Question:
A uniform rope of mass 0.1 kg and length 2.5 m hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point 0.5 m distance from lower end will be
A uniform rope of mass 0.1 kg and length 2.5 m hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point 0.5 m distance from lower end will be
Updated On: Jul 6, 2022
- $5\, ms^{-1},2.24\, ms^{-1}$
- $10\, ms^{-1},3.23\, ms^{-1}$
- $7.5\, ms^{-1},1.2\, ms^{-1}$
- None of the above
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The Correct Option is A
Solution and Explanation
Mass per unit length $m = \frac{M}{L}$
Tension at the point T = mass of x metre of rope $\times$ g
$\hspace50mm = mxg$
where x is the distance of point from lower end.
Velocity of transverse wave along tihe string
$\hspace40mm v= \sqrt{\frac{T}{m}} =\sqrt{x\frac{mg}{m}}= \sqrt{xg}$
Given, $x = 0.5 $ and $g = 10\, ms^{-2}$
$\hspace15mm v= \sqrt{0.5 \times 10} =\sqrt5 = 2.24\, ms^{-1}$
At upper end, the velocity is given by
$\hspace25mm v =\sqrt {rg} = \sqrt{2.5 \times 10} = 5\, ms^{-1}$
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The waves that are produced when an electric field comes into contact with a magnetic field are known as Electromagnetic Waves or EM waves. The constitution of an oscillating magnetic field and electric fields gives rise to electromagnetic waves.
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Electromagnetic waves can be grouped according to the direction of disturbance in them and according to the range of their frequency. Recall that a wave transfers energy from one point to another point in space. That means there are two things going on: the disturbance that defines a wave, and the propagation of wave. In this context the waves are grouped into the following two categories:
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