Question

What is the fractional change in tension necessary in a sonometer wire of fixed length to produce a note one octave lower than before?

• A. $3/4$
• B. $2/3$
• C. $1/2$
• D. $1/4$

Answer 1

The correct option is A $3/4$

Frequency $\nu$ of sonometer is proportional to $\sqrt{T}$, where $T$ is the tension on the string.

$\frac{{\nu }_2}{{\nu }_1}=\sqrt{\frac{T_2}{T_1}}$

$\frac{{\nu }_2^2}{{\nu }_1^2}=\frac{T_2}{T_1}$

$1-\frac{{\nu }_2^2}{{\nu }_1^2}=1-\frac{T_2}{T_1}$

It is given that: $\frac{{\nu }_2}{{\nu }_1}=\frac{1}{2}$

Hence, fractional change in tension $=\frac{T_1-T_2}{T_1}=1-1/4=3/4$