A wave travelling in the positive x-direction having maximum displacement along y-direction as $1 ext{ m}$,

Question

A wave travelling in the positive x-direction having maximum displacement along y-direction as $1 	ext{ m}$, wavelength $2\pi 	ext{ m}$ and frequency of $1/\pi 	ext{ Hz}$ is represented by

Accepted Answer

1. **Identify the given parameters:** Maximum displacement (Amplitude), $A = 1 	ext{ m}$; Wavelength, $\lambda = 2\pi 	ext{ m}$; Frequency, $f = \frac{1}{\pi} 	ext{ Hz}$.
2. **Calculate wave number ($k$):** The wave number is given by $k = \frac{2\pi}{\lambda}$.
   $$k = \frac{2\pi}{2\pi} = 1 	ext{ m}^{-1}$$
3. **Calculate angular frequency ($\omega$):** The angular frequency is given by $\omega = 2\pi f$.
   $$\omega = 2\pi 	imes \frac{1}{\pi} = 2 	ext{ rad/s}$$
4. **Formulate the wave equation:** The general equation for a progressive wave travelling in the positive x-direction is $y = A \sin(kx - \omega t)$ or $y = A \sin(\omega t - kx)$ .
   Substituting the calculated values into the first form:
   $$y = 1 \cdot \sin(1 \cdot x - 2 \cdot t) = \sin(x - 2t)$$

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