The equation of a wave traveling in a horizontal direction is expressed as y = 15 sin $\frac{2\pi}{5}$ (60t - x). What is its wavelength?

Analyze the question: We're given a wave equation and asked for the wavelength. The trick is to compare the equation with the standard form of a travelling wave.

Concept: A progressive wave can be written as

y = A sin(2π/λ)(vt − x)

where A is the amplitude, v is the wave speed and λ is the wavelength. The coefficient multiplying (vt − x) is 2π/λ.

Solution:

Given: y = 15 sin (2π/5)(60t − x)

Compare with: y = A sin (2π/λ)(vt − x)

• Amplitude: A = 15 m
• 2π/λ = 2π/5, so λ = 5 m
• Wave speed: v = 60 m/s

Check with the alternative form y = A sin(ωt − kx):

• k = 2π/5, and k = 2π/λ gives λ = 5 m
• ω = (2π/5)(60) = 24π rad/s, so f = ω/2π = 12 Hz
• v = fλ = 12 × 5 = 60 m/s, which matches the equation

Answer: The wavelength is 5 m, which is option C.

Tip: In any wave equation of the form sin(2π/λ)(vt − x), the wavelength is the number under the 2π. Don't be distracted by 60 (that's the speed) or 15 (that's the amplitude). JAMB often includes those as wrong options.