A string of length 0.5 m and mass 10⁻³ kg is tightly clamped at its ends. The tension in the string is 0.8 N. Identical wave pulses are produced at one end at equal intervals of time Δ t. What is the minimum value of Δ t which allows constructive interference between successive pulses? (a) 0.40 s (b) 0.20 s (c) 0.10 s (d) 0.05 s

Answer: (d). μ = 10⁻³/0.5 = 2×10⁻³ kg/m, v = √0.8/(2×10⁻³) = 20 m/s. A pulse reflects at both fixed ends (two inversions), returning upright after a round trip 2L. Minimum Δ t = 2L/v = (2×0.5)/(20) = 0.05 s So the answer is (d) 0.05 s.

A string of length 0.5 m and mass 10⁻³ kg is tightly clamped at its… | MHT CET 2026 (11 Apr, Shift 1)

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Speed of Waves

A string of length $0.5$ m and mass $10^{-3}$ kg is tightly clamped at its ends. The tension in the string is $0.8$ N. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$ . What is the minimum value of $\Delta t$ which allows constructive interference between successive pulses?

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Answer: (d)

$\mu = 10^{-3}/0.5 = 2\times10^{-3}$ kg/m, $v = \sqrt{0.8/(2\times10^{-3})} = 20$ m/s.
A pulse reflects at both fixed ends (two inversions), returning upright after a round trip $2L$ .
Minimum $\Delta t = \dfrac{2L}{v} = \dfrac{2\times0.5}{20} = 0.05\ \text{s}$
So the answer is (d) $0.05$ s.

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