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

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=0.2\, m$
$\omega=2 \pi f=2 \pi $
$\Rightarrow f=1 \,Hz$
The sign is negative inside the bracket.
Therefore this wave travels in the positive $x$-direction.