Question

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

• A. 5
• B. 3
• C. 7
• D. 2
• E. 4

Answer 1

Answer: (C)

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