Question 528: 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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