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Problem 6.89: Two waves of the same frequency have amplitudes $1.00$ and $2.00$. They interfere at a point where their phase difference is $60^0$.What is the resultant amplitude?

Solution:

When two waves of amplitude $A$ and $B$ interfere at a point with a phase difference of $\phi$, then the resultant amplitude is given by $R\:=\:\sqrt{A^2+B^@+2AB cos\:\phi}$.

Here $A\:=\:1.00$ and $B\:=\:2.00$ with $\phi\:=\:60^0\:=\:\frac{\pi}{3}$.

Therefore resultant amplitude, $R\:=\:\sqrt{(1.00)^2+(2.00)^@+2(1.00)(2.00) cos\:(\frac{\pi}{3})}$.

Thus, $R\:=\:\sqrt{1+4+2}\:=\:\sqrt{7}$.