Question

The wave described by $y=0.25\sin (10\pi x-2\pi t),$ where x and y are in meters and t in seconds, is a wave travelling along the

• A. +ve x direction with frequency 1 Hz and wavelength $\lambda =0.2m$
• B. -ve x direction with amplitude 0.25 m and wavelength $\lambda =0.2m$
• C. -ve x direction with frequency 1 Hz
• D. +ve x direction with frequency p Hz and wavelength $\lambda =0.2m$

Answer 1

Answer: (A)

$y=0.25\sin (10\pi x-2\pi t)$
$y_{\max }=0.25$
$k=\frac{2\pi }{\lambda }=10\pi$
$\Rightarrow \lambda =0.2m$
$\omega =2\pi f=2\pi$
$\Rightarrow f=1Hz$
The sign is negative inside the bracket.
Therefore this wave travels in the positive $x$-direction.