JEE Main 2021 · 24 February · evening · Single correct · +4 / −1
Which of the following equations represents a travelling wave?
- (a) y = Aeˣcos(ωt - θ)
- (b) y = Ae -x² (vt + θ)
- (c) y = A sin (15x - 2t)
- (d) y = A sinx cosωt
Answer and solution
Answer (c) y = A sin (15x - 2t)
Solution
Physics sir · 3 steps
A travelling wave needs x and t locked together as x - vt. Check every option for that pairing.
- The test. A wave travels only if y depends on x and t through one combination, x - vt or x + vt. Then the whole shape slides along the x-axis with speed v. If x and t sit in separate factors, the shape stays where it is.
Option How x and t appear Written as f(x ± vt)? Verdict (a) Aeˣ cos(ω t - θ) x only in eˣ, t only in the cosine No not travelling (b) Ae^(-x²)(vt + θ) x only in e^(-x²), t in a separate factor No not travelling (c) A sin(15x - 2t) x and t together in one argument Yes travelling wave (d) A sin x cos ω t sin x multiplied by cos ω t No standing wave - Check option (c). Take 15 out as a common factor. This gives 15x - 2t = 15(x - 2/15t), which is exactly the form k(x - vt). So the sine wave moves in the +x direction with speed v = ω/k = 2/15.
- So. Only (c) has the form f(x - vt), so (c) is the travelling wave.
The idea to keep. If x and t appear only as x ± vt, the wave travels with speed v = ω/k. A product of a function of x and a function of t never travels.
Answer from the NTA final answer key. Solution by PrepWiser.