Which of the following equations correctly represents a travelling wave having wavelength λ = 4.0 cm, frequency ν = 100 Hz and travelling in positive x-axis direction? (a) y = Asin [(0.50π cm⁻¹)x - (100π s⁻¹)t] (b) y = Asin 2π[(0.25 cm⁻¹)x - (50 s⁻¹)t] (c) y = Asin [(2π/4 cm⁻¹)x - ((2π)/(100) s⁻¹)t] (d) y = Asin π[(0.5 cm⁻¹)x - (200 s⁻¹)t]

Answer: (d). k = (2π)/(λ) = 2π/4 = 0.5π cm⁻¹ ω = 2πν = 200π s⁻¹ y = Asin (0.5π x - 200π t) = Asin π[(0.5)x - (200)t] So the answer is (d).

Which of the following equations correctly represents a travelling… | JEE Main 2022 (30 Jun, Shift 1)

Q63JEE Main 2022 · 30 JUN · SHIFT 1Easy

Progressive Wave Equation

Which of the following equations correctly represents a travelling wave having wavelength $\lambda$ = 4.0 cm, frequency $\nu$ = 100 Hz and travelling in positive x-axis direction?

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Answer: (d)

$k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{4} = 0.5\pi\text{ cm}^{-1}$
$\omega = 2\pi\nu = 200\pi\text{ s}^{-1}$
$y = A\sin(0.5\pi x - 200\pi t) = A\sin\pi[(0.5)x - (200)t]$
So the answer is (d).

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