Question

A wave is expressed by the equation $y= a\,sin [\frac{\pi x}{2a} - \frac{\pi t}{2}]$ where $x$ and $y$ are in $m$ and $t$ in $s$. The distance travelled by the wave in $3 \,s$ is

• A. $a$
• B. $2a$
• C. $3a$
• D. $4a$

Answer 1

Answer: (C)

$3a$

Answer 2

The given wave equation is $y=a\, sin \left(\frac{\pi x}{2a} - \frac{\pi t}{2}\right) \quad...\left(i\right)$ The standard wave equation is $y=a \,sin \left(kx- ax\right) \quad...\left(ii\right)$ $k =\frac{\pi}{2a}, \omega = \frac{\pi}{2}$ The speed of the wave is $\upsilon= \frac{\omega}{k} = \frac{\frac{\pi}{2}}{\frac{\pi}{2a}} = a$ Distance travelled by the wave in $3\, s$ is $=\upsilon t = a\left( 3\right) = 3a$