Question

Two long strings $A$ and $B$, each having linear mass density $1.2\times {10}^{-2}$ kg/m is stretched by different tensions $4.8N$ 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 $t=0$ on string $A$ and at $t=20$ $ms$ on string $B$. When and where will the pulse on $B$ overtake that on $A$ ?

Answer 1

Velocity of string wave is given by the expression

$V=\sqrt{\frac{T}{\mu }}\mu =massperunitlength\mu =\frac{6\times {10}^{-3}}{8}\mu =7.5\times {10}^{-4}30=\sqrt{\frac{T}{7.5\times {10}^{-4}}}T=0.675Averagepower=\frac{1}{2}{\left(2\pi v\right)}^2{A}^{2}V\mu 50=\frac{1}{2}\times 2\pi \times \left(\frac{30}{0.2}\right)A^2\times 30\times 7.5\times {10}^{-4}A=0.176m$.