A violin emits sound waves of frequency ' n 1 ' under tension T. When tension is increased by 44% , keeping the length and mass per unit length constant, frequency of sound waves becomes &

Question

A violin emits sound waves of frequency ' n 1 ​ ' under tension T. When tension is increased by 44% , keeping the length and mass per unit length constant, frequency of sound waves becomes ' n 2 ​ '. The ratio of frequency ' n 2 ​ ' to frequency ' n 1 ​ ' is

TestHub · Accepted Answer

The frequency of a stretched string is given by $n = \frac{1}{2 L} \frac{T}{μ}$

Since length $L$ and mass per unit length $μ$ are constant, $n \propto T$

Given initial tension $T_{1} = T$ and final tension $T_{2} = T + 0.44 T = 1.44 T$

$\frac{n _{2}}{n _{1}} = \frac{T _{2}}{T _{1}}$

$\frac{n _{2}}{n _{1}} = \frac{1.44 T}{T} = 1.44 = 1.2$

$\frac{n _{2}}{n _{1}} = \frac{12}{10} = \frac{6}{5}$

The ratio of frequency $n_{2}$ to $n_{1}$ is $6 : 5$ .

Answer: $6 : 5$

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