Two waves of the same frequency have opposite phase when the phase angle between them is
A
$360°$
B
$180°$
C
$90°$
D
$0°$

Question

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

Examoogle · Accepted Answer

$180^\circ$

Explanation: Two waves are said to be in opposite phase (or antiphase) when the phase difference between them is exactly $180^\circ$ (or $\pi$ radians). At this phase shift, the peak of one wave corresponds exactly to the trough of the other, resulting in destructive interference.

Working Principle: In sinusoidal waveforms represented by $y_1 = A \sin(\omega t)$ and $y_2 = A \sin(\omega t + \phi)$, the phase difference is $\phi$. When $\phi = 180^\circ$, $y_2 = A \sin(\omega t + 180^\circ) = -A \sin(\omega t)$. The instantaneous sum of these two waves at any time $t$ is zero, causing complete cancellation.

Key Formulas: $\Delta \phi = 180^\circ = \pi 	ext{ radians}$ — condition for opposite phase; $y_1 + y_2 = A \sin(\omega t) + A \sin(\omega t + 180^\circ) = 0$ — destructive interference result

Key Points: Opposite phase implies a shift of half a wavelength ($\lambda/2$); Resultant amplitude of two equal magnitude waves in opposite phase is zero; Also referred to as being in 'anti-phase'; Crucial for noise cancellation and differential signaling technologies

Advantages: Complete destructive interference useful in active noise control; High common-mode rejection in differential signal transmission

Disadvantages: Leads to loss of signal power in parallel transmission systems; Can cause signal cancellation errors in poorly designed circuits

Applications: Active noise-cancelling headphones; Balanced audio transmission systems (XLR cables); Differential amplifiers in IC design

Additional Info: A phase shift of $0^\circ$ or $360^\circ$ indicates the waves are in-phase (constructive interference).. A phase shift of $90^\circ$ indicates the waves are in quadrature.

Answer: B is correct — Two waves have opposite phase when the phase angle between them is $180^\circ$.

Exam Tip: Always remember that $360^\circ$ shift is equivalent to being in-phase with the original wave, while $180^\circ$ is the fundamental condition for anti-phase.

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