Question

$x_{1}=12 \, sin\left(\right.484\pi t-7\pi x\left.\right)$ and $x_{2}=12 \, sin\left(\right.480\pi t-7\pi x\left.\right)$ represent the equation of two sound waves and $x$ and $t$ are in metre and second. Beat frequency (in $Hz$ ) produced by these two waves is

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (C)

$x_{1}=12sin\left(\right.484\pi t-7\pi x\left.\right)$
$=12sin2\pi \left(242 t - \frac{7 x}{2}\right)$
$\therefore $ frequency $n_{1}=242Hz$
$x_{2}=12sin\left(\right.480\pi t-7\pi x\left.\right)$
$=12sin2\pi \left(240 t - \frac{7 x}{2}\right)$
$\therefore $ frequency $n_{2}=240Hz$
Beat frequency $=n_{1}-n_{2}=2$