AIIMS2019Physics-Waves

AIIMS 2019 Physics Wave Equation MCQ Question

Type: MCQ-numerical-Medium-Class 11

A string wave equation is given y = 0.002sin(300t - 15x) and mass density is μ = 0.1 kg/m. Then find the tension in the string.

A

30 N

B

20 N

C

40 N

D

45 N

Correct Answer

Option C

Detailed Explanation

To find the tension TT in the string, we can use the wave equation y=Asin(ωtkx)y = A \sin(\omega t - kx) where ω=300rad/s\omega = 300 \, \text{rad/s} and k=15rad/mk = 15 \, \text{rad/m}. The relationship between tension, mass density μ\mu, angular frequency, and wave number is given by the formula T=μω2/k2T = \mu \omega^2 / k^2. Substituting the values, we find T=0.1×(300)2/(15)2=30NT = 0.1 \times (300)^2 / (15)^2 = 30 \, \text{N}, confirming that option (A) is indeed the correct choice, while options (B) and (C) being marked as N/A indicate they are not valid answers.

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