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NEET 2012
Exam
NEET
Year
2012
Subject
Physics
Chapter
Waves and Sound

NEET 2012 · Physics · Waves and Sound

When a string is divided into three segments of lengths l_1, l_2...

When a string is divided into three segments of lengths l1,l2l_1, l_2 and l3l_3, the fundamental frequencies of these three segments are v1v_1, v2v_2 and v3v_3 respectively. The original fundamental frequency (v)(v) of the string is

Options

  1. Av=v1+v2+v3\sqrt{v}=\sqrt{v_1}+\sqrt{v_2}+\sqrt{v_3}
  2. Bv=v1+v2+v3v=v_1+v_2+v_3
  3. C1v=1v1+1v2+1v3\frac{1}{v}=\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}
  4. D1v=1v1+1v2+1v3\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{v_1}}+\frac{1}{\sqrt{v_2}}+\frac{1}{\sqrt{v_3}}

Correct answer

C. 1v=1v1+1v2+1v3\frac{1}{v}=\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}

Step-by-step solution

The fundamental frequency of string v=12lTm∴v1l1=v2l2=v2l3=k\begin{aligned} v & =\frac{1}{2 l} \sqrt{\frac{T}{m}} \\ \therefore v_1 l_1 & =v_2 l_2=v_2 l_3=k \end{aligned} From Eq. (i) l1=kv1,l2=kv2,l3=kv3l_1=\frac{k}{v_1}, l_2=\frac{k}{v_2}, l_3=\frac{k}{v_3} Original length l=kvl=l1+l2+l3kv=kv1+kv2+kv31v=1v1+1v2+1v3\begin{aligned} l & =\frac{k}{v} \\ l & =l_1+l_2+l_3 \\ \frac{k}{v} & =\frac{k}{v_1}+\frac{k}{v_2}+\frac{k}{v_3} \\ \frac{1}{v} & =\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3} \end{aligned} Here, l=l1+l2+l3kv=kv1+kv2+kv31v=1v1+1v2+1v3\begin{aligned} & l=l_1+l_2+l_3 \\ & \frac{k}{v}=\frac{k}{v_1}+\frac{k}{v_2}+\frac{k}{v_3} \\ & \frac{1}{v}=\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3} \end{aligned}
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