### Waves - Result Question 1

#### 1. A wave travelling in the +ve $x$-direction having displacement along $y$-direction as $1 m$, wavelength $2 \pi m$ and frequency $\frac{1}{\pi} Hz$ is represented by [2013]

(a) $y=\sin (2 \pi x-2 \pi t)$

(b) $y=\sin (10 \pi x-20 \pi t)$

(c) $y=\sin (2 \pi x+2 \pi t)$

(d) $y=\sin (x-2 t)$

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#### Solution:

- (d) The standard equation of a wave travelling along $x$-axis (+ve direction) is given by, $Y=A \sin (k x-\omega t)$ where, angular frequency, $\omega=2 \pi f$

$\Rightarrow \quad \frac{2 \pi}{\pi}=2 \quad[\because f=\frac{1}{\pi}]$

angular wave number, $k=\frac{2 \pi}{\lambda} \Rightarrow \frac{2 \pi}{2 \pi}=1$

$[\because \lambda=2 \pi]$ $\therefore Y=1 \sin (x-2 t)[\because$ Amplitude, $A=1 m]$

If the sign between $t$ and $x$ terms is negative the wave is propagating along +(ve) $X$-axis and if the sign is positive then wave moves in -(ve) $X$-axis direction.