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Calculate the length of an iron rod which can be used to produce ultrasonic waves of 20kHz Given - Y = 11.6 × 1010N/m2, ρ = 7.23 × 103 kg/m3
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Given:$Young's \ Modulus\ (Y)=11.6\times 10^{10}\ N/m^2$   $Density\ (\rho)=7.23\times 10^3\ kg/m^3$ $Frequency\ (\eta )=20\ kHz=20\times 10^3\ Hz$

 

$\eta =\dfrac{1}{2l}\sqrt{\dfrac{Y}{\rho}}\\ l=\dfrac{1}{2\eta }\sqrt{\dfrac{Y}{\rho}}=\dfrac{1}{2\times 20\times 10^3}\sqrt{\dfrac{11.6\times 10^{10}}{7.23\times 10^3}}$

$Length\ (l) = \ 0.1\ m$

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