The equation of a certain progressive transverse wave is y = 2 sin 2 ( t/0.01 - x/30) , where x and y are in…

Analyze the question: We are given a wave equation and asked for the period. We compare it with the standard form of a progressive wave.

Concept: The standard equation of a progressive wave is

y = A sin 2π(t/T − x/λ)

where

• A = amplitude
• T = period (in seconds)
• λ = wavelength

Solution:

Given: y = 2 sin 2π(t/0.01 − x/30)

Compare term by term:

• A = 2 cm
• t/T = t/0.01, so T = 0.01 s
• x/λ = x/30, so λ = 30 cm

Check: The frequency is f = 1/T = 1/0.01 = 100 Hz. This is reasonable, and the period of 0.01 s matches option B. (Option D, 100, is the frequency, not the period. That is the trap.)

Answer: The period is 0.010 s, which is option B.

Tip: When a wave equation is written in the form 2π(t/T − x/λ), just read off the numbers under t and x. They are directly the period and wavelength. If the equation is written as sin(ωt − kx), use T = 2π/ω instead. Also watch out for confusing period with frequency, since examiners often include the frequency as a distractor.