Final answer:
The question pertains to concepts in physics related to the Fourier transform and the properties of waves, such as amplitude, wavelength, and frequency. Specific calculations cannot be provided without the correct information, but general principles can be explained.
Step-by-step explanation:
Mathematics of Waves
The question deals with concepts related to the Fourier transform of signals, and the properties of waves, specifically amplitude, wavelength, wave speed, and frequency. Unfortunately, the provided information is not directly related to the initial question about the Fourier transform of the signal x(t). Hence, a specific answer to this initial question cannot be provided. However, a general approach to finding Fourier transforms can be explained, and details regarding wave properties can be provided in the broader context of wave equations.
Fourier Transform of a Signal
Given a time-domain signal x(t), its Fourier transform X(f) is calculated to analyze the signal in the frequency domain. The Fourier transform provides a representation of the signal's frequency components. The process involves integrating the product of the signal and a complex exponential function over time.
Properties of Waves
For a wave described by a wave function, the amplitude is the peak value of the wave, the wavelength is the distance over which the wave's shape repeats, and the frequency is the number of cycles per second. The wave speed can be determined by multiplying the wavelength and frequency, and the period is the inverse of the frequency.