A wave travelling in the $+ve$ $x-$ direction having displacement along $y-$ direction as $1\,\, m,$ wavelength $2\pi\,\, m$ and frequency of $\frac{1}{\pi}$ $Hz$ is represented by
AIPMT 2013, Medium
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The standard equation of a wave travelling along $+ve $ $x -direction$ is given by
$y=A \sin (k x-\omega t)$
where
$A=$ Amplitude of the wave
$k=$ angular wave number
$\omega=$angular frequency of the wave
Given: $A=1 \mathrm{m}, \lambda=2 \pi \mathrm{m}, \quad v=\frac{1}{\pi} \mathrm{Hz}$
As $\quad k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{2 \pi}=1$
$\omega=2 \pi v=2 \pi \times \frac{1}{\pi}=2$
$\therefore$ The equation of the given wave is
$y=1 \sin (1 x-2 t)=\sin (x-2 t)$
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