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Equation for two waves is given as `y_(1)=asin(omegat+phi_(1)), y_(2)=asin(omegat+phi_(2))`. If ampitude and time period of resultant wave does not change, then calculate `(phi_(1)-phi_(2))`. |
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Answer» The equation of resultant wave is , `y=y_(1)+Y_(2)=asin(omegat+phi_(1))+asin(omegat+phi_(2))` `=2asin(((omegat+phi_(1))+(omegat+phi_(2)))/(2))` `cos(((omegat+phi_(1))-(omegat+phi_(2)))/(2))` `=2acos((phi_(1)-phi_(2))/(2))sin[omegat+(phi_(1)+phi_(2))/(2)]` The amplitude of the resultant wave is, `A=2acos((phi_(1)-pphi_(2))/(2))` ltbgt Given, `A=a, ` then `a=2acos((phi_(1)-phi_(2))/(2))` or `cos((phi_(1)-phi_(2))/(2))=(1)/(2)=cos60^(@)` or `(phi_(1)-phi_(2))/(2)=60^(@) or phi_(1)-phi_(2)=120^(@)` |
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