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The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown. In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
The phase velocity is given in terms of the wavelength λ (lambda) and period T as =. A wave with the group and phase velocities going in different directions Group velocity is a property of waves that have a defined envelope, measuring propagation through space (that is, phase velocity) of the overall shape of the waves' amplitudes ...
When two signals with these waveforms, same period, and opposite phases are added together, the sum + is either identically zero, or is a sinusoidal signal with the same period and phase, whose amplitude is the difference of the original amplitudes. The phase shift of the co-sine function relative to the sine function is +90°.
In mechanics, as a linear motion over time, this is simple harmonic motion; as rotation, it corresponds to uniform circular motion. Sine waves occur often in physics, including wind waves, sound waves, and light waves, such as monochromatic radiation.
(the apparent motion of the wave due to the successive oscillations of particles or fields about their equilibrium positions) propagates at the phase and group velocities parallel or antiparallel to the propagation direction, which is common to longitudinal and transverse waves.
The phase velocity is given in terms of the wavelength λ (lambda) and time period T as =. Equivalently, in terms of the wave's angular frequency ω, which specifies angular change per unit of time, and wavenumber (or angular wave number) k, which represent the angular change per unit of space,
Here = / is the wavelength, the distance between two wavefronts where the field is equal to the amplitude ; and = / is the period of the field's variation over time, seen at any fixed point in space. Its reciprocal = / is the temporal frequency of the wave measured in f
It is used as the starting point for subtractive synthesis, as a sawtooth wave of constant period contains odd and even harmonics that decrease at −6 dB/octave. The Fourier series describes the decomposition of periodic waveforms, such that any periodic waveform can be formed by the sum of a (possibly infinite) set of fundamental and harmonic ...