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Question

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
26.46 cm, 0.71 rad
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B
28.50 cm, 1 rad
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C
30 cm, 0.71 rad
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D
30.46 cm, 0.6 rad
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Solution

The correct option is A 26.46 cm, 0.71 rad
Let 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=tan1(0.866)=40.89
ϕ1=0.714 rad
Hence, option (a) is the correct answer.

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