A string of length 0.4 m and mass $10^{-2}$ kg is tightly clamped at its ends. The tension in the string is…
A string of length 0.4 m and mass $10^{-2}$ kg is tightly clamped at its ends. The tension in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. The minimum value of $\Delta t$ which allows constructive interference between successive pulses is
0.05 s
0.10 s
0.20 s
0.40 s
Solution
For string, $\frac{\text{Mass}}{\text{Length}} = \mu = \frac{10^{-2}}{0.4} = 2.5 \times 10^{-2}\text{ kgm}^{-1}$
$\therefore \text{Velocity, } v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{1.6}{2.5 \times 10^{-2}}} = 8\text{ ms}^{-1}$
For constructive interference between successive pulses,
$\Delta t_{\min} = \frac{2l}{v} = \frac{2(0.4)}{8} = 0.10\text{ s}$