Two strings 1 and 2 are taut between two fixed supports (as shown in figure) such that the tension in both…
Two strings 1 and 2 are taut between two fixed supports (as shown in figure) such that the tension in both strings is same. Mass per unit length of 2 is more than that of 1. Explain which string is denser for a transverse travelling wave.
Solution
Sol. Speed of a transverse wave on a string, v = $\sqrt{T/\alpha}$
or $v \propto \frac{1}{\sqrt{\alpha}}$
Now, $\alpha_2 > \alpha_1$ (Given)
∴ $v_2 < v_1$
i. e . Medium 2 is denser and medium 1 is rarer.
an object with a mass of 5 kg. The tube is struck to a transverse blow at one end. Find the time required for the pulse to reach the other end. (Take, $g = 9.8\ \mathrm{ms}^{-2}$)
Sol. Tension in the rubber tube AB,
$T = mg$ or $T = (5.0) (9.8) = 49\ \mathrm{N}$
Mass per unit length of rubber tube,
$\alpha = \frac{0.9}{12} = 0.075\ \mathrm{kg\ m}^{-1}$
∴ Speed of wave on the tube,
$v = \sqrt{\frac{T}{\alpha}} = \sqrt{\frac{49}{0.075}} = 25.56\ \mathrm{ms}^{-1}$
∴ The required time,
$t = \frac{AB}{v} = \frac{12}{25.56} = 0.47\ \mathrm{s}$
Answer: $0.47\ \mathrm{s}$