For four sine waves, moving on a string along positive x direction, displacement-distance curves (y-x curves) are shown at time t = 0. In the right column, expressions for y as function of distance x and time t for sinusoidal waves are given. All terms in the equations have general meaning. Correctly match y-x curves with corresponding equations.
Column – I Column – II
A)
P) $y = A \cos (ω t - k x)$
B)
Q) $y = - A \cos (ω t - k x)$
C)
R) $y = A \sin (ω t - k x)$
D)
S) $y = A \sin (k x - ω t)$

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$A - R, B - P, C - S, D - Q$

$A - P, B - Q, C - R, D - S$

$A - R, B - S, C - P, D - Q$

$A - R, B - R, C - S, D - Q$

answer is A.

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Detailed Solution

Use x = 0; t = 0 for y and particle velocity $\frac{\partial y}{\partial t} .$ Like for (a), y = 0 at x = 0 and t = 0. $\frac{\partial y}{\partial t} > 0$ i.e. positive therefore it matches with (R).

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	Column – I		Column – II
A)		P)	$y = A \cos (ω t - k x)$
B)		Q)	$y = - A \cos (ω t - k x)$
C)		R)	$y = A \sin (ω t - k x)$
D)		S)	$y = A \sin (k x - ω t)$