SATHEE: Waves - Result Question 44

Waves - Result Question 44

46. If $n_{1}, n_{2}$ and $n_{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by :

[2014, 2012, 2000]

(a) $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$

(b) $\frac{1}{\sqrt{n}} = \frac{1}{\sqrt{n_{1}}} + \frac{1}{\sqrt{n_{2}}} + \frac{1}{\sqrt{n_{3}}}$

(c) $\sqrt{n} = \sqrt{n_{1}} + \sqrt{n_{2}} + \sqrt{n_{3}}$

(d) $n = n_{1} + n_{2} + n_{3}$

Show Answer

Answer:

Correct Answer: 46. (a)

Solution:

(a)

$n = \frac{1}{2 l} \sqrt{\frac{T}{m}}$ or, $n \propto \frac{1}{l}$ or $n l =$ constant, $K$

$∴ n_{1} l_{1} = K$

$n_{2} l_{2} = K, n_{3} l_{3} = K$

Also, $l = l_{1} + l_{2} + l_{3}$

or, $\frac{K}{n} = \frac{K}{n_{1}} + \frac{K}{n_{2}} + \frac{K}{n_{3}}$

or, $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$

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