A wave is represented by the equation y = 0.5 sin 0.4π(X - 60t), where the distance (X) is measured in…

Analyze the question: We're given a wave equation and asked for its wavelength. We compare it with the standard form of a travelling wave.

Concept: The standard wave equation is

y = A sin(kx − ωt), where k = 2π/λ

Our equation can be written as y = A sin k(x − vt), where k = 2π/λ and v is the wave speed.

Solution:

Given: y = 0.5 sin 0.4π(X − 60t)

Expanding the bracket: y = 0.5 sin(0.4πX − 24πt)

Comparing with y = A sin(kX − ωt):

• A = 0.5 cm
• k = 0.4π rad/cm
• ω = 24π rad/s

Since k = 2π/λ:

λ = 2π / k = 2π / 0.4π = 5.0 cm

Check using speed: v = ω/k = 24π / 0.4π = 60 cm/s, which matches the "60" in the equation. Frequency f = ω/2π = 12 Hz, and v = fλ = 12 × 5 = 60 cm/s ✓.

Answer: The wavelength is 5.0 cm, which is option D.

Tip: When the equation is written as y = A sin k(x − vt), just take the number multiplying the bracket as k and use λ = 2π/k. The π cancels neatly, so you only need to compute 2 ÷ 0.4 = 5.