The beat frequency observed when two sound waves $y_{1} = 0.5 sin (410 t)$ and $y_{2} = 0.5 sin (454 t)$ travel in the same direction is

5

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3

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7

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2

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4

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Solution

The correct option is C $7$
We have, $y_{1} = 0.5 sin (410 t)$
and $y_{2} = 0.5 sin (454 t)$
From this equation gives $ω_{1}$ and $ω_{2}$
i.e., $ω_{1} = 410$
$2 π n_{1} = 410$
$n_{1} = \frac{410}{2 π} = 65.2$
again $ω_{2} = 454$
$2 π n_{2} = 454$
$n_{2} = \frac{454}{2 π} = 72.2$
The beat frequency $n = n_{1} - n_{2}$
$= 72.2 - 65.2 = 7$

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