A transverse displacement of vibrating string is y = 0.06sin (2π/3x)cos (120π t). If the mass per unit length of a string is 4 × 10⁻² kg/m, then the tension in the string will be (a) 1296 N (b) 1000 N (c) 720 N (d) 500 N

Answer: (a). Stationary wave: k = 2π/3 m⁻¹, ω = 120π rad/s Speed of component waves v = (ω)/(k) = (120π × 3)/(2π) = 180 m/s T = μ v² = 4×10⁻² × 32400 = 1296 N So the answer is (a) 1296 N.

A transverse displacement of vibrating string is y = 0.06sin… | MHT CET 2025 (21 Apr, Shift 2)

Q34MHT CET 2025 · 21 APR · SHIFT 2Medium

Progressive Wave Equation

A transverse displacement of vibrating string is $y = 0.06\sin\left(\frac{2\pi}{3}x\right)\cos(120\pi t)$ .

If the mass per unit length of a string is $4 \times 10^{-2}\text{ kg/m}$ , then the tension in the string will be

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Answer: (a)

Stationary wave: $k = \frac{2\pi}{3}\text{ m}^{-1}$ , $\omega = 120\pi\text{ rad/s}$
Speed of component waves $v = \frac{\omega}{k} = \frac{120\pi \times 3}{2\pi} = 180\text{ m/s}$
$T = \mu v^2 = 4\times10^{-2} \times 32400 = 1296\text{ N}$
So the answer is (a) 1296 N.

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