Question Number 38816 by NECx last updated on 30/Jun/18
$${Two}\:{waves}\:{are}\:{represented}\:{by} \\ $$$${y}_{\mathrm{1}} ={Asin}\omega{t}\:{and}\:{y}_{\mathrm{2}} ={Asin}\left(\omega{t}−\delta\right). \\ $$$${What}\:{is}\:{the}\:{resultant}\:{of}\:{the}\:{two} \\ $$$${waves}? \\ $$$$\left.{ii}\right){determine}\:{the}\:{amplitude}\:{of}\:{the} \\ $$$${resultant}\:{wave}\:{and}\:{under}\:{which} \\ $$$${condition}\:{will}\:{it}\:{be}\:{constructive}\:{or} \\ $$$${destructive}. \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 30/Jun/18
$${y}_{\mathrm{1}} +{y}_{\mathrm{2}} =\mathrm{2}{Asin}\left({wt}−\frac{\delta}{\mathrm{2}}\right){cos}\left(\frac{\delta}{\mathrm{2}}\right) \\ $$$${amplitude}=\mathrm{2}{Acos}\left(\frac{\delta}{\mathrm{2}}\right) \\ $$$${constructive}\:{when}\:{cos}\left(\frac{\delta}{\mathrm{2}}\right)=\pm\mathrm{1} \\ $$$${cos}\left(\frac{\delta}{\mathrm{2}}\right)={cos}\left({n}\Pi\right) \\ $$$$\delta=\mathrm{2}{n}\Pi \\ $$$${destructive}\:{when}\:{cos}\left(\frac{\delta}{\mathrm{2}}\right)=\mathrm{0}={cos}\left({n}\frac{\Pi}{\mathrm{2}}\right) \\ $$$$\delta={n}\Pi \\ $$$$ \\ $$
Commented by NECx last updated on 30/Jun/18
$${wow}…..\:{Thank}\:{you}\:{so}\:{much}. \\ $$