First slide

Stationary waves

Question

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 $Δt$ . The minimum value of $Δt$ which allows constructive interference between successive pulses is

Moderate

A

0.05 s
B

0.10 s
C

0.20 s
D

0.40 s

Solution

For string, $\frac{Mass}{Length} = m = \frac{10^{- 2}}{0 .4} = 2 .5 \times 10^{- 2} kg / m$
$∴$ Velocity $v = \sqrt{\frac{T}{m}} = \sqrt{\frac{16}{2 .5 \times 10^{- 2}}} = 8 m / s$
For constructive interference between successive pulses.
${Δt}_{\min} = \frac{2 l}{v} = \frac{2 (0 .4)}{8} = 0 .1 \sec$
(After two reflections, the wave pulse is in same phase as it was produced since in one reflection it’s phase changes by $π$ , and If at this moment next identical pulse is produced, then constructive interference will be obtained.

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