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The speed of a wave on a string is $150 \mathrm{~ms}^{-1}$ when the tension is 120 N . The percentage…
The speed of a wave on a string is $150 \mathrm{~ms}^{-1}$ when the tension is 120 N . The percentage increase in the tension in order to raise the wave speed by $20 \%$ is
44 40 20 22 Solution
For wave on a string,
$\begin{aligned}
& \mathrm{v}_1=150 \mathrm{~ms}^{-1}, \mathrm{~T}_1=120 \mathrm{~N}, \mathrm{v}_2=1.2 \mathrm{v}_1 \\
& \therefore \text { Speed of wave, } \mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mu}} \Rightarrow \mathrm{v} \propto \sqrt{\mathrm{~T}} \\
& \therefore \frac{\mathrm{v}_2}{\mathrm{v}_1}=\sqrt{\frac{\mathrm{T}_2}{\mathrm{~T}_1}} \Rightarrow \frac{1.2 \mathrm{v}_1}{\mathrm{v}_1}=\sqrt{\frac{\mathrm{T}_2}{120}} \\
& \therefore \mathrm{~T}_2=172.8 \mathrm{~N}
\end{aligned}$
$\therefore \quad \%$ increase in tension,
$\begin{aligned}
& \% \Delta \mathrm{~T}=\frac{\mathrm{T}_2-\mathrm{T}_1}{\mathrm{~T}_1} \times 100=\frac{172.8-120}{120} \times 100 \\
& =44 \%
\end{aligned}$
Asked in: AP EAMCET 2024 (19 May Shift 2)
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