JEE Main 2025 · 2 April · evening · Single correct · +4 / −1
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec . The crest P is at x=0 at t=0 sec and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?
- (a) y=2 cos (0.83 x-3.35 t) cm
- (b) y=2 sin (0.83 x-3.5 t) cm
- (c) y=2 cos (0.13 x-0.5 t) cm
- (d) y=2 cos (3.35 x-0.83 t) cm
Answer and solution
Answer (a) y=2 cos (0.83 x-3.35 t) cm
Solution
Physics sir · 4 steps
Get k from λ and v from distance over time, then ω = kv; a crest at the origin means cosine.
- Wave number. k = 2π/λ = 2π/(7.5 cm) ≈ 0.838 cm⁻¹, which the options write as 0.83.
- Wave speed. The wave covers 1.2 cm in 0.3 s, so v = 1.2/0.3 = 4 cm s⁻¹.
ω = kv = 0.838 × 4 ≈ 3.35 rad s⁻¹
- Choose the function. At x = 0, t = 0 the displacement is the maximum, +2 cm. Cosine gives y = 2 cos 0 = 2 there, while sine would give 0. The wave moves along +x, so the phase is kx - ω t.
- So. The wave is y = 2 cos(0.83x - 3.35t) cm, which is option (a).
The idea to keep. Build every wave equation from three facts: amplitude, k = 2π/λ and ω = kv. Then use the condition at t = 0 to decide between sine and cosine.
Answer from the NTA final answer key. Solution by PrepWiser.