A string of length $0.4 m & mass 10^{2} kg$ 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, $Δ$ t. The minimum value of $Δ$ t which allows constructive interference between successive pulses is :

0.05 s

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0.10 s

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0.20 s

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0.40 s

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Solution

The correct option is C $0.10 s$
Time between successive waves for constructive interference is minimum for first harmonic.
Thus $Δ t = f = \frac{1}{2 L} \sqrt{\frac{T}{μ}}$
$= \frac{1}{2 \times 0.4} \times \sqrt{\frac{1.6}{100 / 0.4}} = 0.1$

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A string of length 0.4 m & mass 102 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 :

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A string of length $0.4 m & mass 10^{2} kg$ 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, $Δ$ t. The minimum value of $Δ$ t which allows constructive interference between successive pulses is :

The correct option is C $0.10 s$
Time between successive waves for constructive interference is minimum for first harmonic.
Thus $Δ t = f = \frac{1}{2 L} \sqrt{\frac{T}{μ}}$
$= \frac{1}{2 \times 0.4} \times \sqrt{\frac{1.6}{100 / 0.4}} = 0.1$