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Grade: 11
        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?
5 years ago

Answers : (1)

Navjyot Kalra
askIITians Faculty
654 Points
							Sol. Phase difference  ∅ = π/2
f and λ are same. So, ω is same.
Y base 1 = r sin wt, y base 2 = rsin(wt + π/2)
From the principle of superposition
y = y base 1 + y base 2 → = r sin wt + r sin (wt + π/2)
= r[sin wt + sin(wt + π/2)]
= r[2sin{(wt + wt + π /2)/2} cos {(wt – wt – π/2)/2}]
⇒ y = 2r sin (wt + π /4) cos (–π/4)
Resultant amplitude = √2 r = 4 √2 mm (because r = 4 mm)

						
5 years ago
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