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Physics-

General

Easy

Question

In a sine wave, position of different particles at time $t equals 0$ is shown in figure. The equation for this wave travelling along positive $x minus a x i s$ can be

$y = A s i n (ω t - k x)$
$y = A \cos (k x - ω t)$
$y = A \cos (ω t - k x)$
$y = A s i n (k x - ω t)$

The correct answer is: $y equals A blank s i n invisible function application left parenthesis k x minus omega t right parenthesis$

As is clear from figure, at $t equals 0 comma x equals 0$ , displacement $y equals 0$ . Therefore, option (a)or (d)may be correct.
In case of (d); $y equals A sin invisible function application left parenthesis k x minus omega t right parenthesis$
$fraction numerator d y over denominator d t end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets negative omega close square brackets$
$fraction numerator d y over denominator d x end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets k close square brackets$
$fraction numerator fraction numerator d y over denominator d t end fraction over denominator d y divided by d x end fraction equals fraction numerator negative omega A cos invisible function application left parenthesis k x minus omega t right parenthesis over denominator k A cos invisible function application left parenthesis k x minus omega t right parenthesis end fraction equals negative fraction numerator omega over denominator k end fraction equals negative v$
$fraction numerator d y over denominator d t end fraction equals negative v open parentheses fraction numerator d y over denominator d x end fraction close parentheses$
$i e blank p a r t i c l e blank v e l o c i t y equals negative left parenthesis w a v e blank s p e e d right parenthesis cross times s l o p e$ .
And slope at $x equals 0$ and $t equals 0$ is positive, in figure. Therefore, particle velocity is in negative y-direction.

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