The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4 %$ will be ___________ $%$ .

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Solution

Speed of transverse wave is

$v = \sqrt{\frac{T}{μ}}$
Taking log on both sides
$ln v = \frac{1}{2} ln T - \frac{1}{2} ln μ$
Or, $\frac{Δ v}{v} = \frac{1}{2} \frac{Δ T}{T}$
$\Rightarrow \frac{Δ v}{v} \times 100 = \frac{1}{2} \frac{Δ T}{T} \times 100 = \frac{1}{2} \times 4$
$[μ is constant for a string]$

$∴ \frac{Δ v}{v} \times 100 = 2 %$

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The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4% will be ___________%.

Speed of transverse wave is v=√Tμ Taking log on both sides lnv=12lnT−12lnμ Or, Δvv=12ΔTT ⇒Δvv×100=12ΔTT×100=12×4 [μ is constant for a string ] ∴Δvv×100=2%

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4 %$ will be ___________ $%$ .