For a travelling harmonic wave y (x, t) = 2.0 2π (10t - 0.0080x + 0.35),$$y (x, t) = 2.0 \cos 2\pi (10t - 0.0080x + 0.35),$$ here x$x$ and y$y$ are in cm$\mathrm{cm}$ and t$t$ in s$\mathrm{s}$. The phase difference between oscillatory motion of two points separated by a distance of 0.5 ~m$0.5 \mathrm{~m}$ is:

Related Formula

Phase φ = 2π ( ft - (x)/(λ) ) k = 2π × (coefficient of x)$\phi = 2\pi \left( ft - \frac{x}{\lambda} \right) \implies k = 2\pi \times (\text{coefficient of } x)$

Core Logic

From the given wave equation y = 2.0 (20π t - 0.016π x + 0.7π)$y = 2.0 \cos(20\pi t - 0.016\pi x + 0.7\pi)$: The wave number k$k$ (which is the coefficient of x$x$ in the phase) is:

Given separation Δ x = 0.5 ~m = 50 ~cm$\Delta x = 0.5 \mathrm{~m} = 50 \mathrm{~cm}$ (since x$x$ is defined in cm$\mathrm{cm}$ in the equation).

Step 1: Calculate Phase Difference

Pattern Recognition

Always ensure the unit of Δ x$\Delta x$ matches the unit of x$x$ mandated by the wave equation. Omitting the conversion from meters to cm leads to an incorrect magnitude factor of 100$100$.

Chapter Mix

Class 11 Physics: Waves