Question

A string of length 0.4 m and mass $10^{-2} kg$ is tightly clamped at its ends. The tensior 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

• A. 0.05 s
• B. 0.10 s
• C. 0.20 s
• D. 0.40 s

Answer 1

Answer: (B)

0.10 s

Answer 2

Mass per unit length of the string.

\hspace20mm =2.5 \times 10^{-2} kg/m
$\therefore$ Velocity of wave in the string,
\hspace15mm v = \sqrt{\frac{T}{m}}=\sqrt{\frac{1.6}{2.5 \times 10^{-2}}}
\hspace20mm v = 8\, m/s
For constructive interference between successive pulses
\hspace15mm \Delta t_{min} = \frac{2l}{v}
\hspace20mm = \frac{(2)(0.4)}{8}=0.10\, s
(After two reflections, the wave pulse is in same phase as it was produced, since in one reflection its phase changes by $p$, and if at this moment next identical pulse is produced, then constructive interference will be obtained.)