Question 489: Waves

Question

The equations of two waves acting in perpendicular directions are given as
x = $a$cos($\omega $t +$\delta $) and y = $a$cos($\omega $t + $\alpha $), where $\delta $ = $\alpha $ +  ${\pi  \over 2}$, the resultant wave represents

Accepted Answer

Given : x = acos($\omega $t + $\delta $)
and y = acos($\omega $t + $\alpha $)     ...(i)
where, $\delta  = \alpha  + \pi /2$
$ 	herefore {m{x  =  acos(}}\omega {m{t  +  }}\alpha {m{  +  }}\pi {m{/2)}}$
= Ã¢ÂÂasin($\omega $t + $\alpha $) ...(ii)
Given the two waves are acting in perpendicular direction with the same frequency and phase difference $\pi $/2.
From equations (i) and (ii),
x
2
+ y
2
= a
2
which represents the equation of a circle.

Answer

a parabola

Answer

a circle

Answer

an ellipse

Answer

a straight line

Waves

The equations of two waves acting in perpendicular directions are given as x = acos(\omega t +\delta ) and y = acos(\omega t + \alpha ), where \delta = \alpha + {\pi \over 2}, the resultant wave represents

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