Beat phenomenon is physically meaningful, only if

| ω_{1} - ω_{2} | >> | ω_{1} + ω_{2} |

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| ω_{1} - ω_{2} | << | ω_{1} + ω_{2} |

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\frac{ω_{1}}{ω_{2}} < 17

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| ω_{1} + ω_{2} | >> \frac{ω_{1}}{ω_{2}}

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Solution

The correct option is B $| ω_{1} - ω_{2} | << | ω_{1} + ω_{2} |$
$y_{1} = s i n w_{1} t$
$y_{2} = s i n w_{2} t$
$y_{1} + y_{2} = A (s i n w_{1} t + s i n w_{2} t)$

$y = 2 A s i n (\frac{w_{1} + w_{2}}{2}) t c o s (\frac{w_{1} - w_{2}}{2}) t$

$y = A^{'} s i n w^{'} t$

$w^{'} = \frac{w_{1} + w_{2}}{2}$

$A^{'} = 2 A c o s (\frac{w_{1} - w_{2}}{2}) t$

For beat to be meaningful, $| w_{1} - w_{2} | << | w_{1} + w_{2} |$

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If $ω_{1}, ω_{2}$ and $ω_{3}$ represent the work done in moving a particle from A to B along three different paths 1, 2, and 3 respectively in the presence of a gravitational field, then find the correct relation between $ω_{1}, ω_{2}$ and $ω_{3}$ .