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STANDARD Physics Transverse Waves MCQ Question

Type: MCQ-numerical-Medium-Class 11

The transverse displacement of a string clamped at its both ends is given by y(x,t) = 0.06sin(\frac{2π\pi}{3} x)cos(120π\pi t) where x and y are in m, and t in s. The length of the string is 1.5 m and its mass is 3 ×\times 10−210^{-2} kg. The tension in the string is

A

324 N

B

648 N

C

832 N

D

972 N

Correct Answer

Option B

Detailed Explanation

The given equation is y(x,t) = 0.06sin(\frac{2π\pi}{3} x)cos(120π\pi t). Compare it with y(x, t) = 2 asin kx cos ωt to find k = \frac{2π\pi}{3} and λ = 3 m. The angular frequency ω = 120π, so v = 60 Hz. The velocity of the wave is v = λf = (60 s−1s^{-1})(3 m) = 180 m s−1s^{-1}. The mass per unit length of the string is μ = \frac{3 ×\times 10−210^{-2} kg}{1.5 m} = 2 ×\times 10−210^{-2} kg m−1m^{-1}. The tension T = (180 m s−1s^{-1})^2 (2 ×\times 10−210^{-2} kg m−1m^{-1}) = 648 N.

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