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Assuming that frequency V of a vibration string may depend upon (i) applied load F (ii) length L of the string and mass per unit length (m) . Prove that V = 1/L * root F/m

Assuming that frequency V of a vibration string may depend upon (i) applied load F (ii) length L of the string and mass per unit length (m) . Prove that V = 1/L * root F/m

Grade:10

1 Answers

Arun
25750 Points
5 years ago

v=La Tb mc ________________ EQ. 1

v=T-1 , L=L , T=MLT-2 , m=ML-1

Putting values of v,L,T and m in eq 1

T-1=[L]a [MLT-2] b [ML-1]C

T-1=La+b-c Mb+c T-2b

Comparing powers on both sides,

a+b-c=0 => a=-1

b+c=0 => C=-2

-2b=-1 => b=1

Putting values of a,b and c in eq. 1 , we get

v=L-1 T-2 M-1/2

v=k 1/L √T/ √M where k is constant

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