JEE Main 2022 · 30 June · morning · Single correct · +4 / −1
Which of the following equations correctly represents a travelling wave having wavelength λ = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis direction?
- (a) y = A sin [(0.50 π cm⁻¹)x - (100 π s⁻¹)t]
- (b) y = A sin 2π [(0.25 cm⁻¹)x - (50 s⁻¹)t]
- (c) y = A sin [ ( 2π/4 cm⁻¹ )x - ( 2π/100 s⁻¹ )t ]
- (d) y = A sin π [(0.5 cm⁻¹)x - (200 s⁻¹)t]
Answer and solution
Answer (d) y = A sin π [(0.5 cm⁻¹)x - (200 s⁻¹)t]
Solution
Physics sir · 2 steps
Turn λ and ν into k and ω, then expand each option to read off its k and ω.
- Standard form. A wave moving along +x has the form y = A sin(kx - ω t). The minus sign between the x and t terms gives the +x direction, and all four options have it. So only k and ω can decide the answer.
k = 2π/λ = 2π/(4 cm) = 0.5π cm⁻¹, ω = 2πν = 2π × 100 = 200π s⁻¹
Option k (in cm⁻¹) ω (in s⁻¹) Matches? (a) 0.5π 100π No, ω is half (b) 2π × 0.25 = 0.5π 2π × 50 = 100π No, ω is half (c) 2π/4 = 0.5π 2π/100 = 0.02π No (d) π × 0.5 = 0.5π π × 200 = 200π Yes - So. All four options have the right k, but only (d) also has ω = 200π s⁻¹. The answer is (d).
The idea to keep. Always rewrite a wave as sin(kx - ω t) before comparing. Then check k = 2π/λ and ω = 2πν. A factor pulled outside the bracket multiplies both terms.
Answer from the NTA final answer key. Solution by PrepWiser.