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# A wave is represented by y1=10cos(5x+25t), where x and y are measured in centimetres and t in seconds. A second wave for which y2=20cos(5x+25t+π/3) interferes with the first wave. Find the amplitude and phase of the resultant wave.

A
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B
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C
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D
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Solution

## The correct option is A 26.46 cm, 0.71 radLet Anet be the amplitude and ϕ1 be the phase of the resultant wave. From the given wave function, Amplitude (A1) of wave-1 =10 cm and A2=20 cm Phase difference (ϕ)=π/3 From formula, Anet=√A21+A22+2A1A2cosϕ =√102+202+2×10×20×cos(π/3) =26.46 cm From figure, tanϕ1=A2sinϕA1+A2cosϕ ⇒tanϕ1=20sin6010+20cos60=0.866 ⇒ϕ1=tan−1(0.866)=40.89∘ ⇒ϕ1=0.714 rad Hence, option (a) is the correct answer.  Suggest Corrections  0      Similar questions
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