A wave traveling in the +ve x-direction having maximum displacement along y-direction as $1 ext{ m}$, wavele

Question

A wave traveling in the +ve 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

Given:
Amplitude (maximum displacement), $A = 1 	ext{ m}$
Wavelength, $\lambda = 2\pi 	ext{ m}$
Frequency, $f = \frac{1}{\pi} 	ext{ Hz}$

The wave number $k$ is calculated as:
$$k = \frac{2\pi}{\lambda} = \frac{2\pi}{2\pi} = 1 	ext{ m}^{-1}$$

The angular frequency $\omega$ is calculated as:
$$\omega = 2\pi f = 2\pi 	imes \frac{1}{\pi} = 2 	ext{ rad/s}$$

The general equation for a wave traveling in the positive x-direction is given by:
$$y = A \sin(kx - \omega t)$$

Substituting the derived values into the equation:
$$y = 1 \sin(1x - 2t) = \sin(x - 2t)$$

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