Question

Equation of $251mpu$ harmonic progression wave arriving at a point in the medium simultaneously
$y_1=0.05\sin 2\pi (50t-\frac{x}{\lambda })m$
$y_2=0.05\sin 2\pi (55t-\frac{x}{2})m$
Calculate wavelength of first wave and beat frequency when sounded together.

Answer 1

$y_1=0.05\sin 2\pi (50t-\frac{x}{2})$

$y=A\sin 2\pi (\frac{t}{T}-\frac{x}{\lambda })$

$⟹\lambda =2$ by comparing

$T_1=\frac{1}{50},f_1=\frac{1}{T_1}=50Hz$

$y_2=0.05\sin 2\pi (55t-\frac{x}{20})m$

$T_2=\frac{1}{55},f_2=55Hz$

Beat frequency $=55-50$

$=5Hz$