For a travelling harmonic wave$y(x,t) = 2.0cos2\pi(10t - 0.0080x + 0.35)$, where $x$ and $y$ are in

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For a travelling harmonic wave$y(x,t) = 2.0cos2\pi(10t - 0.0080x + 0.35)$, where $x$ and $y$ are in cm and $t$ in $s$. The phase difference between oscillatory motion of two points separated by a distance of 0.5 m is:

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Sol. [Key Concept: Travelling wave y=A cos(ωt−kx) — read ω, k, v] $y(x,t) = 2.0cos2\pi(10t - 0.008x + 0.35)$Total phase$$\begin{matrix} & \phi = 20\pi - 2\pi 	imes 8 	imes 10^{- 3}x + 2\pi 	imes 0.35 \ & \Delta\phi = k\Delta x \ & \Delta\phi = 2\pi 	imes 8 	imes 10^{- 3}\Delta x \ & \ = 2\pi 	imes 8 	imes 10^{- 3} 	imes \left( \frac{100}{2} ight) \ & \ = 8\pi 	imes 10^{- 1} = 0.8\pi \end{matrix}$$

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