Question

What is the period of a wave described by the following function?

y(x,t) = (2.00 m)cos[(6.00 m^-1)x + (10.00 s^-1)t1 + (2.00 m)cos[(3.00 m^-1)x + (5.00 s^-1)t]
A) 0.628 s
B) 5.00 s
C) 1.26 s
D) 10.0 s
E) This is not a periodic function, so it does not have a period.

Answer 1

The period of the wave described by the given wave function is 0.2 seconds, which is the least common multiple of the periods of the two component waves, though this option is not listed in the provided choices.

Step-by-step explanation:

The period of a wave is the time it takes for one complete cycle of the wave to pass a point. Given the wave function y(x,t) = (2.00 m)cos[(6.00 m-1)x + (10.00 s-1)t] + (2.00 m)cos[(3.00 m-1)x + (5.00 s-1)t], you can determine the period of each component cosine wave by looking at the angular frequencies (the coefficients of t) which are 10.00 s-1 and 5.00 s-1. The period is the reciprocal of the angular frequency, so for the first component, the period is 0.1 s, and for the second component, the period is 0.2 s. The overall period must be a common multiple of these two periods. The least common multiple of 0.1 and 0.2 is 0.2, thus the period of the wave is 0.2 s, which is not listed in the options provided. Therefore, the question appears to be flawed as it does not present the correct answer based on the given wave function.