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Preeti Dabral 2 years, 8 months ago
According to Newton the change in pressure & volume in air is an isothermal process.
Therefore he calculated,v =√(p/p) on substituting the require value he found, the velocity of sound was not in close agreement with the observation value. Then Laplace pointed out the error in Newton’s formula. According to Laplace the change in pressure and volume is an adiabatic process. So he calculated the value of sound as, v =√(yr/p) on putting require value he found velocity of sound as 332m/s very closed to observed theory.
Posted by Monisha Malgotra 2 years, 8 months ago
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Preeti Dabral 2 years, 8 months ago
You need to know the equation of motion. The force for the pendulum is given by F=−kx. Newtons equation tell you F=ma=mx¨. So you need to solve
mx¨=−kx.(1)
You know that the solution will be of oscillatory form. So you set x=Acos(2πt/T) and you want to obtain T. Plugging this ansatz into the equation (1), you obtain
−m(2π)2T2Acos(2πt/T)=−kAcos(2πt/T).
You see that the equation is fulfilled if
m(2π)2T2=k.
Solving for T, you obtain the result.
Posted by Ruhi Deshmukh 2 years, 8 months ago
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M.S.Bhati Bhati 2 years, 8 months ago
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Posted by Harshita Mehta 2 years, 8 months ago
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Preeti Dabral 2 years, 8 months 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:
- 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]
- 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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