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Question

If n1,n2 and n3 are the fundamental frequencies of three segments of a string of length l, then the original fundamental frequency n of the string is given by

A
1n=1n1+1n2+1n3
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B
1n=1n1+1n2+1n3
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C
n=n1+n2+n3
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D
n=n1+n2+n3
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Solution

The correct option is A 1n=1n1+1n2+1n3

Total length of the string l=l1+l2+l3 .......(1)
We know that,
Fundamental frequency of a string,
n=12lTμ
l=12nTμ

Similarly,

l1=12n1Tμ ; l2=12n2Tμ ; l3=12n3Tμ

From (1) we can write that,

12nTμ=12n1Tμ+12n2Tμ+12n3Tμ

1n=1n1+1n2+1n3

Thus, option (a) is the correct answer.

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