Question

The equation of a progressive wave is $y=8\sin [\pi \left(\frac{t}{10}-\frac{x}{4}\right)+\frac{\pi }{4}]$. The wavelength of the wave is

• A. $8m$
• B. $4m$
• C. $2m$
• D. $10m$

Answer 1

The correct option is A $8m$

The given equation is :
$y=8\sin [\pi (\frac{t}{10}-\frac{x}{4})+\frac{\pi }{4}]$

on simplifying

$y=8\sin [\frac{\pi t}{10}-\frac{\pi x}{4}+\frac{\pi }{4}]$

Hence the equation is of the form :
$y=A\sin (kx-\omega t+\varphi )$
where, A=amplitude $\varphi =$initial phase

Hence, $k=\frac{2\pi }{\lambda }=\frac{\pi }{4}$

$⟹\lambda =8m$