Question

Find beat frequency if the motion of two particles is given by

$y_{1}=0.25sin \left(310 t\right)$

$y_{2}=0.25sin \left(316 t\right)$

• A. $3$
• B. $\frac{3}{\pi }$
• C. $\frac{6}{\pi }$
• D. 6

Answer 1

Answer: (B)

The given equations of waves be written as
$y_{1}=0.25sin \left(310 t\right) \, \ldots \left(i\right)$
And $y_{2}=0.25sin \left(316 t\right) \, \, \, \ldots \left(i i\right)$
Comparing Eqs. (i) and (ii) with the standard wave equation, written as
$y=asin \left(\omega t\right) \, \, \ldots \left(i i i\right)$
We have, $\omega _{1}=310$
$\Longrightarrow v_{1}=\frac{310}{2 \pi }unit$
And $\omega _{2}=316$
$\Longrightarrow v_{2}=\frac{316}{2 \pi }unit$
Hence, beat frequency= $v_{2}-v_{1}$
$=\frac{316}{2 \pi }-\frac{310}{2 \pi }=\frac{3}{\pi } \, unit$