Question

The beat frequency observed when two sound waves $y_1=0.5\sin \left(410t\right)$ and $y_2=0.5\sin \left(454t\right)$ travel in the same direction is

• A. $5$
• B. $3$
• C. $7$
• D. $2$
• E. $4$

Answer 1

The correct option is C $7$

We have, $y_1=0.5\sin \left(410t\right)$
and $y_2=0.5\sin \left(454t\right)$
From this equation gives ${\omega }_1$ and ${\omega }_2$
i.e., ${\omega }_1=410$
$2\pi n_1=410$
$n_1=\frac{410}{2\pi }=65.2$
again ${\omega }_2=454$
$2\pi n_2=454$
$n_2=\frac{454}{2\pi }=72.2$
The beat frequency $n=n_1-n_2$
$=72.2-65.2=7$