Question

Two identical strings $X$ and $Z$ made of same material have tension $T_X\text{and}{T}_Z$ in them. If their fundamental frequencies are $450\text{Hz}$ and $300\text{Hz}$, respectively, then the ratio $\frac{T_X}{T_Z}$ is:

• A. $2.25$
• B. $0.44$
• C. $1.25$
• D. $1.5$

Answer 1

The correct option is A $2.25$

Te fundamental frequency in the string is given by,

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

Where, $T\to \text{tension}$ and $\mu =\frac{\text{mass}}{\text{length}}$

$f_X=\frac{1}{2l}\sqrt{\frac{T_X}{\mu }}\text{and}{f}_Z=\frac{1}{2l}\sqrt{\frac{T_Z}{\mu }}$

As the strings are identical and made of same material, $l$ and $\mu$ are same for both the string,

$\Rightarrow \frac{f_X}{f_Z}=\frac{450}{300}=\sqrt{\frac{T_X}{T_Z}}$

$\Rightarrow \frac{T_X}{T_Z}=\frac{9}{4}=2.25$.

Hence, option $\left(A\right)$ is correct.