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
Aiden Mathew Denny , 6 Years ago
Grade 10
1 Answers
Arun
Last Activity: 6 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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