Explain in stepwise manner
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T=tension in the string
l=length of the string
d=mass density of the string= mass of the string/length of the string
formula for fundamental frequency (f)=1/2l(√(T/d))
d=m/(l1+l2+l3)
Since the T/d of the string is at all the points of the string it can be substituted by a constant k
v1=(1/2l1)×k
1/v1=2l1/k....(i)
Similarly,
1/v2=2l2/k....(ii)
1/v3=2l3/k....(iii)
v=(1/2(l1+l2+l3))×k
1/v=2(l1+l2+l3)/k
Adding (i),(ii) and (iii),
1/v1+1/v2+1/v3=2l1/k+2l2/k+2l3/k=2(l1+l2+l3)/k=1/v
So 1/v=1/v1+1/v2+1/v3
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adj. 1 arranged in the manner of or resembling steps. 2 (Music) (U.S.) proceeding by melodic intervals of a second.
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