A violin emits sound waves of frequency ' $\mathrm{n}_1$ ' under tension T. When tension is increased by $44…

A violin emits sound waves of frequency ' $\mathrm{n}_1$ ' under tension T. When tension is increased by $44 \%$, keeping the length and mass per unit length constant, frequency of sound waves becomes ' $\mathrm{n}_2$ '. The ratio of frequency ' $\mathrm{n}_2$ ' to frequency ' $n_1$ ' is
  1. $5: 6$
  2. $6: 7$
  3. $6: 5$
  4. $7: 6$

Solution

Frequency, $\mathrm{n}_1=\frac{1}{2 \mathrm{~L}} \sqrt{\frac{\mathrm{~T}_1}{\mu}}$
Tension is increased by $44 \%$, $\begin{aligned} & \mathrm{T}_2=\mathrm{T}_1+\frac{44}{100} \mathrm{~T}_1=1.44 \mathrm{~T}_1 \\ \therefore \quad \mathrm{n}_2 & =\frac{1}{2 \mathrm{~L}} \sqrt{\frac{1.44 \mathrm{~T}_1}{\mu}} \\ & \frac{\mathrm{n}_2}{\mathrm{n}_1}=\sqrt{\frac{1.44 \mathrm{~T}_1}{\mathrm{~T}_1}}=\frac{6}{5} \end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 2)

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