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Question: Two long strings \(A\) and \(B\), each having linear mass density \[1.2 \times {10^{ - 2}}\;{\rm{kg}...

Two long strings AA and BB, each having linear mass density 1.2×10−2  kg  m−11.2 \times {10^{ - 2}}\;{\rm{kg}}\;{{\rm{m}}^{ - 1}}, are stretched by different tensions 4.8 N4.8\,N and 7.5 N7.5\,N respectively and are kept parallel to each other with their left ends at x = 0. Wave pulses are produced on the strings at the left ends at t=0t = 0 on string AA and at t=20 mst = 20\,ms on string BB. When and where will the pulse on BB overtake that on AA ?

Explanation

Solution

Tension is defined in physics as the pulling force conveyed axially by a thread, cable, cord, or other one-dimensional continuous component, or by each end of a pole, truss member, or other three-dimensional object; tension may also be defined as the action-reaction pair of forces acting at each end of such elements. Tension can be thought of as the polar opposite of compression.

Complete step by step answer:
A pulse is a term used in physics to describe a single disturbance moving through a propagation medium. This medium could be a vacuum (in the case of electromagnetic radiation) or matter, and it could be infinite or finite in size.

Given, mA=1.2×10−2  kg/m{{\rm{m}}_{\rm{A}}} = 1.2 \times {10^{ - 2}}\;{\rm{kg}}/{\rm{m}}
TA=4.8N {{\bf{T}}_{\bf{A}}} = {\bf{4}}.{\bf{8N}} \\\
\Rightarrow {{\bf{V}}_{\rm{A}}} = \sqrt {{\rm{T}}/{\rm{m}}} = {\bf{20m}}/{\rm{s}} \\\
⇒mB=1.2×10−2  kg/m\Rightarrow {{\rm{m}}_{\rm{B}}} = 1.2 \times {10^{ - 2}}\;{\rm{kg}}/{\rm{m}} \\\\
⇒TB=7.5  N\Rightarrow {{\rm{T}}_{\rm{B}}} = 7.5\;{\rm{N}} \\\\

\Rightarrow {{\rm{V}}_{\rm{B}}}= {\bf{25\,m}}/{\rm{s}}$$ On string $A$ at $t = 0$ $${{\rm{t}}_1} = 0 + 20\;{\rm{ms}} = 20 \times {10^{ - 3}} = 0.02\,{\rm{sec}}$$ In 0.02 sec, $A$ has travelled 20 × 0.02 = 0.4m = s Relative speed between $A$ and $B$ =25−20 = 5m/s = v Time taken for B to overtake A: $$\text{Time} = \dfrac{s}{v}$$ $$\Rightarrow \text{Time}= \dfrac{{0.4}}{5}$$ $$\therefore \text{Time}= 0.8\,sec$$ **Note:** When atoms or molecules are pulled apart and gain potential energy while a restoring force is still present, the restoring force will cause stress. In order to return the string/rod to its relaxed length, each end of a string or rod under a certain strain could tug on the object it is attached to.