The equation of a wave traveling along the positive x-direction is given by;
y = 0.25 x 10\(^{-3}\) sin (500t - 0.025x).
Determine the angular frequency of the wave motion.
A
0.25 x 10-3rad s-1
B
0.25 x 10-1rad s-1
C
5.00 x 102rad s-1
D
2.50 x 103rad s-1
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
The general wave equation is given by;
y = A Sin(wt - 2\pix/Wavelength)
where w = angular velocity
Thus, comparing this equation with the equation
y = 0.25 x 10-3 Sin (500t - 0.025x)
That Amplitude = 0.25 x 10-3m
The angular velocity(w) = 500 (the coefficient of t in both equations)
∴ w = 500 rad s\(^{-1}\)
= 5.00 x 10\(^2\)rad s\(^{-1}\)
Source: Myschool Past Questions Archive (Record #558)