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 (410 t)$
and $ y_{2}=0.5 \sin (454 t)$
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 $n=n_{1} \sim n_{2}$
$=72.2-65.2=7$