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VITEEE 2009 Paper

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PART - I (PHYSICS)

When a wave transverses a medium the displacement of a particle located at x at a time t is given by y = a sin (bt-cx). Where a , b and c are constants of the wave. Which of the following is a quantity with dimensions?

$\frac{y}{a}$
bt
cx
$\frac{b}{c}$

Solution:

Here, y = a sin (bt-cx)

Comparing this equation with general wave equation

y = a \sin\left(\frac{2\pi t}{T} - \frac{2\pi x}{\lambda}\right)

we get

b=\frac{2\pi}{T}, c=\frac{2\pi}{\lambda}

(a) Dimensions of

\frac{y}{a} = \frac{\text{[L]}}{\text{[L]}} =

Dimensionless

(b) Dimensions of

bt = \frac{2\pi}{T} \cdot t = \frac{\text{[T]}}{\text{[T]}} =

Dimensionless

(c) Dimensions of

cx = \frac{2\pi}{\lambda} \cdot x = \frac{\text{[L]}}{\text{[L]}} =

Dimensionless

(d) Dimensions of

\frac{b}{c} = \frac{\frac{2\pi}{T}}{\frac{2\pi}{\lambda}} = \frac{\lambda}{T} = \text{[LT}^{-1}\text{]}

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