Find beat frequency if the motion of two particles is given by
$y_{1} = 0.25 \sin (310 t)$
$y_{2} = 0.25 \sin (316 t)$

Question

Find beat frequency if the motion of two particles is given by y 1 = 0.25 sin ⁡ 310 t y 2 = 0.25 sin ⁡ 316 t

TestHub · Accepted Answer

The given equations of waves be written as

$y_{1} = 0.25 \sin (310 t) \dots (i)$

And $y_{2} = 0.25 \sin (316 t) \dots (i i)$

Comparing Eqs. (i) and (ii) with the standard wave equation, written as

$y = a \sin (ω t) \dots (i i i)$

We have, $ω_{1} = 310$

$⟹ ν_{1} = \frac{310}{2 π} u n i t$

And $ω_{2} = 316$

$⟹ ν_{2} = \frac{316}{2 π} u n i t$

Hence, beat frequency= $ν_{2} - ν_{1}$

$= \frac{316}{2 π} - \frac{310}{2 π} = \frac{3}{π} u n i t$

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