Question Detail
Question
A wave is described by the equation y(x,t) = (8cm) sin 2π(0.3x−0.5t). Based on the standard wave equation y = Asin(kx - ωt) or its variations discussed, what is the wave number (k) for this wave?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The general form of a wave equation is y = A sin(kx - ωt). The provided equation is y(x,t) = (8cm) sin 2π(0.3x−0.5t). Expanding this, we get y(x,t) = (8cm) sin (2π * 0.3x - 2π * 0.5t), which simplifies to y(x,t) = (8cm) sin (0.6πx - 1.0πt). By comparing this to the standard form, we can identify k = 0.6π rad/m. This matches the 'Example' section on page 3 where k is associated with the x term.
Hint
Compare the given equation with the general form y = A sin(kx - ωt) and distribute the 2π. The wave number k is the coefficient of x.