Verified Solution • 2025–26 Session moderate

QAIPM-2012-Ph-1768: NEET 2012 Physics - Class 11 AIPM-2012-Ph-1768 Solution: When a string is divided into three segments of length \(l_1\), …

When a string is divided into three segments of length l1l_1, l2l_2 and l3l_3 the fundamental frequencies of these three segments are ν1\nu_1, ν2\nu_2 and ν3\nu_3 respectively. The original fundamental frequency (ν\nu) of the string is

Multiple Choice Options

  • A ν=ν1+ν2+ν3\sqrt{\nu}=\sqrt{\nu_1}+\sqrt{\nu_2}+\sqrt{\nu_3}
  • B ν=ν1+ν2+ν3\nu=\nu_1+\nu_2+\nu_3
  • C 1ν=1ν1+1ν2+1ν3\frac{1}{\nu}=\frac{1}{\nu_1}+\frac{1}{\nu_2}+\frac{1}{\nu_3}
  • D 1ν=1ν1+1ν2+1ν3\frac{1}{\sqrt{\nu}}=\frac{1}{\sqrt{\nu_1}}+\frac{1}{\sqrt{\nu_2}}+\frac{1}{\sqrt{\nu_3}}

Step-by-Step Verified Solution

Let l be the length of the string. Fundamental frequency is given by _ = 1 2 l T _ _ v _ 1 l   ( _ T and _ are constants) Here, l 1 = k _ 1 , l 2 = k _ 2 , l 3 = k _ 3 and l = k _ But l = l 1 + l 2 + l 3 1 _ = 1 _ 1 + 1 _ 2 + 1 _ 3

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