Question
In an experiment, it was found that the string vibrates in $3$ loops when 'x' g was as mass of placed on the scale pan. What must be placed on the pan to make the string vibrate in 9 loops?
✓
Answer
Frequency of vibration of string vibrating in P loops is
$\text{v}=\frac{\text{P}}{2\text{l}}\sqrt{\frac{\text{T}}{\mu}}$
$TP^2 =$ constant
$\text{T}_1\text{P}^2_1=\text{T}_2\text{P}^2_2$
$\text{T}_2=\text{T}_1\Big(\frac{\text{P}_1}{\text{P}_2}\Big)^2$
$=\text{x}\Big(\frac{3}{9}\Big)^2=\text{x}\frac{9}{81}=\frac{\text{x}}{9}$
$\text{v}=\frac{\text{P}}{2\text{l}}\sqrt{\frac{\text{T}}{\mu}}$
$TP^2 =$ constant
$\text{T}_1\text{P}^2_1=\text{T}_2\text{P}^2_2$
$\text{T}_2=\text{T}_1\Big(\frac{\text{P}_1}{\text{P}_2}\Big)^2$
$=\text{x}\Big(\frac{3}{9}\Big)^2=\text{x}\frac{9}{81}=\frac{\text{x}}{9}$
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