A string of length 0.4 m and mass 10−2 kg is tightly clampled at its ends

Question

A string of length 0.4 m and mass

10^{- 2}

kg is tightly clampled 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 ∆t. The minimum value of ∆t, which allows constructive interference between succesive pulses, is :

Options:

A . 0.05 s

B . 0.10 s

C . 0.20 s

D . 0.40 s

Answer: Option B
:
B
Mass per unit length of the string,

m = \frac{10^{- 2}}{0.4} = 2.5 \times 10^{- 2}

kg/m

∴

Velocity of wave in the string.

v = \sqrt{\frac{T}{m}} = \sqrt{\frac{1.6}{2.5 \times 10^{- 2}}}

v = 8 m / s

For constructive interference between successive pulses:

△ t_{m i n} = \frac{2 l}{v} = \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

π

and if at this moment next identical pulse is produced, then constructive interference will be obtained.)

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