Question

A piano wire B vibrates at a fundamental frequency of 600 Hz. A second identical wire A produces 6 beats per second with it when the tension in A is slightly increased. Find the ratio of the tension in A to the tension in B.

• A. 1.02
• B. 0.5
• C. 2
• D. 3

Answer 1

The correct option is A 1.02

Here given $f_B=600=\frac{1}{2L}\sqrt{\frac{T_B}{\mu }}$

$2^{nd}$ identical wire A will have same tension and frequency.

As the tension increases frequency increases

It is given that 6 beats are produces when tension in A is increased.

so, $f_A=600=\frac{1}{2L}\sqrt{\frac{T_A}{\mu }}$

$\Rightarrow \frac{f_B}{f_A}=\frac{600}{606}=\sqrt{\frac{T_B}{T_A}}$

$\Rightarrow \frac{\sqrt{T_A}}{\sqrt{T_B}}=\frac{606}{600}=1.01$ $\Rightarrow \frac{T_A}{T_B}=1.02$.