amplitudes

Amplitudes refer to a measure of the size or strength of a periodic phenomenon. In a wave, the amplitude is typically the maximum displacement from the rest position. For a sinusoidal wave described by y(t) = A sin(ωt + φ), A is the amplitude, representing the peak value. The term peak-to-peak amplitude is 2A, since the wave reaches A in one direction and −A in the opposite.

In physics, amplitude influences energy in many systems. For a simple harmonic oscillator, the energy is proportional to the square of the amplitude. For mechanical and acoustic waves, larger amplitudes generally correspond to louder sounds and greater vibrations, though material properties and damping also matter.

In signal processing and electronics, amplitude denotes the magnitude of a waveform. Practical signals are often described by peak, peak-to-peak, and root-mean-square (RMS) amplitudes; for a sine wave, RMS equals A/√2. Amplitude modulation uses changes in the signal’s amplitude to encode information onto a carrier wave.

In mathematics, amplitude can refer to the magnitude of a complex number or of a complex-valued signal. The amplitude spectrum obtained from a Fourier transform shows how different frequency components contribute to a signal’s overall amplitude.

In quantum mechanics, a probability amplitude is a complex quantity whose modulus squared yields a probability. Interference effects arise from the relative phases of such amplitudes.

Overall, amplitude is a central, context-dependent measure of size, strength, or intensity across physics, engineering, and mathematics.