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Oscillations

Question

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Vibrations of rope tied by two rigid ends shown by equation y = cos 2πt sin2πx, then minimum length of the rope will be

1 m

$\frac{1}{2} m$

5 m

2πm

Solution

B.

$\frac{1}{2} m$

Equation of vibration

y = 1( cos2 $πt$ sin2 $πx$ )

= 1 cos2 $π$ sin $\frac{π x}{\frac{1}{2}}$

Comparing this equation with

y = $a \cos 2 π \sin \frac{π x}{λ}$

Hence fro above equation

a = 1

Minimum length of string

= $\frac{1}{2} a$

= $\frac{1}{2} \times 1$

Mininmum length of string

= $\frac{1}{2} m$

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