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Which equation correctly represents a travelling wave of wavelength λ=4.0 cm and frequency u=100 Hz moving along the positive x-direction?

Asked in JEE Main 30th June 1st Shift 2022 · Identifying a travelling wave

• (1) y=A sin [(0.50π cm⁻¹)x-(100π s⁻¹)t]
• (2) y=A sin 2π[(0.25 cm⁻¹)x-(50 s⁻¹)t]
• (3) y=A sin [((2π)/4 cm⁻¹)x-((2π)/(100) s⁻¹)t]
• (4) y=A sin π[(0.5 cm⁻¹)x-(200 s⁻¹)t]

Step-by-step solution

Why the other options are wrong

• (1) The wave number is right but ω=100π gives 50 Hz, not 100 Hz.
• (2) Again a frequency of 50 Hz.
• (3) Uses (2π)/u for ω instead of 2π u.

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