Velocity of sound Assignment Help

Assignment Help: >> Waves and Sound >> Velocity of sound

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

(ii) If string is operated by some weight then

               T = mg

               => v =  √{(Mg)/m}

 

 

         35_Velocity of sound.png

(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

1573_Velocity of sound1.png

(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 

1108_Velocity of sound2.png

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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