The speed of a transverse ray in a stretched string is given by v = √T/m ; where T ¾ Tension in the string; m ¾ Linear density of string (mass per unit length).
(i) If A is the area of cross-part of the line then m ¾ ρA
=> v=√(T/ρA) = √(S/ρ) ; where S ¾ Stress = T/A
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(ii) If string is operated by some weight then
T = mg
=> v = √{(Mg)/m}
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(iii) If removed weight is immersed in a liquid of density s and r ¾ density of material of the suspended load then
T = mg(1 - σ/ρ)
=> v = √{Mg(1-σ/ρ)}/m
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(iv) If two hard systems help of stretched string are maintained at temperature difference of Dq then due to elasticity of string.
T = YAαΔθ => v = √{YAαΔθ)/m = √{YαΔθ)/d
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where Y ¾ Young's modulus of elasticity of string. A ¾ Area of cross section of string, a ¾ Temperature coefficient of thermal relation, d ¾ Density of wire m/A
(v) In a solid body ; v = √η/ρ where h ¾ Modulus of rigidity ; ρ = Density of the material.
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