A plane progressive wave is represented by the equation y = 0.2sin (200πt - 0.5.x) where x and y are measured…

Analyze the question: We're given a progressive wave equation and asked for its frequency. We compare it to the standard form.

Concept: The standard form of a progressive wave is

y = A sin(ωt − kx)

where

• A = amplitude
• ω = angular frequency (rad/s)
• k = wave number (2π/λ)
• ω = 2πf, so f = ω/2π

Solution:

Given: y = 0.2 sin(200πt − 0.5x)

Comparing with the standard form:

• A = 0.2 cm
• ω = 200π rad/s
• k = 0.5 cm⁻¹

Frequency:

f = ω / 2π = 200π / 2π = 100 Hz

Checking the options: 100 Hz matches option D. The value 200 (option E) is a trap: it comes from forgetting to divide by 2π and only dropping the π. Remember that ω = 2πf, not πf.

Tip: In any equation of the form y = A sin(ωt − kx), the number multiplying t is ω, so divide it by 2π to get frequency. The number multiplying x is k, so wavelength is 2π/k. Here, λ = 2π/0.5 ≈ 12.57 cm, and the wave speed is v = fλ = ω/k = 200π/0.5 = 400π cm/s.