For the travelling harmonic wave $y(x,t) = 2.0 \cos[2\pi(10t - 0.0080x + 0.35)]$ with $x$ in cm and

Question

For the travelling harmonic wave $y(x,t) = 2.0 \cos[2\pi(10t - 0.0080x + 0.35)]$ with $x$ in cm and $t$ in seconds, what is the phase difference between oscillatory motion of two points separated by a distance of 0.5 m?

Professor PC Thomas Classes · Answer

Phase difference $\Delta \phi = k \Delta x$. Here, $k = 2\pi(0.0080)$ rad/cm. For $\Delta x = 0.5$ m = 50 cm, $\Delta \phi = 2\pi(0.0080) 	imes 50 = 0.8\pi$ rad.