A wave moving in the positive x direction has an amplitude of 0.4 m, a frequency of 0.25 Hz, and a wavelength of 24 m. An equation, in which the units are SI, that might describe this wave is
A) yx, t) = 0.2 sin 2t/4 + x/24).
B) yx, t) = 0.4 sin 2t/4 - x/24).
C) yx, t) = 0.4 sin 8t - x/6).
D) yx, t) = 0.2 sin 0.5t/4 - x/24).
E) yx, t) = 0.4 sin 2t/4 + x/6).

Question

Quizplus · Accepted Answer

The general equation for a wave is y(x,t) = A sin(kx - wt + phi), where A is the amplitude, k is the wave number (2pi/wavelength), w is the angular frequency (2pi*frequency), and phi is the phase angle.

Plugging in the given values, we get y(x,t) = 0.4 sin((2pi/24)x - (2pi*0.25)t)

Simplifying, we get y(x,t) = 0.4 sin(2pi/4 - pi/2)t - (pi/12)x

Since 2pi/4 = pi/2 and pi/2 - pi/2 = 0, we can further simplify to y(x,t) = 0.4 sin(0)t - (pi/12)x

Finally, since sin(0) = 0, we can eliminate the sine term and get y(x,t) = - (pi/12)x + constant

The negative sign in front of the x term indicates that the wave is traveling in the positive x direction. Choice B matches this form, and is therefore the best choice.

A Wave Moving in the Positive X Direction Has an Amplitude