A wave travelling in the positive $x$-direction having displacement along $y$-direction as 1 m, wavelength…
A wave travelling in the positive $x$-direction having displacement along $y$-direction as 1 m, wavelength $2\pi\text{ m}$ and frequency of $1/\pi\text{ Hz}$ is represented by
$y = \sin (x - 2t)$
$y = \sin (2\pi x - 2\pi t)$
$y = \sin (10\pi x - 20\pi t)$
$y = \sin (2\pi x + 2\pi t)$
Solution
Given, amplitude, $A = 1\text{ m}$
The wave is represented by the equation,
$y = A \sin (kx - \omega t)$
$= \sin \left(\frac{2\pi}{2\pi} x - 2\pi \times \frac{1}{\pi} t\right) = \sin (x - 2t)$