Two waves of the same frequency have opposite phase when the phase angle between them is ____
A
360 degree
B
180 degree
C
90 degree
D
degree

Question

Two waves of the same frequency have opposite phase when the phase angle between them is ____

Examoogle · Accepted Answer

180 degree

Explanation: Two waves of the same frequency are said to be in 'opposite phase' (or phase opposition) when their phase difference is $180^\circ$ or $\pi$ radians. At this phase angle, the peak of one wave corresponds exactly to the trough of the other, resulting in destructive interference. Working Principle: In a sinusoidal waveform, the instantaneous value is given by $v(t) = V_m \sin(\omega t + \phi)$. If two waves have a phase difference of $180^\circ$, their expressions become $v_1 = V_m \sin(\omega t)$ and $v_2 = V_m \sin(\omega t + 180^\circ) = -V_m \sin(\omega t)$. Because $\sin( heta + 180^\circ) = -\sin( heta)$, the waves are exact negatives of each other, leading to total cancellation if summed. Key Formulas: $v_1(t) = V_m \sin(\omega t)$; $v_2(t) = V_m \sin(\omega t \pm 180^\circ) = -V_m \sin(\omega t)$ Key Points: Phase opposition occurs at odd multiples of $180^\circ$ (i.e., $\Delta \phi = (2n+1)180^\circ$).; Destructive interference occurs when two signals are $180^\circ$ out of phase.; Noise cancellation technologies often utilize this principle by generating an 'anti-noise' wave at $180^\circ$ phase shift. Advantages: Used in active noise cancellation.; Essential in differential signaling to improve common-mode noise rejection. Disadvantages: Can lead to complete signal cancellation if not intended in communication circuits.; Causes phase distortion in analog filters. Applications: Active noise cancelling headphones.; Differential amplifier input stages.; Push-pull power amplifier configurations. Additional Info: A phase angle of $0^\circ$ or $360^\circ$ indicates the waves are 'in phase'.. A phase angle of $90^\circ$ indicates the waves are in 'quadrature'. Answer: B is correct — Waves are in opposite phase when the phase angle difference between them is $180^\circ$ or $\pi$ radians. Exam Tip: Always remember that $180^\circ$ phase shift is equivalent to a sign inversion in electrical signals, which is the foundational principle of differential amplifiers.

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