coming

So,

$f\propto \sqrt{T}$

Therefore,

$\frac{T_x}{T_z}=\frac{f_x^2}{f_z^2}=\frac{450}{300}$

$\frac{T_x}{T_z}={\left(\frac{3}{2}\right)}^2$

$\frac{T_x}{T_z}=\frac{9}{4}$

$\frac{T_x}{T_z}=2.25$

Hence, Option (A) is correct. The ratio $\frac{T_x}{T_z}$ is 2.25.