Final answer:
The amplitude of y = -3cos(1/4x) is 3, which represents the maximum value the function can reach. Additionally, the comparison between two wave functions, y1, and y2, shows they share the same amplitude but differ in wave number and phase, affecting their wavelength, frequency, and direction of travel.
Step-by-step explanation:
The amplitude of a trigonometric function like cosine or sine is the coefficient in front of the function that represents the maximum value the function can attain. In the equation y = -3cos(1/4x), the coefficient in front of the cosine function is -3. However, the amplitude is always a positive value because it represents a distance, which cannot be negative. Therefore, the amplitude of the given function is 3.
Comparing the given waves:
1. y1(x, t) = 0.50 m sin(3.00 m-1x - 4.00 s-1t)
2. y2(x, t) = 0.50 m sin(-6.00 m-1x + 4.00 s-1t)
The similarities include:
• Both waves have the same amplitude of 0.50 m.
• Both waves are sinusoidal, which means they have a sine function as their base function.
The differences include:
• The wave number, which is the coefficient in front of 'x': 3.00 m-1 in the first wave and -6.00 m-1 in the second wave. This affects the wavelength and spatial frequency of the waves.
• The phase of the waves, which includes different signs in front of 't': a negative sign in y1 indicating the wave is moving in the positive x-direction, and a positive sign in y2 indicating the wave is moving in the negative x-direction.
The mentioned correct option in the final part for the amplitude of y = -3cos(1/4x) is d. 3.