Final answer:
The amplitude of the sinusoidal function f(x) = 3sin(2x) is 3. In general, the amplitude is the coefficient in front of the sine function in a wave equation, and for sinusoidal waves that are 180 degrees out of phase, their resultant amplitude is 0 due to destructive interference.
Step-by-step explanation:
Finding the Amplitude of a Sinusoidal Function
The student's question involves finding the amplitude of the sinusoidal function f(x) = 3sin(2x). The general form of a sinusoidal function is given as y(x, t) = A sin(kx - wt + p), where A represents the amplitude of the wave. For the given function, the coefficient in front of the sine function, 3, is the amplitude. Therefore, the amplitude of the function f(x) = 3sin(2x) is indeed 3.
When considering the combination of two sine waves, the resultant amplitude depends on their relative phases. If two waves of amplitude A are 180° out of phase (or π radians), they will cancel each other out when they interact due to destructive interference, leading to a resultant amplitude of 0. Conversely, if they were in phase, they would add constructively, leading to a resultant amplitude of 2A.
In scenarios such as double slit experiments or wave pulses interacting on a rope, similar principles apply. The amplitude of the resultant wave is dependent on the individual amplitudes and the phase difference between the interacting waves. Thus, understanding sinusoidal waves and their behavior is critical for numerous applications in physics and engineering.