A sinusoidal wave is propagating in negative x -direction in a string stretched along x-axis. A particle of string at $x = 2 m$ is found at its mean position and it is moving in positive y-direction at $t = 1 \sec$ . The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1 meter, $π / 2$ meter and $2 π rad / \sec$ respectively. The equation of the wave is

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None of these

$y = 0.1 \sin (2 π (t - 1) + 4 (x - 2))$

$y = 0.1 \sin (4 π (t - 1) + 8 (x - 2))$

$y = 0.1 \sin ((t - 1) - (x - 2))$

answer is C.

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Detailed Solution

$\begin{array}{l} The equation of wave moving in negative x -direction, \\ assuming origin of position at x = 2 and origin of time \\ (i.e. initial time) at t = 1 sec . \\ y = 0.1 \sin (2 π t + 4 x) \\ Shifting the origin of position to left by 2 m , that is, to x \\ = 0 . Also shifting the origin of time backwards by 1 sec , \\ that is to t = 0 sec . \\ y = 0.1 \sin (2 π (t - 1) + 4 (x - 2)) \end{array}$