wave_mechanics critical_thinking Question 9
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 Dt. The minimum value of Dt which allows constructive interference between successive pulses is
[IIT 1998]
Options:
A) 0.05 s
B) 0.10 s
C) 0.20 s
D) 0.40 s
Show Answer
Answer:
Correct Answer: B
Solution:
For string, $ \frac{\text{Mass}}{\text{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}}}}=8m/s $ For constructive interference between successive pulses.
$ \Delta {t _{\min }}=\frac{2l}{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 p, and If at this moment next identical pulse is produced, then constructive interference will be obtained.
BETA
