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Limiting Reagent or Reactant

If n1, n2, ...

Question

If $n_{1}, n_{2}, n_{3}$ be the frequency of the segments of a stretched string, then the frequency $n$ of the string itself in terms of $n_{1}, n_{2}$ and $n_{3}$ is

A

\frac{(n_{1} n_{2} + n_{2} n_{3} + n_{1} n_{3})}{n_{1} n_{2} n_{3}}

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B

\frac{(n_{1} n_{2} + n_{3} n_{1})}{n_{1} n_{2} n_{3}}

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C

\frac{n_{1} n_{2} n_{3}}{(n_{1} n_{2} + n_{3} n_{1})}

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D

\frac{n_{1} n_{2} n_{3}}{(n_{1} n_{2} + n_{2} n_{3} + n_{3} n_{1})}

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Solution

The correct option is C $\frac{n_{1} n_{2} n_{3}}{(n_{1} n_{2} + n_{2} n_{3} + n_{3} n_{1})}$
frequency $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$
$\Rightarrow \frac{1}{n} = \frac{n_{1} n_{2} + n_{2} n_{3} + n_{3} n_{1}}{n_{1} n_{2} n_{3}}$
$\Rightarrow n = \frac{n_{1} n_{2} n_{3}}{n_{1} n_{2} + n_{2} n_{3} + n_{3} n_{1}}$

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Similar questions

l_{1}, m_{1}, n_{1}; l_{2}, m_{2}, n_{2}; l_{3}, m_{3}, n_{3}

are real quantities satisfying the six relations

l_{1}^{2} + m_{1}^{2} + n_{1}^{2} = l_{2}^{2} + m_{2}^{2} + n_{2}^{2} = l_{3}^{2} + m_{3}^{2} + n_{3}^{2} = 1

l_{2} l_{3} + m_{2} m_{3} + n_{2} n_{3} = l_{3} l_{1} + m_{3} m_{1} + n_{3} n_{1} = l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2} = 0

∣ ∣ ∣ ∣ \begin{matrix} l_{1} & m_{1} & n_{1} l_{2} & m_{2} & n_{2} l_{3} & m_{3} & n_{3} \end{matrix} ∣ ∣ ∣ ∣ = \pm k

. Find the value of

k

n_{1}, n_{2}

n_{3}

are the fundamental frequencies of three segments of a string of length

l

, then the original fundamental frequency

n

of the string is given by

n_{1}, n_{2}, n_{3}, . . .

are frequencies of segments of a stretched string, the frequency

n

of the string is given by

n_{1}, n_{2}, n_{3} . . . .

are the frequencies of segments of a stretched string, then the frequency

n

of the string can be given by

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

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