For simple harmonic vibrations y 1 = 8 c o s ω t y 2 = 4 c o s ⁡ ( ω t + π 2 ) y 3 = 2 c o s ⁡ ( ω t + π ) y 4 = cos ⁡ ω t + 3 π 2 are superimposed on one another. The resulting amplitude and phase are respectively

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PhysicsSound WaveInterferenceMedium2 minPYQ_2020

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For simple harmonic vibrations $y_{1} = 8 c o s ω t$
$y_{2} = 4 c o s (ω t + \frac{π}{2})$
$y_{3} = 2 c o s (ω t + π)$
$y_{4} = \cos (ω t + \frac{3 π}{2})$ are superimposed on one another. The resulting amplitude and phase are respectively

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Answer:

Solution:

Resultant displacement along $X$ - axis is $x = y_{1} - y_{3} = 8 - 2 = 6$

Resultant displacement along $Y$ - axis is $y = y_{2} - y_{4} = 4 - 1 = 3$

Net displacement,

$r = \sqrt{x^{2} + y^{2}} = \sqrt{6^{2} + 3^{2}} = \sqrt{45}$

Also, $\tan θ = \frac{y}{x} = \frac{3}{6} = \frac{1}{2}$

Stream:JEESubject:PhysicsTopic:Sound WaveSubtopic:Interference

⏱ 2mℹ️ Source: PYQ_2020

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