Question

the frequency of vibration (v)of a string depends upon length (l),tension (T) and mass per unit length (m) of string . draw the relation of m,l and T with V using dimensions

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Answer 1

Answer:

f = kl^-2Tm^-1 = (KT)/ml^2

Ezplanation :

According to the question , frequency f=F(l,T,m)=k la Tb mc, here k=any dimensionless constant, l=length of string , T= tension in string

using property of dimension, i.e, dimension of LHS=RHS

    [M0L0T−1]=[La][MLT−2]b[ML−1]c

                       =[La+b−c][Mb+c][T−2b−c]

comparing both sides we get :

   (1)   b+c=0⇒b=−c

    (2)  −2b−c=−1⇒b=1,c=−1

  (3)   a+b−c=0⇒a=−2

so, we get the following formula , 

f=k l−2T m−1=ml2kT