A long rubber tube having mass 0.9 kg is fastened to a fixed support and the free end of the tu

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A long rubber tube having mass 0.9 kg is fastened to a...

A long rubber tube having mass $0.9 \mathrm{~kg}$ is fastened to a fixed support and the free end of the tube is attached to a cord which passes over a pulley and supports an object, with a mass of $5 \mathrm{~kg}$ as shown in fig. If the tube is struck by a transverse blow at one end, the time required for the pulse to reach the other end is : (a) $5 \mathrm{~s}$ (b) $0.47 \mathrm{~s}$ (c) $4.7 \mathrm{~s}$ (d) $3.2 \mathrm{~s}$

A long rubber tube having mass $0.9 \mathrm{~kg}$ is fastened to a fixed support and the free end of the tube is attached to a cord which passes over a pulley and supports an object, with a mass of $5 \mathrm{~kg}$ as shown in fig. If the tube is struck by a transverse blow at one end, the time required for the pulse to reach the other end is :
(a) $5 \mathrm{~s}$
(b) $0.47 \mathrm{~s}$
(c) $4.7 \mathrm{~s}$
(d) $3.2 \mathrm{~s}$

Key Concepts

Wave Propagation in a Stretched Medium

This concept involves the behavior of mechanical disturbances as they travel along a medium that is under tension. In such systems, the speed at which a pulse or wave travels is controlled by both the tension in the medium and its mass per unit length. Understanding this propagation is fundamental in topics such as vibrations and wave mechanics in continuous media.

Tension Due to Gravitational Force

In many physical setups, a flexible medium such as a string or tube is subjected to tension as a result of a weight or force acting at its end. The gravitational force on a mass attached to the medium generates a nearly uniform tension along its length, which directly influences the wave speed in the medium.

Linear Mass Density

Linear mass density is defined as the mass of a medium per unit length. It is a key parameter in wave mechanics because it quantifies how the mass is distributed along the string or tube, affecting how quickly disturbances can travel through the medium.

Wave Speed Formula

For transverse waves on a stretched string or tube, the speed of the wave is given by the formula v = ?(T/?), where T is the tension in the medium and ? is its linear mass density. This formula provides the link between the physical properties of the medium and the time it takes for a pulse to travel a given distance.

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