Waves and its Characteristics: Practice Problem & Solution
Two waves are represented by the equation $y_1 = a\sin(\omega t + kx + 0.57)text{ m}$ and $y_2 = a\cos(\omega t + kx)text{ m}$, where $x$ is in meter and $t$ in sec. The phase difference between them is (2011 Pre)
Solution Explained:
To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:
The second wave can be rewritten as $y_2 = a\cos(\omega t + kx) = a\sin(\omega t + kx + \pi/2)$. The phase of $y_2$ is $\phi_2 = \pi/2 \approx 1.57text{ rad}$. The phase of $y_1$ is $\phi_1 = 0.57text{ rad}$. The phase difference is $\Delta\phi = 1.57 - 0.57 = 1.0text{ radian}$.
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