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Question

Two waves, travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitude of each wave is 4 mm and the phase difference between the waves is 90, what is the resultant amplitude ?

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Solution

Phase difference, ϕ=π2,

f and λ are same. So, ω is same

y1=r sin wt

y2=r sin(wt+π2)

From the principle of superposition

y=y1+y2

=r sin wt+r sin(wt+π2)

=r[sin wt+sin(wt+π2)]

=r[2 sin{(wt+wt+π22)}cos{wtwtπ22}]

y=2r sin(wt+π4)cos(π4)y=2r sin(wt+(π4))

Resultant amplitude

=2r=42mm

(because r = 4 mm)


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