Question

A wave has an amplitude of 0.35 m, a frequency of 1.05 x 10⁶ Hz, and travels in the positive x direction at the speed of light, 3.00 x 10⁸ m/s. Which one of the following equations correctly represents this wave?

A) y = 0.35 sin (286t+ 1.05 x 10⁶x)
B) y = 0.35 sin (6.60 x 10⁶t - 0.022x)
C) y = 0.35 sin (6.60 x 10⁶t + 0.022x)
D) y = 0.35 sin (1.05 x 10⁶t+ 3.00 x 10⁸ x)
E) y = 0.35 sin (286t - 1.05 x 10⁶ x)

Answer 1

The correct wave equation that represents a wave with an amplitude of 0.35 m, a frequency of 1.05 x 10^6 Hz and that travels at the speed of light is Option C) y = 0.35 sin(6.60 x 10^6t + 0.022x).

Step-by-step explanation:

To determine which equation correctly represents the wave described, we need to consider the wave's amplitude, frequency, speed, and direction of travel. The general form of a traveling wave can be expressed as y(x, t) = A sin(kx − ωt), where A is the amplitude, k is the wave number, ω is the angular frequency, and t is time.

Given that the wave is traveling at the speed of light (c = 3.00 × 108 m/s) and has a frequency (f = 1.05 × 106 Hz), we can determine the angular frequency using ω = 2πf, and the wave number using k = ω/c. After substituting the values, ω is found to be 6.60 × 106 rad/s, and k is approximately 0.022 m−1. Considering the positive x-direction of the wave travel, the wave equation should have the form y = 0.35 sin(6.60 × 106t + 0.022x). Hence, the correct option that represents this wave is: Option C) y = 0.35 sin(6.60 × 106t + 0.022x)