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 .... $s$
IIT 1998, Diffcult
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(b) For string, $\frac{{{\rm{Mass}}}}{{{\rm{Length}}}}$$ = m = \frac{{{{10}^{ - 2}}}}{{0.4}} = 2.5 \times {10^{ - 2}}kg/m$
$\therefore$ Velocity $v = \sqrt {\frac{T}{m}} = \sqrt {\frac{{16}}{{2.5 \times {{10}^{ - 2}}}}} = 8m/s$
For constructive interference between successive pulses.
$\Delta {t_{\min }} = \frac{{2l}}{v} = \frac{{2(0.4)}}{8} = 0.1\sec $
(After two reflections, the wave pulse is in same phase as it was produced since in one reflection it’s phase changes by $\pi$, and If at this moment next identical pulse is produced, then constructive interference will be obtained.
$\therefore$ Velocity $v = \sqrt {\frac{T}{m}} = \sqrt {\frac{{16}}{{2.5 \times {{10}^{ - 2}}}}} = 8m/s$
For constructive interference between successive pulses.
$\Delta {t_{\min }} = \frac{{2l}}{v} = \frac{{2(0.4)}}{8} = 0.1\sec $
(After two reflections, the wave pulse is in same phase as it was produced since in one reflection it’s phase changes by $\pi$, and If at this moment next identical pulse is produced, then constructive interference will be obtained.
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