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Question

If n1, n2, n3, ... are frequencies of segments of a stretched string, the frequency n of the string is given by

A
n=n1×n2×n3×...
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B
n=n1+n2+n3+...
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C
1n=1n1+1n2+1n3+...
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D
none of the above
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Solution

The correct option is B 1n=1n1+1n2+1n3+...
Frequency of the first segment can be given by:
n1=12l1Tml1=12n1Tm
Similarly the frequency of the second segment can be given by:
n2=12l2Tml2=12n2Tm and so on.
The total length of the string can be given by:
l=l1+l2+....=12n1Tm+12n2Tm+...=d12Tm[1n1+1n2+...]
1=12lTm[1n1+1n2+...]=ν[1n1+1n2+...]
1n=[1n1+1n2+...]

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