Wave Mechanics Vibration Of String Question 40
Question: Three similar wires of frequency n1, n2 and n3 are joined to make one wire. Its frequency will be
[CBSE PMT 2000]
Options:
A) $ n=n _{1}+n _{2}+n _{3} $
B) $ \frac{1}{n}=\frac{1}{n _{1}}+\frac{1}{n _{2}}+\frac{1}{n _{3}} $
C) $ \frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n _{1}}}+\frac{1}{\sqrt{n _{2}}}+\frac{1}{\sqrt{n _{3}}} $
D) $ \frac{1}{n^{1}}=\frac{1}{n _{1}^{2}}+\frac{1}{n _{2}^{2}}+\frac{1}{n _{3}^{2}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ n=\frac{1}{2l}\sqrt{\frac{T}{m}} $
Therefore $ n _{1}l _{1}=n _{2}l _{2}=n _{3}l _{3}=k $
$ l _{1}+l _{2}+l _{3}=l $
Therefore $ \frac{k}{n _{1}}+\frac{k}{n _{2}}+\frac{k}{n _{3}}=\frac{k}{n} $
Therefore $ \frac{1}{n}=\frac{1}{n _{1}}+\frac{1}{n _{2}}+\frac{1}{n _{3}}+……..
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BETA
