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# On the basis of dimensional consideration …

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On the basis of dimensional consideration write the formula for speed of transfer way on a string and in a solid

Preeti Dabral 2 months, 3 weeks ago

Speed of a transverse wave on a stretched string. The wave velocity through a medium depends on its inertial and elastic properties. So the transverse wave through a stretched string is determined by two factors:

1. Tension T in the string is a measure in the string. Without tension no can propagate in the string. of elasticity disturbance Dimensions of T = [Force] = [MLT 2]
2. Mass per unit length or linear mass density m of the string so that the string can store kinetic energy.
Dimensions of  {tex}m=\frac{[\text { Mass }]}{[\text { Length }]}=\left[\mathrm{ML}^{-1}\right]{/tex}
Now, dimensions of ratio {tex}\frac{T}{m}=\frac{\left[\mathrm{MLT}^{-2}\right]}{\left[\mathrm{ML}^{-1}\right]}=\left[\mathrm{L}^{2} \mathrm{~T}^{-2}\right]{/tex}
As the speed v has the dimensions [LT-1] so we can express v in terms of T and m as {tex}v=C \sqrt{\frac{T}{m}}{/tex}
From detailed mathematical analysis! or from experiments, the dimensionless constant C = 1. Hence the speed of transverse waves on a stretched string is given by
{tex}v=\sqrt{\frac{T}{m}}{/tex}

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