A sonometer wire is divided into many segments using bridges. If fundamental natural frequencies of the segments are $n_{1}, n_{2}, n_{3}, . . . .$ then the fundamental natural frequency of entire sonometer wire will be (if the divisions were not made)

n = n_{1} + n_{2} + n_{3} + . . . .

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n = \sqrt{n_{1} \times n_{2} \times n_{3} \times . . .}

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\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}} + . . .

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none of the above

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Solution

The correct option is C $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}} + . . .$
Fundamental frequency
$n = \frac{1}{2 L} \sqrt{\frac{T}{μ}} \Rightarrow n α \frac{1}{l} l = l_{1} + l_{2} + l_{3} + . . .$
Since $l α \frac{1}{n}$
$∴ \frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}} + . . .$
Hence option (C) is correct

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A sonometer wire is divided into many segments using bridges. If fundamental natural frequencies of the segments are n1,n2,n3,.... then the fundamental natural frequency of entire sonometer wire will be (if the divisions were not made)

The correct option is C 1n=1n1+1n2+1n3+...Fundamental frequencyn=12L√Tμ⇒nα1ll=l1+l2+l3+...Since lα1n∴1n=1n1+1n2+1n3+...Hence option (C) is correct

A sonometer wire is divided into many segments using bridges. If fundamental natural frequencies of the segments are $n_{1}, n_{2}, n_{3}, . . . .$ then the fundamental natural frequency of entire sonometer wire will be (if the divisions were not made)