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VITEEE 2013 Paper

Section: Physics

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Question : 5 of 120

Marks: +1, -0

If a progressive wave is represented as y = 2 sin π

\left(\frac{t}{2}-\frac{x}{2}\right)

where x is in metre and t is in second, then the distance travelled by the wave in 5 s is

5 m
10 m
25 m
32 m

Solution:

Given, y = 3 sin π

\left(\frac{t}{2}-\frac{x}{4}\right)

= 3 sin

\left(\frac{\pi t}{2} - \frac{\pi x}{4}\right)

Comparing it with standard equation

y = r sin

\frac{2\pi}{\lambda}

(vt - x)

= r sin

\left(\frac{2\pi v t}{\lambda} - \frac{2\pi x}{\lambda}\right)

We have,

\frac{2\pi v}{\lambda}

=

\frac{\pi}{2}

or v =

\frac{\lambda}{4}

and

\frac{2\pi}{4}

=

\frac{\pi}{4}

or λ = 8m

∴ v =

\frac{8}{4}

= 2 m/s

So, the distance travelled by wave in t second = vt = 2 x 5 = 10 m

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